Upload permutation-groups.py with huggingface_hub

permutation-groups.py

@@ -3,2509 +3,117 @@ import json
 import os
 import pyarrow as pa
 
-_DESCRIPTION = "A comprehensive collection of permutation composition datasets for various mathematical groups including symmetric, alternating, cyclic, dihedral, and sporadic groups."
+_DESCRIPTION = "A comprehensive collection of permutation composition datasets for various mathematical groups including symmetric, alternating, cyclic, dihedral, and special groups."
 _HOMEPAGE = "https://huggingface.co/datasets/BeeGass/permutation-groups"
 _LICENSE = "MIT"
 
 class PermutationGroupsConfig(datasets.BuilderConfig):
-    def __init__(self, *args, group_name=None, group_degree=None, group_order=None, data_dir=None, max_len=None, **kwargs):
-        super().__init__(*args, **kwargs)
+    def __init__(self, group_name=None, max_len=512, **kwargs):
+        # Handle the name parameter
+        name = kwargs.get("name", "")
+        
+        # If name is provided, parse it to get group_name and max_len
+        if name:
+            if "_data" in name:
+                # Old style: s5_data
+                group_name = name.replace("_data", "").upper()
+            elif "_len" in name:
+                # Old style: s5_len32
+                parts = name.split("_len")
+                group_name = parts[0].upper()
+                if "max_len" not in kwargs:  # Don't override if explicitly provided
+                    max_len = int(parts[1])
+            else:
+                # New style: just s5
+                group_name = name.upper() if name != "all" else "All"
+        
+        # Ensure we have a name for the config
+        if "name" not in kwargs:
+            kwargs["name"] = group_name.lower() if group_name else "default"
+        
+        super().__init__(**kwargs)
         self.group_name = group_name
-        self.group_degree = group_degree
-        self.group_order = group_order
-        self.data_dir = data_dir
         self.max_len = max_len
+        self.data_dir = f"data/{group_name.lower()}_data" if group_name and group_name != "All" else None
 
 class PermutationGroups(datasets.ArrowBasedBuilder):
-    """Use ArrowBasedBuilder for better performance with Arrow files."""
+    """Permutation groups dataset with dynamic length filtering."""
     
-    VERSION = datasets.Version("2.0.0")
-
-    BUILDER_CONFIGS = [
-        PermutationGroupsConfig(
-            name="s3_data",
-            description="Symmetric Group S3 (order 6).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data",
-        ),
-        PermutationGroupsConfig(
-            name="s4_data",
-            description="Symmetric Group S4 (order 24).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data",
-        ),
-        PermutationGroupsConfig(
-            name="s5_data",
-            description="Symmetric Group S5 (order 120).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data",
-        ),
-        PermutationGroupsConfig(
-            name="s6_data",
-            description="Symmetric Group S6 (order 720).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data",
-        ),
-        PermutationGroupsConfig(
-            name="s7_data",
-            description="Symmetric Group S7 (order 5040).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data",
-        ),
-        PermutationGroupsConfig(
-            name="a3_data",
-            description="Alternating Group A3 (order 3).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data",
-        ),
-        PermutationGroupsConfig(
-            name="a4_data",
-            description="Alternating Group A4 (order 12).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data",
-        ),
-        PermutationGroupsConfig(
-            name="a5_data",
-            description="Alternating Group A5 (order 60).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data",
-        ),
-        PermutationGroupsConfig(
-            name="a6_data",
-            description="Alternating Group A6 (order 360).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data",
-        ),
-        PermutationGroupsConfig(
-            name="a7_data",
-            description="Alternating Group A7 (order 2520).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data",
-        ),
-        PermutationGroupsConfig(
-            name="c3_data",
-            description="Cyclic Group C3 (order 3).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data",
-        ),
-        PermutationGroupsConfig(
-            name="c4_data",
-            description="Cyclic Group C4 (order 4).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data",
-        ),
-        PermutationGroupsConfig(
-            name="c5_data",
-            description="Cyclic Group C5 (order 5).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data",
-        ),
-        PermutationGroupsConfig(
-            name="c6_data",
-            description="Cyclic Group C6 (order 6).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data",
-        ),
-        PermutationGroupsConfig(
-            name="c7_data",
-            description="Cyclic Group C7 (order 7).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data",
-        ),
-        PermutationGroupsConfig(
-            name="c8_data",
-            description="Cyclic Group C8 (order 8).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data",
-        ),
-        PermutationGroupsConfig(
-            name="c10_data",
-            description="Cyclic Group C10 (order 10).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data",
-        ),
-        PermutationGroupsConfig(
-            name="c12_data",
-            description="Cyclic Group C12 (order 12).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data",
-        ),
-        PermutationGroupsConfig(
-            name="z3_data",
-            description="Cyclic Group Z3 (order 3).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data",
-        ),
-        PermutationGroupsConfig(
-            name="z4_data",
-            description="Cyclic Group Z4 (order 4).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data",
-        ),
-        PermutationGroupsConfig(
