s6_subgroups.json

{
    "C2_transposition": {
        "size": 2,
        "generators": [
            [[0, 1, 2, 3, 5, 4]],
            [[0, 1, 2, 4, 3, 5]], 
            [[0, 1, 2, 5, 4, 3]], 
            [[0, 1, 3, 2, 4, 5]], 
            [[0, 1, 4, 3, 2, 5]], 
            [[0, 1, 5, 3, 4, 2]], 
            [[0, 2, 1, 3, 4, 5]],
            [[0, 3, 2, 1, 4, 5]], 
            [[0, 4, 2, 3, 1, 5]], 
            [[0, 5, 2, 3, 4, 1]], 
            [[1, 0, 2, 3, 4, 5]], 
            [[2, 1, 0, 3, 4, 5]], 
            [[3, 1, 2, 0, 4, 5]], 
            [[4, 1, 2, 3, 0, 5]], 
            [[5, 1, 2, 3, 4, 0]]
        ]
    },
    "C2_triple_transposition": {
        "size": 2,
        "generators": [
            [[1, 0, 3, 2, 5, 4]], 
            [[1, 0, 4, 5, 2, 3]], 
            [[1, 0, 5, 4, 3, 2]], 
            [[2, 3, 0, 1, 5, 4]], 
            [[2, 4, 0, 5, 1, 3]], 
            [[2, 5, 0, 4, 3, 1]], 
            [[3, 2, 1, 0, 5, 4]], 
            [[3, 4, 5, 0, 1, 2]], 
            [[3, 5, 4, 0, 2, 1]], 
            [[4, 2, 1, 5, 0, 3]], 
            [[4, 3, 5, 1, 0, 2]], 
            [[4, 5, 3, 2, 0, 1]], 
            [[5, 2, 1, 4, 3, 0]], 
            [[5, 3, 4, 1, 2, 0]], 
            [[5, 4, 3, 2, 1, 0]]
        ]
    },
    "C2_double_transposition": {
        "size": 2, 
        "generators": [
            [[0, 1, 3, 2, 5, 4]],
            [[0, 1, 4, 5, 2, 3]], 
            [[0, 1, 5, 4, 3, 2]], 
            [[0, 2, 1, 3, 5, 4]], 
            [[0, 2, 1, 4, 3, 5]], 
            [[0, 2, 1, 5, 4, 3]], 
            [[0, 3, 2, 1, 5, 4]], 
            [[0, 3, 4, 1, 2, 5]],
            [[0, 3, 5, 1, 4, 2]], 
            [[0, 4, 2, 5, 1, 3]], 
            [[0, 4, 3, 2, 1, 5]], 
            [[0, 4, 5, 3, 1, 2]], 
            [[0, 5, 2, 4, 3, 1]], 
            [[0, 5, 3, 2, 4, 1]], 
            [[0, 5, 4, 3, 2, 1]], 
            [[1, 0, 2, 3, 5, 4]], 
            [[1, 0, 2, 4, 3, 5]], 
            [[1, 0, 2, 5, 4, 3]], 
            [[1, 0, 3, 2, 4, 5]], 
            [[1, 0, 4, 3, 2, 5]], 
            [[1, 0, 5, 3, 4, 2]], 
            [[2, 1, 0, 3, 5, 4]], 
            [[2, 1, 0, 4, 3, 5]], 
            [[2, 1, 0, 5, 4, 3]], 
            [[2, 3, 0, 1, 4, 5]], 
            [[2, 4, 0, 3, 1, 5]], 
            [[2, 5, 0, 3, 4, 1]], 
            [[3, 1, 2, 0, 5, 4]], 
            [[3, 1, 4, 0, 2, 5]], 
            [[3, 1, 5, 0, 4, 2]], 
            [[3, 2, 1, 0, 4, 5]], 
            [[3, 4, 2, 0, 1, 5]], 
            [[3, 5, 2, 0, 4, 1]], 
            [[4, 1, 2, 5, 0, 3]], 
            [[4, 1, 3, 2, 0, 5]], 
            [[4, 1, 5, 3, 0, 2]], 
            [[4, 2, 1, 3, 0, 5]], 
            [[4, 3, 2, 1, 0, 5]], 
            [[4, 5, 2, 3, 0, 1]], 
            [[5, 1, 2, 4, 3, 0]], 
            [[5, 1, 3, 2, 4, 0]], 
            [[5, 1, 4, 3, 2, 0]], 
            [[5, 2, 1, 3, 4, 0]], 
            [[5, 3, 2, 1, 4, 0]], 
            [[5, 4, 2, 3, 1, 0]]
        ]
    },    
    "C3_three_cycle": {
        "size": 3, 
        "generators": [
            [[0, 1, 2, 5, 3, 4]], 
            [[0, 1, 4, 2, 3, 5]], 
            [[0, 1, 5, 2, 4, 3]], 
            [[0, 1, 5, 3, 2, 4]], 
            [[0, 3, 1, 2, 4, 5]], 
            [[0, 4, 1, 3, 2, 5]], 
            [[0, 5, 1, 3, 4, 2]], 
            [[0, 4, 2, 1, 3, 5]], 
            [[0, 5, 2, 1, 4, 3]], 
            [[0, 5, 2, 3, 1, 4]], 
            [[2, 0, 1, 3, 4, 5]], 
            [[3, 0, 2, 1, 4, 5]], 
            [[4, 0, 2, 3, 1, 5]], 
            [[5, 0, 2, 3, 4, 1]], 