-            name="z5_data",
-            description="Cyclic Group Z5 (order 5).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data",
-        ),
-        PermutationGroupsConfig(
-            name="z6_data",
-            description="Cyclic Group Z6 (order 6).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data",
-        ),
-        PermutationGroupsConfig(
-            name="d3_data",
-            description="Dihedral Group D3 (order 6).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data",
-        ),
-        PermutationGroupsConfig(
-            name="d4_data",
-            description="Dihedral Group D4 (order 8).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data",
-        ),
-        PermutationGroupsConfig(
-            name="d5_data",
-            description="Dihedral Group D5 (order 10).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data",
-        ),
-        PermutationGroupsConfig(
-            name="d6_data",
-            description="Dihedral Group D6 (order 12).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data",
-        ),
-        PermutationGroupsConfig(
-            name="d7_data",
-            description="Dihedral Group D7 (order 14).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data",
-        ),
-        PermutationGroupsConfig(
-            name="d8_data",
-            description="Dihedral Group D8 (order 16).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data",
-        ),
-        PermutationGroupsConfig(
-            name="psl25_data",
-            description="PSL Group PSL25 (order 60).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data",
-        ),
-        PermutationGroupsConfig(
-            name="f20_data",
-            description="Frobenius Group F20 (order 20).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data",
-        ),
-        PermutationGroupsConfig(
-            name="s3_len4",
-            description="Symmetric Group S3 (max_len=4).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len4",
-            description="Symmetric Group S4 (max_len=4).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len4",
-            description="Symmetric Group S5 (max_len=4).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len4",
-            description="Symmetric Group S6 (max_len=4).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len4",
-            description="Symmetric Group S7 (max_len=4).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len4",
-            description="Alternating Group A3 (max_len=4).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len4",
-            description="Alternating Group A4 (max_len=4).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len4",
-            description="Alternating Group A5 (max_len=4).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len4",
-            description="Alternating Group A6 (max_len=4).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len4",
-            description="Alternating Group A7 (max_len=4).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len4",
-            description="Cyclic Group C3 (max_len=4).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len4",
-            description="Cyclic Group C4 (max_len=4).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len4",
-            description="Cyclic Group C5 (max_len=4).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len4",
-            description="Cyclic Group C6 (max_len=4).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len4",
-            description="Cyclic Group C7 (max_len=4).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len4",
-            description="Cyclic Group C8 (max_len=4).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len4",
-            description="Cyclic Group C10 (max_len=4).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len4",
-            description="Cyclic Group C12 (max_len=4).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len4",
-            description="Cyclic Group Z3 (max_len=4).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len4",
-            description="Cyclic Group Z4 (max_len=4).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len4",
-            description="Cyclic Group Z5 (max_len=4).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len4",
-            description="Cyclic Group Z6 (max_len=4).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len4",
-            description="Dihedral Group D3 (max_len=4).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len4",
-            description="Dihedral Group D4 (max_len=4).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len4",
-            description="Dihedral Group D5 (max_len=4).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len4",
-            description="Dihedral Group D6 (max_len=4).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len4",
-            description="Dihedral Group D7 (max_len=4).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len4",
-            description="Dihedral Group D8 (max_len=4).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len4",
-            description="PSL Group PSL25 (max_len=4).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len4",
-            description="Frobenius Group F20 (max_len=4).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len4",
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len8",
-            description="Symmetric Group S3 (max_len=8).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len8",
-            description="Symmetric Group S4 (max_len=8).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len8",
-            description="Symmetric Group S5 (max_len=8).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len8",
-            description="Symmetric Group S6 (max_len=8).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len8",
-            description="Symmetric Group S7 (max_len=8).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len8",
-            description="Alternating Group A3 (max_len=8).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len8",
-            description="Alternating Group A4 (max_len=8).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len8",
-            description="Alternating Group A5 (max_len=8).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len8",
-            description="Alternating Group A6 (max_len=8).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len8",
-            description="Alternating Group A7 (max_len=8).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len8",
-            description="Cyclic Group C3 (max_len=8).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len8",
-            description="Cyclic Group C4 (max_len=8).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len8",
-            description="Cyclic Group C5 (max_len=8).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len8",
-            description="Cyclic Group C6 (max_len=8).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len8",
-            description="Cyclic Group C7 (max_len=8).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len8",
-            description="Cyclic Group C8 (max_len=8).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len8",
-            description="Cyclic Group C10 (max_len=8).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len8",
-            description="Cyclic Group C12 (max_len=8).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len8",
-            description="Cyclic Group Z3 (max_len=8).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len8",
-            description="Cyclic Group Z4 (max_len=8).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len8",
-            description="Cyclic Group Z5 (max_len=8).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len8",
-            description="Cyclic Group Z6 (max_len=8).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len8",
-            description="Dihedral Group D3 (max_len=8).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len8",
-            description="Dihedral Group D4 (max_len=8).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len8",
-            description="Dihedral Group D5 (max_len=8).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len8",
-            description="Dihedral Group D6 (max_len=8).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len8",
-            description="Dihedral Group D7 (max_len=8).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len8",
-            description="Dihedral Group D8 (max_len=8).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len8",
-            description="PSL Group PSL25 (max_len=8).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len8",
-            description="Frobenius Group F20 (max_len=8).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len8",
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len16",
-            description="Symmetric Group S3 (max_len=16).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len16",
-            description="Symmetric Group S4 (max_len=16).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len16",
-            description="Symmetric Group S5 (max_len=16).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len16",
-            description="Symmetric Group S6 (max_len=16).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len16",
-            description="Symmetric Group S7 (max_len=16).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len16",
-            description="Alternating Group A3 (max_len=16).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len16",
-            description="Alternating Group A4 (max_len=16).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len16",
-            description="Alternating Group A5 (max_len=16).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len16",
-            description="Alternating Group A6 (max_len=16).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len16",
-            description="Alternating Group A7 (max_len=16).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len16",
-            description="Cyclic Group C3 (max_len=16).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len16",
-            description="Cyclic Group C4 (max_len=16).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len16",
-            description="Cyclic Group C5 (max_len=16).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len16",
-            description="Cyclic Group C6 (max_len=16).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len16",
-            description="Cyclic Group C7 (max_len=16).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len16",
-            description="Cyclic Group C8 (max_len=16).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len16",
-            description="Cyclic Group C10 (max_len=16).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len16",
-            description="Cyclic Group C12 (max_len=16).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len16",
-            description="Cyclic Group Z3 (max_len=16).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len16",
-            description="Cyclic Group Z4 (max_len=16).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len16",
-            description="Cyclic Group Z5 (max_len=16).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len16",
-            description="Cyclic Group Z6 (max_len=16).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len16",
-            description="Dihedral Group D3 (max_len=16).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len16",
-            description="Dihedral Group D4 (max_len=16).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len16",
-            description="Dihedral Group D5 (max_len=16).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len16",
-            description="Dihedral Group D6 (max_len=16).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len16",
-            description="Dihedral Group D7 (max_len=16).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len16",
-            description="Dihedral Group D8 (max_len=16).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len16",
-            description="PSL Group PSL25 (max_len=16).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len16",