            [[3, 1, 0, 2, 4, 5]], 
            [[4, 1, 0, 3, 2, 5]], 
            [[5, 1, 0, 3, 4, 2]], 
            [[4, 1, 2, 0, 3, 5]], 
            [[5, 1, 2, 0, 4, 3]], 
            [[5, 1, 2, 3, 0, 4]]
        ]
    },
    "C3_double_three_cycle": {
        "size": 3, 
        "generators": [
            [[1, 2, 0, 4, 5, 3]],
            [[2, 0, 1, 4, 5, 3]], 
            [[1, 3, 4, 0, 5, 2]], 
            [[3, 0, 4, 1, 5, 2]], 
            [[1, 4, 3, 5, 0, 2]], 
            [[4, 0, 3, 5, 1, 2]], 
            [[1, 5, 3, 4, 2, 0]], 
            [[5, 0, 3, 4, 2, 1]], 
            [[2, 3, 4, 5, 0, 1]], 
            [[2, 3, 5, 4, 1, 0]], 
            [[2, 4, 3, 0, 5, 1]], 
            [[5, 3, 0, 4, 1, 2]], 
            [[3, 4, 0, 2, 5, 1]], 
            [[4, 3, 0, 5, 2, 1]], 
            [[3, 2, 4, 5, 1, 0]], 
            [[3, 2, 5, 4, 0, 1]], 
            [[3, 4, 1, 5, 2, 0]], 
            [[3, 5, 1, 4, 0, 2]], 
            [[4, 2, 3, 1, 5, 0]], 
            [[4, 3, 1, 2, 5, 0]]
        ]
    },
    "C2xC2_double_transposition": {
        "size": 4,
        "generators": [
            [[0, 1, 3, 2, 5, 4], [1, 0, 2, 3, 5, 4]],
            [[0, 1, 4, 5, 2, 3], [1, 0, 4, 3, 2, 5]], 
            [[0, 1, 5, 4, 3, 2], [1, 0, 2, 4, 3, 5]],
            [[0, 2, 1, 3, 5, 4], [3, 2, 1, 0, 4, 5]],
            [[5, 1, 2, 4, 3, 0], [5, 2, 1, 3, 4, 0]],
            [[0, 2, 1, 5, 4, 3], [4, 1, 2, 5, 0, 3]],
            [[2, 1, 0, 3, 5, 4], [2, 3, 0, 1, 4, 5]],
            [[0, 3, 4, 1, 2, 5], [5, 3, 2, 1, 4, 0]],
            [[0, 3, 5, 1, 4, 2], [4, 1, 5, 3, 0, 2]],
            [[0, 4, 2, 5, 1, 3], [2, 4, 0, 3, 1, 5]],
            [[0, 4, 3, 2, 1, 5], [5, 1, 3, 2, 4, 0]],
            [[0, 4, 5, 3, 1, 2], [3, 1, 5, 0, 4, 2]],
            [[0, 5, 2, 4, 3, 1], [2, 5, 0, 3, 4, 1]],
            [[0, 5, 3, 2, 4, 1], [4, 1, 3, 2, 0, 5]],
            [[3, 1, 4, 0, 2, 5], [3, 5, 2, 0, 4, 1]]
        ]
    },
    "C2xC2_double_transposition_disjoint": {
        "size": 4,
        "generators": [
            [[0, 1, 3, 2, 5, 4], [0, 1, 4, 5, 2, 3]],
            [[0, 4, 5, 3, 1, 2], [0, 5, 4, 3, 2, 1]],
            [[0, 2, 1, 4, 3, 5], [0, 3, 4, 1, 2, 5]],
            [[0, 3, 5, 1, 4, 2], [0, 5, 3, 2, 4, 1]],
            [[0, 3, 2, 1, 5, 4], [0, 4, 2, 5, 1, 3]],
            [[1, 0, 2, 3, 5, 4], [4, 5, 2, 3, 0, 1]],
            [[3, 4, 2, 0, 1, 5], [4, 3, 2, 1, 0, 5]],
            [[1, 0, 2, 5, 4, 3], [3, 5, 2, 0, 4, 1]],
            [[1, 0, 3, 2, 4, 5], [2, 3, 0, 1, 4, 5]],
            [[2, 4, 0, 3, 1, 5], [4, 2, 1, 3, 0, 5]],
            [[2, 5, 0, 3, 4, 1], [5, 2, 1, 3, 4, 0]],
            [[4, 1, 5, 3, 0, 2], [5, 1, 4, 3, 2, 0]],
            [[2, 1, 0, 4, 3, 5], [3, 1, 4, 0, 2, 5]],
            [[2, 1, 0, 5, 4, 3], [3, 1, 5, 0, 4, 2]],
            [[4, 1, 2, 5, 0, 3], [5, 1, 2, 4, 3, 0]]
        ]
    },
    "C4_four_cycle_transposition": {
        "size": 4,
        "generators": [
            [[1, 0, 4, 5, 3, 2]],
            [[1, 0, 3, 4, 5, 2]], 
            [[1, 0, 4, 2, 5, 3]], 
            [[3, 4, 5, 0, 2, 1]], 
            [[5, 3, 4, 2, 1, 0]], 
    
            [[4, 3, 5, 2, 0, 1]], 
            [[2, 4, 0, 5, 3, 1]], 
            [[5, 2, 3, 4, 1, 0]], 
            [[4, 2, 3, 5, 0, 1]], 
            [[2, 3, 0, 4, 5, 1]], 
            [[5, 3, 1, 4, 2, 0]], 
            [[3, 2, 4, 0, 5, 1]], 
            [[2, 3, 0, 5, 1, 4]], 
            [[4, 3, 1, 5, 0, 2]],
            [[3, 4, 1, 0, 5, 2]], 
            [[5, 4, 3, 2, 0, 1]],