-            description="Frobenius Group F20 (max_len=16).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len16",
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len32",
-            description="Symmetric Group S3 (max_len=32).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len32",
-            description="Symmetric Group S4 (max_len=32).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len32",
-            description="Symmetric Group S5 (max_len=32).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len32",
-            description="Symmetric Group S6 (max_len=32).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len32",
-            description="Symmetric Group S7 (max_len=32).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len32",
-            description="Alternating Group A3 (max_len=32).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len32",
-            description="Alternating Group A4 (max_len=32).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len32",
-            description="Alternating Group A5 (max_len=32).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len32",
-            description="Alternating Group A6 (max_len=32).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len32",
-            description="Alternating Group A7 (max_len=32).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len32",
-            description="Cyclic Group C3 (max_len=32).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len32",
-            description="Cyclic Group C4 (max_len=32).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len32",
-            description="Cyclic Group C5 (max_len=32).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len32",
-            description="Cyclic Group C6 (max_len=32).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len32",
-            description="Cyclic Group C7 (max_len=32).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len32",
-            description="Cyclic Group C8 (max_len=32).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len32",
-            description="Cyclic Group C10 (max_len=32).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len32",
-            description="Cyclic Group C12 (max_len=32).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len32",
-            description="Cyclic Group Z3 (max_len=32).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len32",
-            description="Cyclic Group Z4 (max_len=32).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len32",
-            description="Cyclic Group Z5 (max_len=32).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len32",
-            description="Cyclic Group Z6 (max_len=32).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len32",
-            description="Dihedral Group D3 (max_len=32).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len32",
-            description="Dihedral Group D4 (max_len=32).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len32",
-            description="Dihedral Group D5 (max_len=32).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len32",
-            description="Dihedral Group D6 (max_len=32).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len32",
-            description="Dihedral Group D7 (max_len=32).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len32",
-            description="Dihedral Group D8 (max_len=32).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len32",
-            description="PSL Group PSL25 (max_len=32).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len32",
-            description="Frobenius Group F20 (max_len=32).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len32",
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len64",
-            description="Symmetric Group S3 (max_len=64).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len64",
-            description="Symmetric Group S4 (max_len=64).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len64",
-            description="Symmetric Group S5 (max_len=64).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len64",
-            description="Symmetric Group S6 (max_len=64).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len64",
-            description="Symmetric Group S7 (max_len=64).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len64",
-            description="Alternating Group A3 (max_len=64).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len64",
-            description="Alternating Group A4 (max_len=64).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len64",
-            description="Alternating Group A5 (max_len=64).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len64",
-            description="Alternating Group A6 (max_len=64).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len64",
-            description="Alternating Group A7 (max_len=64).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len64",
-            description="Cyclic Group C3 (max_len=64).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len64",
-            description="Cyclic Group C4 (max_len=64).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len64",
-            description="Cyclic Group C5 (max_len=64).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len64",
-            description="Cyclic Group C6 (max_len=64).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len64",
-            description="Cyclic Group C7 (max_len=64).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len64",
-            description="Cyclic Group C8 (max_len=64).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len64",
-            description="Cyclic Group C10 (max_len=64).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len64",
-            description="Cyclic Group C12 (max_len=64).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len64",
-            description="Cyclic Group Z3 (max_len=64).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len64",
-            description="Cyclic Group Z4 (max_len=64).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len64",
-            description="Cyclic Group Z5 (max_len=64).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len64",