            [[3, 4, 5, 1, 0, 2]], 
            [[5, 3, 4, 0, 2, 1]], 
            [[2, 3, 1, 0, 5, 4]], 
            [[2, 4, 1, 5, 0, 3]], 
            [[2, 5, 1, 4, 3, 0]], 
            [[1, 2, 3, 0, 5, 4]], 
            [[1, 2, 4, 5, 0, 3]], 
            [[1, 2, 5, 4, 3, 0]], 
            [[2, 0, 3, 1, 5, 4]], 
            [[1, 3, 4, 5, 2, 0]], 
            [[1, 3, 5, 4, 0, 2]], 
            [[2, 0, 4, 5, 1, 3]], 
            [[1, 4, 3, 2, 5, 0]], 
            [[3, 0, 5, 4, 1, 2]], 
            [[2, 0, 5, 4, 3, 1]], 
            [[4, 0, 3, 2, 5, 1]], 
            [[3, 0, 4, 5, 2, 1]], 
            [[4, 3, 5, 1, 2, 0]], 
            [[3, 5, 4, 2, 0, 1]], 
            [[3, 4, 5, 2, 1, 0]], 
            [[2, 3, 4, 1, 5, 0]], 
            [[2, 3, 5, 1, 0, 4]], 
            [[2, 4, 3, 5, 1, 0]], 
            [[3, 4, 0, 5, 1, 2]], 
            [[2, 5, 3, 4, 0, 1]], 
            [[2, 5, 4, 0, 3, 1]], 
            [[4, 2, 1, 5, 3, 0]], 
            [[3, 2, 1, 4, 5, 0]], 
            [[3, 2, 1, 5, 0, 4]]
        ]
    },
    "C2xC2_single_double_transposition_disjoint": {
        "size": 4,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [1, 0, 3, 2, 4, 5]],
            [[0, 1, 2, 3, 5, 4], [2, 3, 0, 1, 4, 5]],
            [[0, 1, 2, 3, 5, 4], [3, 2, 1, 0, 4, 5]],
            [[0, 1, 2, 4, 3, 5], [1, 0, 5, 3, 4, 2]],
            [[0, 1, 2, 4, 3, 5], [2, 5, 0, 3, 4, 1]],
            [[0, 1, 2, 4, 3, 5], [5, 2, 1, 3, 4, 0]],
            [[0, 1, 2, 5, 4, 3], [1, 0, 4, 3, 2, 5]], 
            [[0, 1, 2, 5, 4, 3], [2, 4, 0, 3, 1, 5]],
            [[0, 1, 2, 5, 4, 3], [4, 2, 1, 3, 0, 5]],
            [[0, 1, 3, 2, 4, 5], [1, 0, 2, 3, 5, 4]],
            [[0, 1, 3, 2, 4, 5], [4, 5, 2, 3, 0, 1]],
            [[0, 1, 3, 2, 4, 5], [5, 4, 2, 3, 1, 0]],
            [[0, 1, 3, 2, 5, 4], [1, 0, 2, 3, 4, 5]],
            [[0, 1, 4, 3, 2, 5], [1, 0, 2, 5, 4, 3]],
            [[0, 1, 4, 3, 2, 5], [3, 5, 2, 0, 4, 1]],
            [[0, 1, 4, 3, 2, 5], [5, 3, 2, 1, 4, 0]],
            [[0, 1, 4, 5, 2, 3], [1, 0, 2, 3, 4, 5]],
            [[0, 1, 5, 3, 4, 2], [1, 0, 2, 4, 3, 5]],
            [[0, 1, 5, 3, 4, 2], [3, 4, 2, 0, 1, 5]],
            [[0, 1, 5, 3, 4, 2], [4, 3, 2, 1, 0, 5]],
            [[0, 1, 5, 4, 3, 2], [1, 0, 2, 3, 4, 5]],
            [[0, 2, 1, 3, 4, 5], [3, 1, 2, 0, 5, 4]],
            [[0, 2, 1, 3, 4, 5], [4, 1, 2, 5, 0, 3]],
            [[0, 2, 1, 3, 4, 5], [5, 1, 2, 4, 3, 0]],
            [[0, 2, 1, 3, 5, 4], [3, 1, 2, 0, 4, 5]],
            [[0, 2, 1, 4, 3, 5], [5, 1, 2, 3, 4, 0]],
            [[0, 2, 1, 5, 4, 3], [4, 1, 2, 3, 0, 5]],
            [[0, 3, 2, 1, 4, 5], [2, 1, 0, 3, 5, 4]],
            [[0, 3, 2, 1, 4, 5], [4, 1, 5, 3, 0, 2]],
            [[0, 3, 2, 1, 4, 5], [5, 1, 4, 3, 2, 0]],
            [[0, 3, 2, 1, 5, 4], [2, 1, 0, 3, 4, 5]],
            [[0, 3, 4, 1, 2, 5], [5, 1, 2, 3, 4, 0]],
            [[0, 3, 5, 1, 4, 2], [4, 1, 2, 3, 0, 5]],
            [[0, 4, 2, 3, 1, 5], [2, 1, 0, 5, 4, 3]],
            [[0, 4, 2, 3, 1, 5], [3, 1, 5, 0, 4, 2]],
            [[0, 4, 2, 3, 1, 5], [5, 1, 3, 2, 4, 0]],
            [[0, 4, 2, 5, 1, 3], [2, 1, 0, 3, 4, 5]],
            [[0, 4, 3, 2, 1, 5], [5, 1, 2, 3, 4, 0]],
            [[0, 4, 5, 3, 1, 2], [3, 1, 2, 0, 4, 5]],
            [[0, 5, 2, 3, 4, 1], [2, 1, 0, 4, 3, 5]],
            [[0, 5, 2, 3, 4, 1], [3, 1, 4, 0, 2, 5]],
            [[0, 5, 2, 3, 4, 1], [4, 1, 3, 2, 0, 5]],
            [[0, 5, 2, 4, 3, 1], [2, 1, 0, 3, 4, 5]],
            [[0, 5, 3, 2, 4, 1], [4, 1, 2, 3, 0, 5]],