-            description="Cyclic Group Z6 (max_len=64).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len64",
-            description="Dihedral Group D3 (max_len=64).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len64",
-            description="Dihedral Group D4 (max_len=64).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len64",
-            description="Dihedral Group D5 (max_len=64).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len64",
-            description="Dihedral Group D6 (max_len=64).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len64",
-            description="Dihedral Group D7 (max_len=64).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len64",
-            description="Dihedral Group D8 (max_len=64).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len64",
-            description="PSL Group PSL25 (max_len=64).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len64",
-            description="Frobenius Group F20 (max_len=64).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len64",
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len128",
-            description="Symmetric Group S3 (max_len=128).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len128",
-            description="Symmetric Group S4 (max_len=128).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len128",
-            description="Symmetric Group S5 (max_len=128).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len128",
-            description="Symmetric Group S6 (max_len=128).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len128",
-            description="Symmetric Group S7 (max_len=128).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len128",
-            description="Alternating Group A3 (max_len=128).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len128",
-            description="Alternating Group A4 (max_len=128).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len128",
-            description="Alternating Group A5 (max_len=128).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len128",
-            description="Alternating Group A6 (max_len=128).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len128",
-            description="Alternating Group A7 (max_len=128).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len128",
-            description="Cyclic Group C3 (max_len=128).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len128",
-            description="Cyclic Group C4 (max_len=128).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len128",
-            description="Cyclic Group C5 (max_len=128).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len128",
-            description="Cyclic Group C6 (max_len=128).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len128",
-            description="Cyclic Group C7 (max_len=128).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len128",
-            description="Cyclic Group C8 (max_len=128).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len128",
-            description="Cyclic Group C10 (max_len=128).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len128",
-            description="Cyclic Group C12 (max_len=128).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len128",
-            description="Cyclic Group Z3 (max_len=128).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len128",
-            description="Cyclic Group Z4 (max_len=128).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len128",
-            description="Cyclic Group Z5 (max_len=128).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len128",
-            description="Cyclic Group Z6 (max_len=128).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len128",
-            description="Dihedral Group D3 (max_len=128).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len128",
-            description="Dihedral Group D4 (max_len=128).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len128",
-            description="Dihedral Group D5 (max_len=128).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len128",
-            description="Dihedral Group D6 (max_len=128).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len128",
-            description="Dihedral Group D7 (max_len=128).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len128",
-            description="Dihedral Group D8 (max_len=128).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len128",
-            description="PSL Group PSL25 (max_len=128).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len128",
-            description="Frobenius Group F20 (max_len=128).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len128",
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len256",
-            description="Symmetric Group S3 (max_len=256).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len256",
-            description="Symmetric Group S4 (max_len=256).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len256",
-            description="Symmetric Group S5 (max_len=256).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len256",
-            description="Symmetric Group S6 (max_len=256).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len256",
-            description="Symmetric Group S7 (max_len=256).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len256",
-            description="Alternating Group A3 (max_len=256).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len256",
-            description="Alternating Group A4 (max_len=256).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len256",
-            description="Alternating Group A5 (max_len=256).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len256",
-            description="Alternating Group A6 (max_len=256).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len256",
-            description="Alternating Group A7 (max_len=256).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len256",
-            description="Cyclic Group C3 (max_len=256).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len256",
-            description="Cyclic Group C4 (max_len=256).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len256",
-            description="Cyclic Group C5 (max_len=256).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len256",
-            description="Cyclic Group C6 (max_len=256).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len256",
-            description="Cyclic Group C7 (max_len=256).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len256",
-            description="Cyclic Group C8 (max_len=256).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len256",
-            description="Cyclic Group C10 (max_len=256).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len256",
-            description="Cyclic Group C12 (max_len=256).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len256",
-            description="Cyclic Group Z3 (max_len=256).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len256",
-            description="Cyclic Group Z4 (max_len=256).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len256",
-            description="Cyclic Group Z5 (max_len=256).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len256",
-            description="Cyclic Group Z6 (max_len=256).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len256",
-            description="Dihedral Group D3 (max_len=256).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len256",
-            description="Dihedral Group D4 (max_len=256).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len256",
-            description="Dihedral Group D5 (max_len=256).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len256",
-            description="Dihedral Group D6 (max_len=256).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len256",
-            description="Dihedral Group D7 (max_len=256).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len256",
-            description="Dihedral Group D8 (max_len=256).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len256",
-            description="PSL Group PSL25 (max_len=256).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len256",
-            description="Frobenius Group F20 (max_len=256).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len256",
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="s3_len512",
-            description="Symmetric Group S3 (max_len=512).",
-            group_name="S3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/s3_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="s4_len512",
-            description="Symmetric Group S4 (max_len=512).",
-            group_name="S4",
-            group_degree=4,
-            group_order=24,
-            data_dir="data/s4_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="s5_len512",
-            description="Symmetric Group S5 (max_len=512).",
-            group_name="S5",
-            group_degree=5,
-            group_order=120,
-            data_dir="data/s5_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="s6_len512",
-            description="Symmetric Group S6 (max_len=512).",
-            group_name="S6",
-            group_degree=6,
-            group_order=720,
-            data_dir="data/s6_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="s7_len512",
-            description="Symmetric Group S7 (max_len=512).",
-            group_name="S7",
-            group_degree=7,
-            group_order=5040,
-            data_dir="data/s7_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="a3_len512",
-            description="Alternating Group A3 (max_len=512).",
-            group_name="A3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/a3_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="a4_len512",
-            description="Alternating Group A4 (max_len=512).",
-            group_name="A4",
-            group_degree=4,
-            group_order=12,
-            data_dir="data/a4_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="a5_len512",
-            description="Alternating Group A5 (max_len=512).",
-            group_name="A5",
-            group_degree=5,
-            group_order=60,
-            data_dir="data/a5_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="a6_len512",
-            description="Alternating Group A6 (max_len=512).",
-            group_name="A6",
-            group_degree=6,
-            group_order=360,
-            data_dir="data/a6_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="a7_len512",
-            description="Alternating Group A7 (max_len=512).",
-            group_name="A7",
-            group_degree=7,
-            group_order=2520,
-            data_dir="data/a7_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c3_len512",
-            description="Cyclic Group C3 (max_len=512).",
-            group_name="C3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/c3_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c4_len512",
-            description="Cyclic Group C4 (max_len=512).",
-            group_name="C4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/c4_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c5_len512",
-            description="Cyclic Group C5 (max_len=512).",
-            group_name="C5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/c5_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c6_len512",
-            description="Cyclic Group C6 (max_len=512).",
-            group_name="C6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/c6_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c7_len512",
-            description="Cyclic Group C7 (max_len=512).",
-            group_name="C7",
-            group_degree=7,
-            group_order=7,
-            data_dir="data/c7_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c8_len512",
-            description="Cyclic Group C8 (max_len=512).",
-            group_name="C8",
-            group_degree=8,
-            group_order=8,
-            data_dir="data/c8_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c10_len512",
-            description="Cyclic Group C10 (max_len=512).",
-            group_name="C10",
-            group_degree=10,
-            group_order=10,
-            data_dir="data/c10_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="c12_len512",
-            description="Cyclic Group C12 (max_len=512).",