            [[0, 5, 4, 3, 2, 1], [3, 1, 2, 0, 4, 5]]
        ]
    }, 
    "C4_four_cycle": {
        "size": 4, 
        "generators": [
            [[0, 1, 4, 5, 3, 2]], 
            [[0, 1, 3, 4, 5, 2]], 
            [[0, 1, 4, 2, 5, 3]], 
            [[0, 4, 5, 3, 2, 1]], 
            [[0, 3, 4, 2, 1, 5]], 
            [[0, 3, 5, 2, 4, 1]], 
            [[0, 2, 3, 4, 1, 5]], 
            [[0, 2, 3, 5, 4, 1]], 
            [[0, 3, 1, 4, 2, 5]], 
            [[0, 2, 4, 3, 5, 1]], 
            [[0, 3, 1, 5, 4, 2]], 
            [[0, 2, 5, 3, 1, 4]], 
            [[0, 4, 2, 5, 3, 1]], 
            [[0, 3, 2, 4, 5, 1]], 
            [[0, 4, 2, 1, 5, 3]], 
            [[4, 5, 2, 3, 1, 0]], 
            [[4, 3, 2, 0, 1, 5]], 
            [[5, 3, 2, 0, 4, 1]], 
            [[2, 3, 1, 0, 4, 5]], 
            [[2, 4, 1, 3, 0, 5]], 
            [[2, 5, 1, 3, 4, 0]], 
            [[1, 2, 3, 0, 4, 5]], 
            [[1, 2, 4, 3, 0, 5]], 
            [[1, 2, 5, 3, 4, 0]], 
            [[2, 0, 3, 1, 4, 5]], 
            [[1, 3, 2, 4, 0, 5]], 
            [[1, 3, 2, 5, 4, 0]], 
            [[2, 0, 4, 3, 1, 5]], 
            [[3, 0, 2, 4, 1, 5]], 
            [[1, 4, 2, 3, 5, 0]], 
            [[2, 0, 5, 3, 4, 1]], 
            [[3, 0, 2, 5, 4, 1]], 
            [[4, 0, 2, 3, 5, 1]], 
            [[4, 1, 5, 3, 2, 0]], 
            [[3, 1, 4, 2, 0, 5]], 
            [[5, 1, 3, 0, 4, 2]], 
            [[2, 1, 3, 4, 0, 5]], 
            [[2, 1, 3, 5, 4, 0]], 
            [[3, 1, 0, 4, 2, 5]], 
            [[2, 1, 4, 3, 5, 0]], 
            [[2, 1, 5, 0, 4, 3]], 
            [[2, 1, 5, 3, 0, 4]], 
            [[4, 1, 2, 5, 3, 0]], 
            [[3, 1, 2, 4, 5, 0]], 
            [[4, 1, 2, 0, 5, 3]]
        ]
    },
    "C2xC2_single_double_transposition": {
        "size": 4,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [0, 1, 3, 2, 5, 4]],
            [[0, 2, 1, 3, 4, 5], [0, 2, 1, 3, 5, 4]],
            [[0, 1, 2, 3, 5, 4], [0, 3, 2, 1, 5, 4]],
            [[1, 0, 2, 3, 4, 5], [1, 0, 2, 3, 5, 4]],
            [[2, 1, 0, 3, 4, 5], [2, 1, 0, 3, 5, 4]],
            [[0, 1, 2, 3, 5, 4], [3, 1, 2, 0, 5, 4]],
            [[0, 1, 2, 4, 3, 5], [0, 1, 5, 4, 3, 2]],
            [[0, 1, 2, 4, 3, 5], [0, 2, 1, 4, 3, 5]],
            [[0, 5, 2, 3, 4, 1], [0, 5, 2, 4, 3, 1]],
            [[0, 1, 2, 4, 3, 5], [1, 0, 2, 4, 3, 5]],
            [[0, 1, 2, 4, 3, 5], [2, 1, 0, 4, 3, 5]], 
            [[5, 1, 2, 3, 4, 0], [5, 1, 2, 4, 3, 0]], 
            [[0, 1, 2, 5, 4, 3], [0, 1, 4, 5, 2, 3]], 
            [[0, 2, 1, 3, 4, 5], [0, 2, 1, 5, 4, 3]], 
            [[0, 1, 2, 5, 4, 3], [0, 4, 2, 5, 1, 3]], 
            [[1, 0, 2, 3, 4, 5], [1, 0, 2, 5, 4, 3]], 
            [[2, 1, 0, 3, 4, 5], [2, 1, 0, 5, 4, 3]], 
            [[4, 1, 2, 3, 0, 5], [4, 1, 2, 5, 0, 3]], 
            [[0, 1, 3, 2, 4, 5], [0, 4, 3, 2, 1, 5]], 
            [[0, 1, 3, 2, 4, 5], [0, 5, 3, 2, 4, 1]], 
            [[0, 1, 3, 2, 4, 5], [1, 0, 3, 2, 4, 5]], 
            [[0, 1, 3, 2, 4, 5], [4, 1, 3, 2, 0, 5]], 
            [[0, 1, 3, 2, 4, 5], [5, 1, 3, 2, 4, 0]], 
            [[0, 1, 4, 3, 2, 5], [0, 3, 4, 1, 2, 5]], 
            [[0, 5, 2, 3, 4, 1], [0, 5, 4, 3, 2, 1]], 
            [[0, 1, 4, 3, 2, 5], [1, 0, 4, 3, 2, 5]], 
            [[0, 1, 4, 3, 2, 5], [3, 1, 4, 0, 2, 5]], 
            [[5, 1, 2, 3, 4, 0], [5, 1, 4, 3, 2, 0]], 
            [[0, 3, 2, 1, 4, 5], [0, 3, 5, 1, 4, 2]], 
            [[0, 4, 2, 3, 1, 5], [0, 4, 5, 3, 1, 2]], 
            [[1, 0, 2, 3, 4, 5], [1, 0, 5, 3, 4, 2]], 
            [[3, 1, 2, 0, 4, 5], [3, 1, 5, 0, 4, 2]], 
            [[4, 1, 2, 3, 0, 5], [4, 1, 5, 3, 0, 2]], 
            [[0, 2, 1, 3, 4, 5], [3, 2, 1, 0, 4, 5]], 
            [[0, 2, 1, 3, 4, 5], [4, 2, 1, 3, 0, 5]], 
            [[0, 2, 1, 3, 4, 5], [5, 2, 1, 3, 4, 0]], 
            [[0, 3, 2, 1, 4, 5], [2, 3, 0, 1, 4, 5]], 
            [[0, 3, 2, 1, 4, 5], [4, 3, 2, 1, 0, 5]], 
            [[0, 3, 2, 1, 4, 5], [5, 3, 2, 1, 4, 0]], 
            [[2, 1, 0, 3, 4, 5], [2, 4, 0, 3, 1, 5]], 
            [[3, 1, 2, 0, 4, 5], [3, 4, 2, 0, 1, 5]], 
            [[5, 1, 2, 3, 4, 0], [5, 4, 2, 3, 1, 0]], 
            [[2, 1, 0, 3, 4, 5], [2, 5, 0, 3, 4, 1]], 
            [[3, 1, 2, 0, 4, 5], [3, 5, 2, 0, 4, 1]], 
            [[0, 5, 2, 3, 4, 1], [4, 5, 2, 3, 0, 1]]
        ]
    },
    "C2xC2_triple_double_transposition": {
        "size": 4,
        "generators": [
            [[0, 1, 3, 2, 5, 4], [1, 0, 4, 5, 2, 3]],
            [[0, 1, 4, 5, 2, 3], [1, 0, 3, 2, 5, 4]],
            [[0, 1, 5, 4, 3, 2], [1, 0, 3, 2, 5, 4]], 
            [[0, 2, 1, 3, 5, 4], [3, 5, 4, 0, 2, 1]], 
            [[0, 2, 1, 4, 3, 5], [5, 3, 4, 1, 2, 0]], 
            [[0, 2, 1, 5, 4, 3], [4, 5, 3, 2, 0, 1]], 
            [[0, 3, 2, 1, 5, 4], [2, 5, 0, 4, 3, 1]], 
            [[0, 3, 4, 1, 2, 5], [5, 2, 1, 4, 3, 0]], 
            [[0, 3, 5, 1, 4, 2], [4, 5, 3, 2, 0, 1]], 
            [[0, 4, 2, 5, 1, 3], [2, 3, 0, 1, 5, 4]], 
            [[0, 4, 3, 2, 1, 5], [5, 2, 1, 4, 3, 0]], 
            [[0, 4, 5, 3, 1, 2], [3, 5, 4, 0, 2, 1]], 
            [[0, 5, 2, 4, 3, 1], [2, 3, 0, 1, 5, 4]], 
            [[0, 5, 3, 2, 4, 1], [4, 3, 5, 1, 0, 2]], 
            [[0, 5, 4, 3, 2, 1], [3, 2, 1, 0, 5, 4]], 
            [[1, 0, 2, 3, 5, 4], [5, 4, 3, 2, 1, 0]], 
            [[1, 0, 2, 4, 3, 5], [4, 3, 5, 1, 0, 2]], 
            [[1, 0, 2, 5, 4, 3], [5, 3, 4, 1, 2, 0]], 
            [[1, 0, 3, 2, 4, 5], [2, 3, 0, 1, 5, 4]], 
            [[1, 0, 3, 2, 5, 4], [2, 3, 0, 1, 4, 5]], 
            [[1, 0, 3, 2, 5, 4], [3, 2, 1, 0, 4, 5]], 
            [[1, 0, 3, 2, 5, 4], [4, 5, 2, 3, 0, 1]], 
            [[1, 0, 3, 2, 5, 4], [5, 4, 2, 3, 1, 0]], 
            [[1, 0, 4, 3, 2, 5], [4, 2, 1, 5, 0, 3]], 
            [[2, 4, 0, 3, 1, 5], [4, 2, 1, 5, 0, 3]], 
            [[2, 4, 0, 5, 1, 3], [4, 2, 1, 3, 0, 5]], 
            [[1, 0, 4, 5, 2, 3], [3, 5, 2, 0, 4, 1]], 
            [[1, 0, 4, 5, 2, 3], [5, 3, 2, 1, 4, 0]], 
            [[1, 0, 5, 3, 4, 2], [5, 2, 1, 4, 3, 0]], 
            [[2, 5, 0, 3, 4, 1], [5, 2, 1, 4, 3, 0]], 
            [[2, 5, 0, 4, 3, 1], [5, 2, 1, 3, 4, 0]], 
            [[3, 4, 2, 0, 1, 5], [4, 3, 5, 1, 0, 2]], 
            [[3, 4, 5, 0, 1, 2], [4, 3, 2, 1, 0, 5]], 
            [[2, 1, 0, 3, 5, 4], [5, 3, 4, 1, 2, 0]], 
            [[2, 1, 0, 4, 3, 5], [3, 5, 4, 0, 2, 1]], 
            [[2, 1, 0, 5, 4, 3], [5, 4, 3, 2, 1, 0]], 
            [[4, 1, 5, 3, 0, 2], [5, 3, 4, 1, 2, 0]], 
            [[2, 3, 0, 1, 5, 4], [5, 1, 4, 3, 2, 0]], 
            [[2, 4, 0, 5, 1, 3], [3, 1, 5, 0, 4, 2]], 
            [[2, 4, 0, 5, 1, 3], [5, 1, 3, 2, 4, 0]], 
            [[2, 5, 0, 4, 3, 1], [3, 1, 4, 0, 2, 5]], 
            [[2, 5, 0, 4, 3, 1], [4, 1, 3, 2, 0, 5]], 
            [[3, 1, 2, 0, 5, 4], [5, 2, 1, 4, 3, 0]], 
            [[4, 1, 2, 5, 0, 3], [5, 2, 1, 4, 3, 0]], 
            [[3, 2, 1, 0, 5, 4], [5, 1, 2, 4, 3, 0]]
        ]
    },
    "C5": {
        "size": 10, 
        "generators": [
            [[0, 1, 3, 2, 5, 4], [0, 5, 3, 4, 1, 2]],