-            group_name="C12",
-            group_degree=12,
-            group_order=12,
-            data_dir="data/c12_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="z3_len512",
-            description="Cyclic Group Z3 (max_len=512).",
-            group_name="Z3",
-            group_degree=3,
-            group_order=3,
-            data_dir="data/z3_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="z4_len512",
-            description="Cyclic Group Z4 (max_len=512).",
-            group_name="Z4",
-            group_degree=4,
-            group_order=4,
-            data_dir="data/z4_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="z5_len512",
-            description="Cyclic Group Z5 (max_len=512).",
-            group_name="Z5",
-            group_degree=5,
-            group_order=5,
-            data_dir="data/z5_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="z6_len512",
-            description="Cyclic Group Z6 (max_len=512).",
-            group_name="Z6",
-            group_degree=6,
-            group_order=6,
-            data_dir="data/z6_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d3_len512",
-            description="Dihedral Group D3 (max_len=512).",
-            group_name="D3",
-            group_degree=3,
-            group_order=6,
-            data_dir="data/d3_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d4_len512",
-            description="Dihedral Group D4 (max_len=512).",
-            group_name="D4",
-            group_degree=4,
-            group_order=8,
-            data_dir="data/d4_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d5_len512",
-            description="Dihedral Group D5 (max_len=512).",
-            group_name="D5",
-            group_degree=5,
-            group_order=10,
-            data_dir="data/d5_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d6_len512",
-            description="Dihedral Group D6 (max_len=512).",
-            group_name="D6",
-            group_degree=6,
-            group_order=12,
-            data_dir="data/d6_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d7_len512",
-            description="Dihedral Group D7 (max_len=512).",
-            group_name="D7",
-            group_degree=7,
-            group_order=14,
-            data_dir="data/d7_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="d8_len512",
-            description="Dihedral Group D8 (max_len=512).",
-            group_name="D8",
-            group_degree=8,
-            group_order=16,
-            data_dir="data/d8_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="psl25_len512",
-            description="PSL Group PSL25 (max_len=512).",
-            group_name="PSL25",
-            group_degree=6,
-            group_order=60,
-            data_dir="data/psl25_data_len512",
-            max_len=512,
-        ),
-        PermutationGroupsConfig(
-            name="f20_len512",
-            description="Frobenius Group F20 (max_len=512).",
-            group_name="F20",
-            group_degree=5,
-            group_order=20,
-            data_dir="data/f20_data_len512",
-            max_len=512,
-        ),
+    VERSION = datasets.Version("3.0.0")
+    
+    # Define all available groups
+    GROUPS = {
+        # Symmetric Groups
+        "S3": {"type": "Symmetric", "degree": 3, "order": 6},
+        "S4": {"type": "Symmetric", "degree": 4, "order": 24},
+        "S5": {"type": "Symmetric", "degree": 5, "order": 120},
+        "S6": {"type": "Symmetric", "degree": 6, "order": 720},
+        "S7": {"type": "Symmetric", "degree": 7, "order": 5040},
+        # Alternating Groups
+        "A3": {"type": "Alternating", "degree": 3, "order": 3},
+        "A4": {"type": "Alternating", "degree": 4, "order": 12},
+        "A5": {"type": "Alternating", "degree": 5, "order": 60},
+        "A6": {"type": "Alternating", "degree": 6, "order": 360},
+        "A7": {"type": "Alternating", "degree": 7, "order": 2520},
+        # Cyclic Groups
+        "C3": {"type": "Cyclic", "degree": 3, "order": 3},
+        "C4": {"type": "Cyclic", "degree": 4, "order": 4},
+        "C5": {"type": "Cyclic", "degree": 5, "order": 5},
+        "C6": {"type": "Cyclic", "degree": 6, "order": 6},
+        "C7": {"type": "Cyclic", "degree": 7, "order": 7},
+        "C8": {"type": "Cyclic", "degree": 8, "order": 8},
+        "C10": {"type": "Cyclic", "degree": 10, "order": 10},
+        "C12": {"type": "Cyclic", "degree": 12, "order": 12},
+        # Cyclic Groups (Z notation)
+        "Z3": {"type": "Cyclic", "degree": 3, "order": 3},
+        "Z4": {"type": "Cyclic", "degree": 4, "order": 4},
+        "Z5": {"type": "Cyclic", "degree": 5, "order": 5},
+        "Z6": {"type": "Cyclic", "degree": 6, "order": 6},
+        # Dihedral Groups
+        "D3": {"type": "Dihedral", "degree": 3, "order": 6},
+        "D4": {"type": "Dihedral", "degree": 4, "order": 8},
+        "D5": {"type": "Dihedral", "degree": 5, "order": 10},
+        "D6": {"type": "Dihedral", "degree": 6, "order": 12},
+        "D7": {"type": "Dihedral", "degree": 7, "order": 14},
+        "D8": {"type": "Dihedral", "degree": 8, "order": 16},
+        # Special Groups
+        "PSL25": {"type": "PSL(2,5)", "degree": 6, "order": 60},
+        "F20": {"type": "Frobenius", "degree": 5, "order": 20},
+    }
+    
+    BUILDER_CONFIGS = []
+    
+    # Simple configs - just group names
+    for group_name, info in GROUPS.items():
+        BUILDER_CONFIGS.append(
+            PermutationGroupsConfig(
+                name=group_name.lower(),
+                description=f"{info['type']} Group {group_name} (order {info['order']}).",
+                group_name=group_name,
+            )
+        )
+    
+    # Keep old-style configs for backwards compatibility
+    for group_name, info in GROUPS.items():
+        BUILDER_CONFIGS.append(
+            PermutationGroupsConfig(
+                name=f"{group_name.lower()}_data",
+                description=f"{info['type']} Group {group_name} (order {info['order']}).",
+                group_name=group_name,
+            )
+        )
+    
+    # Add "all" configuration
+    BUILDER_CONFIGS.append(
         PermutationGroupsConfig(