            [[0, 3, 1, 4, 5, 2], [0, 5, 2, 4, 3, 1]], 
            [[0, 1, 3, 2, 5, 4], [5, 1, 3, 4, 0, 2]], 
            [[3, 1, 0, 4, 5, 2], [5, 1, 2, 4, 3, 0]], 
            [[0, 3, 5, 1, 4, 2], [0, 4, 1, 5, 3, 2]], 
            [[0, 2, 1, 4, 3, 5], [0, 2, 3, 5, 1, 4]], 
            [[3, 1, 5, 0, 4, 2], [4, 1, 0, 5, 3, 2]], 
            [[2, 1, 0, 4, 3, 5], [2, 1, 3, 5, 0, 4]], 
            [[0, 2, 4, 5, 3, 1], [0, 5, 3, 2, 4, 1]], 
            [[0, 2, 3, 4, 5, 1], [0, 5, 4, 3, 2, 1]], 
            [[2, 1, 4, 5, 3, 0], [5, 1, 3, 2, 4, 0]], 
            [[2, 1, 0, 5, 4, 3], [2, 1, 3, 4, 5, 0]], 
            [[0, 2, 1, 3, 5, 4], [5, 2, 4, 3, 0, 1]], 
            [[2, 0, 4, 3, 5, 1], [5, 1, 4, 3, 2, 0]], 
            [[2, 4, 0, 3, 1, 5], [4, 2, 3, 0, 1, 5]], 
            [[1, 0, 4, 3, 2, 5], [3, 2, 4, 1, 0, 5]], 
            [[1, 3, 0, 5, 4, 2], [5, 3, 2, 1, 4, 0]], 
            [[2, 0, 3, 5, 4, 1], [5, 1, 3, 2, 4, 0]], 
            [[0, 3, 2, 1, 5, 4], [5, 3, 2, 4, 0, 1]], 
            [[3, 0, 2, 4, 5, 1], [5, 1, 2, 4, 3, 0]], 
            [[2, 4, 0, 3, 1, 5], [3, 0, 4, 2, 1, 5]], 
            [[2, 4, 3, 1, 0, 5], [4, 2, 1, 3, 0, 5]], 
            [[1, 0, 2, 5, 4, 3], [2, 3, 1, 5, 4, 0]], 
            [[3, 0, 1, 5, 4, 2], [3, 5, 2, 0, 4, 1]], 
            [[4, 3, 2, 1, 0, 5], [5, 3, 2, 0, 1, 4]], 
            [[1, 0, 2, 4, 3, 5], [1, 3, 2, 5, 0, 4]], 
            [[1, 3, 4, 2, 0, 5], [4, 2, 1, 3, 0, 5]], 
            [[1, 2, 3, 4, 0, 5], [4, 3, 2, 1, 0, 5]], 
            [[1, 0, 2, 3, 5, 4], [2, 4, 1, 3, 5, 0]], 
            [[2, 1, 0, 3, 5, 4], [2, 5, 4, 3, 1, 0]], 
            [[3, 4, 2, 0, 1, 5], [3, 5, 2, 1, 0, 4]], 
            [[0, 5, 2, 4, 3, 1], [1, 3, 2, 4, 5, 0]], 
            [[1, 0, 2, 5, 4, 3], [3, 2, 0, 5, 4, 1]], 
            [[1, 2, 3, 5, 4, 0], [2, 1, 0, 5, 4, 3]], 
            [[0, 5, 4, 3, 2, 1], [5, 0, 4, 3, 1, 2]], 
            [[0, 5, 4, 3, 2, 1], [1, 2, 4, 3, 5, 0]]
        ]
    },
    "S3_transposition_three_cycle": {
        "size": 6,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [0, 1, 2, 4, 5, 3]],
            [[0, 1, 2, 3, 5, 4], [0, 1, 4, 3, 5, 2]],
            [[0, 4, 2, 3, 5, 1], [0, 5, 2, 3, 4, 1]],
            [[4, 1, 2, 3, 5, 0], [5, 1, 2, 3, 4, 0]],
            [[0, 1, 2, 4, 3, 5], [0, 1, 3, 4, 2, 5]],
            [[0, 1, 2, 4, 3, 5], [0, 3, 2, 4, 1, 5]],
            [[0, 1, 2, 4, 3, 5], [3, 1, 2, 4, 0, 5]],
            [[0, 1, 2, 5, 4, 3], [0, 1, 3, 5, 4, 2]],
            [[0, 3, 2, 5, 4, 1], [0, 5, 2, 3, 4, 1]],
            [[3, 1, 2, 5, 4, 0], [5, 1, 2, 3, 4, 0]],
            [[0, 1, 3, 2, 4, 5], [0, 2, 3, 1, 4, 5]],
            [[0, 1, 3, 2, 4, 5], [2, 1, 3, 0, 4, 5]],
            [[0, 1, 4, 3, 2, 5], [0, 2, 4, 3, 1, 5]],
            [[2, 1, 0, 3, 4, 5], [2, 1, 4, 3, 0, 5]],
            [[0, 2, 1, 3, 4, 5], [0, 2, 5, 3, 4, 1]],
            [[2, 1, 0, 3, 4, 5], [2, 1, 5, 3, 4, 0]],
            [[0, 2, 1, 3, 4, 5], [1, 2, 0, 3, 4, 5]],
            [[0, 3, 2, 1, 4, 5], [1, 3, 2, 0, 4, 5]],
            [[1, 0, 2, 3, 4, 5], [1, 4, 2, 3, 0, 5]],
            [[1, 0, 2, 3, 4, 5], [1, 5, 2, 3, 4, 0]]
        ]
    },
    "S3_triple_transposition_double_three_cycle": {
        "size": 6,
        "generators": [
            [[3, 5, 1, 4, 0, 2], [5, 3, 4, 1, 2, 0]],
            [[3, 5, 4, 0, 2, 1], [5, 3, 0, 4, 1, 2]],
            [[3, 4, 1, 5, 2, 0], [4, 3, 5, 1, 0, 2]],
            [[3, 4, 5, 0, 1, 2], [4, 3, 0, 5, 2, 1]],
            [[1, 0, 4, 5, 2, 3], [3, 2, 5, 4, 0, 1]],
            [[1, 0, 4, 5, 2, 3], [2, 3, 5, 4, 1, 0]],
            [[3, 4, 5, 0, 1, 2], [5, 2, 3, 1, 0, 4]],
            [[2, 5, 3, 0, 1, 4], [4, 3, 5, 1, 0, 2]],
            [[3, 2, 4, 5, 1, 0], [4, 5, 3, 2, 0, 1]],
            [[2, 3, 4, 5, 0, 1], [5, 4, 3, 2, 1, 0]],
            [[3, 5, 4, 0, 2, 1], [4, 2, 3, 1, 5, 0]],
            [[2, 4, 3, 0, 5, 1], [5, 3, 4, 1, 2, 0]],
            [[1, 2, 0, 4, 5, 3], [4, 3, 5, 1, 0, 2]],
            [[2, 0, 1, 4, 5, 3], [3, 4, 5, 0, 1, 2]],
            [[1, 3, 4, 0, 5, 2], [4, 2, 1, 5, 0, 3]],
            [[2, 4, 0, 5, 1, 3], [3, 0, 4, 1, 5, 2]],
            [[4, 0, 5, 2, 1, 3], [5, 3, 4, 1, 2, 0]],
            [[1, 4, 5, 2, 0, 3], [3, 5, 4, 0, 2, 1]],
            [[1, 5, 3, 4, 2, 0], [4, 3, 5, 1, 0, 2]],
            [[3, 4, 5, 0, 1, 2], [5, 0, 3, 4, 2, 1]]
        ]
    },
    "C6_six_cycle": {
        "size": 6,
        "generators": [
            [[5, 4, 1, 0, 3, 2]], [[2, 3, 4, 5, 1, 0]], 
            [[4, 5, 0, 1, 3, 2]], [[3, 2, 4, 5, 0, 1]], 
            [[5, 3, 1, 4, 0, 2]], [[2, 4, 3, 1, 5, 0]], 
            [[3, 5, 0, 4, 1, 2]], [[4, 2, 3, 0, 5, 1]], 
            [[4, 3, 1, 5, 2, 0]], [[2, 5, 3, 1, 0, 4]], 
            [[3, 4, 0, 5, 2, 1]], [[5, 2, 3, 0, 1, 4]], 
            [[5, 3, 4, 2, 0, 1]], [[3, 4, 5, 1, 2, 0]], 
            [[4, 5, 3, 0, 1, 2]], [[5, 4, 3, 1, 0, 2]], 
            [[4, 3, 5, 0, 2, 1]], [[3, 5, 4, 2, 1, 0]], 
            [[1, 2, 3, 4, 5, 0]], [[1, 2, 3, 5, 0, 4]], 
            [[1, 2, 4, 0, 5, 3]], [[1, 2, 4, 5, 3, 0]], 
            [[3, 0, 1, 4, 5, 2]], [[4, 0, 1, 5, 3, 2]], 
            [[1, 3, 0, 4, 5, 2]], [[2, 0, 4, 1, 5, 3]], 
            [[5, 2, 3, 4, 0, 1]], [[2, 4, 1, 5, 3, 0]], 
            [[2, 4, 3, 5, 0, 1]], [[1, 3, 4, 2, 5, 0]], 
            [[1, 3, 4, 5, 0, 2]], [[4, 2, 3, 5, 1, 0]], 
            [[4, 2, 0, 5, 3, 1]], [[2, 5, 3, 4, 1, 0]], 
            [[1, 3, 5, 2, 0, 4]], [[1, 3, 5, 4, 2, 0]], 
            [[2, 0, 3, 5, 1, 4]], [[1, 4, 0, 5, 3, 2]], 
            [[3, 0, 5, 2, 1, 4]], [[5, 2, 4, 0, 3, 1]], 
            [[2, 3, 1, 4, 5, 0]], [[2, 3, 4, 0, 5, 1]], 
            [[1, 4, 3, 5, 2, 0]], [[1, 4, 5, 0, 2, 3]], 
            [[3, 2, 4, 1, 5, 0]], [[3, 2, 0, 4, 5, 1]], 
            [[2, 5, 4, 1, 3, 0]], [[5, 0, 3, 4, 1, 2]], 
            [[2, 0, 3, 4, 5, 1]], [[2, 0, 4, 5, 3, 1]], 
            [[3, 0, 4, 2, 5, 1]], [[1, 5, 3, 4, 0, 2]], 
            [[4, 2, 5, 0, 1, 3]], [[2, 3, 1, 5, 0, 4]], 
            [[3, 4, 0, 1, 5, 2]], [[3, 0, 5, 4, 2, 1]], 
            [[1, 5, 4, 2, 0, 3]], [[4, 3, 1, 0, 5, 2]], 
            [[3, 2, 0, 5, 1, 4]], [[2, 4, 5, 1, 0, 3]]
        ]
    },
    "S3_three_cycle_double_transposition": {
        "size": 6,
        "generators": [
            [[0, 1, 2, 4, 5, 3], [0, 2, 1, 4, 3, 5]], 
            [[0, 1, 2, 4, 5, 3], [1, 0, 2, 4, 3, 5]], 
            [[0, 1, 2, 4, 5, 3], [2, 1, 0, 4, 3, 5]], 
            [[0, 2, 1, 3, 5, 4], [0, 2, 3, 1, 4, 5]], 
            [[0, 1, 3, 2, 5, 4], [0, 4, 2, 3, 5, 1]], 
            [[2, 1, 0, 3, 5, 4], [2, 1, 3, 0, 4, 5]], 
            [[0, 1, 3, 2, 5, 4], [4, 1, 2, 3, 5, 0]], 
            [[0, 1, 3, 4, 2, 5], [0, 5, 3, 2, 4, 1]], 
            [[0, 1, 3, 4, 2, 5], [1, 0, 3, 2, 4, 5]], 
            [[0, 1, 3, 4, 2, 5], [5, 1, 3, 2, 4, 0]], 
            [[0, 1, 3, 5, 4, 2], [0, 4, 3, 2, 1, 5]], 
            [[0, 1, 3, 5, 4, 2], [1, 0, 5, 3, 4, 2]], 
            [[0, 1, 3, 5, 4, 2], [4, 1, 3, 2, 0, 5]], 
            [[0, 1, 4, 3, 5, 2], [0, 3, 4, 1, 2, 5]], 