             name="all",
             description="All Permutation Composition Datasets.",
             group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-        ),
-        PermutationGroupsConfig(
-            name="all_len4",
-            description="All Groups (max_len=4).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=4,
-        ),
-        PermutationGroupsConfig(
-            name="all_len8",
-            description="All Groups (max_len=8).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=8,
-        ),
-        PermutationGroupsConfig(
-            name="all_len16",
-            description="All Groups (max_len=16).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=16,
-        ),
-        PermutationGroupsConfig(
-            name="all_len32",
-            description="All Groups (max_len=32).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=32,
-        ),
-        PermutationGroupsConfig(
-            name="all_len64",
-            description="All Groups (max_len=64).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=64,
-        ),
-        PermutationGroupsConfig(
-            name="all_len128",
-            description="All Groups (max_len=128).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=128,
-        ),
-        PermutationGroupsConfig(
-            name="all_len256",
-            description="All Groups (max_len=256).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=256,
-        ),
-        PermutationGroupsConfig(
-            name="all_len512",
-            description="All Groups (max_len=512).",
-            group_name="All",
-            group_degree=None,
-            group_order=None,
-            data_dir=None,
-            max_len=512,
-        ),
-    ]
-
+        )
+    )
+    
     DEFAULT_CONFIG_NAME = "s5_data"
-
+    
     def _info(self):
         return datasets.DatasetInfo(
             description=_DESCRIPTION,
@@ -2516,27 +124,20 @@ class PermutationGroups(datasets.ArrowBasedBuilder):
             homepage=_HOMEPAGE,
             license=_LICENSE,
         )
-
+    
     def _split_generators(self, dl_manager):
         # Handle the "all" configurations
         if self.config.name.startswith("all"):
-            # Determine which groups to include
-            if self.config.name == "all":
-                # Original all - just the base configs
-                all_configs = [f"{g.lower()}_data" for g in ['S3', 'S4', 'S5', 'S6', 'S7', 'A3', 'A4', 'A5', 'A6', 'A7', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C10', 'C12', 'Z3', 'Z4', 'Z5', 'Z6', 'D3', 'D4', 'D5', 'D6', 'D7', 'D8', 'PSL25', 'F20']]
-            else:
-                # Length-specific all
-                length = self.config.max_len
-                all_configs = [f"{g.lower()}_len{length}" for g in ['S3', 'S4', 'S5', 'S6', 'S7', 'A3', 'A4', 'A5', 'A6', 'A7', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C10', 'C12', 'Z3', 'Z4', 'Z5', 'Z6', 'D3', 'D4', 'D5', 'D6', 'D7', 'D8', 'PSL25', 'F20']]
+            all_configs = [f"{g.lower()}_data" for g in self.GROUPS.keys()]
             
-            # Download all arrow files
+            # Download all base datasets
             train_files = []
             test_files = []
             
-            for config in all_configs:
+            for group_lower in all_configs:
                 data_urls = {
-                    "train": f"data/{config}/train/data-00000-of-00001.arrow",
-                    "test": f"data/{config}/test/data-00000-of-00001.arrow",
+                    "train": f"data/{group_lower}/train/data-00000-of-00001.arrow",
+                    "test": f"data/{group_lower}/test/data-00000-of-00001.arrow",
                 }
                 try:
                     downloaded = dl_manager.download(data_urls)
@@ -2551,17 +152,19 @@ class PermutationGroups(datasets.ArrowBasedBuilder):
                     name=datasets.Split.TRAIN,
                     gen_kwargs={
                         "files": train_files,
+                        "max_len": self.config.max_len,
                     },
                 ),
                 datasets.SplitGenerator(
                     name=datasets.Split.TEST,
                     gen_kwargs={
                         "files": test_files,
+                        "max_len": self.config.max_len,
                     },
                 ),
             ]
         else:
-            # Single configuration
+            # Single configuration - always use base data
             data_urls = {
                 "train": [f"{self.config.data_dir}/train/data-00000-of-00001.arrow"],
                 "test": [f"{self.config.data_dir}/test/data-00000-of-00001.arrow"],
@@ -2574,21 +177,32 @@ class PermutationGroups(datasets.ArrowBasedBuilder):
                     name=datasets.Split.TRAIN,
                     gen_kwargs={
                         "files": downloaded_files["train"],
+                        "max_len": self.config.max_len,
                     },
                 ),
                 datasets.SplitGenerator(
                     name=datasets.Split.TEST,
                     gen_kwargs={
                         "files": downloaded_files["test"],
+                        "max_len": self.config.max_len,
                     },
                 ),
             ]
-
-    def _generate_tables(self, files):
-        """Yield arrow tables directly for better performance."""
+    
+    def _generate_tables(self, files, max_len):
+        """Yield arrow tables with length filtering."""
         for file_idx, file in enumerate(files):
-            # Load the dataset using the datasets library format
+            # Load the dataset
             dataset = datasets.Dataset.from_file(file)
+            
+            # Filter by sequence length if needed
+            if max_len < 512:
+                def filter_length(example):
+                    seq_len = len(example["input_sequence"].split())
+                    return seq_len <= max_len
+                
+                dataset = dataset.filter(filter_length)
+            
             # Get the underlying Arrow table
             table = dataset.data.table
-            yield file_idx, table
+            yield file_idx, table