            [[0, 1, 4, 3, 5, 2], [1, 0, 4, 3, 2, 5]], 
            [[0, 1, 4, 3, 5, 2], [3, 1, 4, 0, 2, 5]], 
            [[0, 2, 1, 5, 4, 3], [0, 2, 4, 3, 1, 5]], 
            [[0, 1, 4, 5, 2, 3], [0, 3, 2, 5, 4, 1]], 
            [[2, 1, 4, 3, 0, 5], [4, 1, 2, 5, 0, 3]], 
            [[0, 1, 4, 5, 2, 3], [3, 1, 2, 5, 4, 0]], 
            [[0, 2, 5, 3, 4, 1], [0, 5, 2, 4, 3, 1]], 
            [[0, 3, 2, 4, 1, 5], [0, 3, 5, 1, 4, 2]], 
            [[2, 1, 5, 3, 4, 0], [5, 1, 2, 4, 3, 0]], 
            [[3, 1, 2, 4, 0, 5], [3, 1, 5, 0, 4, 2]], 
            [[1, 0, 2, 3, 5, 4], [1, 2, 0, 3, 4, 5]], 
            [[0, 2, 1, 3, 5, 4], [4, 1, 2, 3, 5, 0]], 
            [[1, 0, 2, 4, 3, 5], [1, 2, 0, 3, 4, 5]], 
            [[3, 1, 2, 4, 0, 5], [3, 2, 1, 0, 4, 5]], 
            [[1, 0, 2, 5, 4, 3], [1, 2, 0, 3, 4, 5]], 
            [[3, 1, 2, 5, 4, 0], [5, 2, 1, 3, 4, 0]], 
            [[0, 2, 3, 1, 4, 5], [4, 2, 1, 3, 0, 5]], 
            [[0, 2, 3, 1, 4, 5], [5, 2, 1, 3, 4, 0]], 
            [[0, 2, 4, 3, 1, 5], [3, 2, 1, 0, 4, 5]], 
            [[0, 2, 4, 3, 1, 5], [5, 4, 2, 3, 1, 0]], 
            [[0, 2, 5, 3, 4, 1], [3, 5, 2, 0, 4, 1]], 
            [[0, 2, 5, 3, 4, 1], [4, 5, 2, 3, 0, 1]], 
            [[1, 0, 2, 3, 5, 4], [1, 3, 2, 0, 4, 5]], 
            [[0, 3, 2, 1, 5, 4], [4, 1, 2, 3, 5, 0]], 
            [[0, 3, 2, 4, 1, 5], [2, 3, 0, 1, 4, 5]], 
            [[0, 3, 2, 4, 1, 5], [5, 3, 2, 1, 4, 0]], 
            [[0, 3, 2, 5, 4, 1], [2, 5, 0, 3, 4, 1]], 
            [[0, 3, 2, 5, 4, 1], [4, 1, 2, 5, 0, 3]], 
            [[1, 0, 4, 3, 2, 5], [1, 3, 2, 0, 4, 5]], 
            [[2, 1, 4, 3, 0, 5], [2, 3, 0, 1, 4, 5]], 
            [[1, 0, 5, 3, 4, 2], [1, 3, 2, 0, 4, 5]], 
            [[2, 1, 5, 3, 4, 0], [5, 3, 2, 1, 4, 0]], 
            [[0, 4, 2, 3, 5, 1], [2, 1, 0, 3, 5, 4]], 
            [[0, 4, 2, 3, 5, 1], [3, 1, 2, 0, 5, 4]], 
            [[1, 4, 2, 3, 0, 5], [4, 1, 2, 5, 0, 3]], 
            [[0, 4, 2, 5, 1, 3], [3, 1, 2, 5, 4, 0]], 
            [[1, 0, 3, 2, 4, 5], [1, 4, 2, 3, 0, 5]], 
            [[2, 1, 3, 0, 4, 5], [2, 4, 0, 3, 1, 5]], 
            [[1, 4, 2, 3, 0, 5], [4, 1, 5, 3, 0, 2]], 
            [[2, 1, 5, 3, 4, 0], [5, 4, 2, 3, 1, 0]], 
            [[1, 5, 2, 3, 4, 0], [5, 1, 2, 4, 3, 0]], 
            [[0, 5, 2, 4, 3, 1], [3, 1, 2, 4, 0, 5]], 
            [[1, 5, 2, 3, 4, 0], [5, 1, 3, 2, 4, 0]], 
            [[2, 1, 3, 0, 4, 5], [2, 5, 0, 3, 4, 1]], 
            [[1, 5, 2, 3, 4, 0], [5, 1, 4, 3, 2, 0]], 
            [[2, 1, 4, 3, 0, 5], [4, 5, 2, 3, 0, 1]]
        ]
    },
    "S3_double_transposition_double_three_cycle": {
        "size": 6,
        "generators": [
            [[0, 1, 3, 2, 5, 4], [2, 4, 3, 0, 5, 1]],
            [[2, 5, 0, 3, 4, 1], [3, 4, 0, 2, 5, 1]],
            [[0, 1, 3, 2, 5, 4], [4, 2, 3, 1, 5, 0]], 
            [[4, 3, 1, 2, 5, 0], [5, 2, 1, 3, 4, 0]], 
            [[0, 1, 4, 5, 2, 3], [2, 3, 4, 5, 0, 1]], 
            [[2, 5, 0, 3, 4, 1], [2, 5, 4, 1, 0, 3]], 
            [[0, 1, 4, 5, 2, 3], [3, 2, 4, 5, 1, 0]], 
            [[5, 2, 1, 3, 4, 0], [5, 2, 4, 0, 1, 3]], 
            [[2, 3, 0, 1, 4, 5], [2, 3, 5, 4, 1, 0]], 
            [[0, 1, 5, 4, 3, 2], [5, 3, 0, 4, 1, 2]], 
            [[3, 2, 1, 0, 4, 5], [3, 2, 5, 4, 0, 1]], 
            [[0, 1, 5, 4, 3, 2], [3, 5, 1, 4, 0, 2]], 
            [[0, 2, 1, 3, 5, 4], [1, 2, 0, 4, 5, 3]], 
            [[0, 2, 1, 3, 5, 4], [2, 0, 1, 4, 5, 3]], 
            [[4, 1, 3, 2, 0, 5], [5, 2, 3, 1, 0, 4]], 
            [[4, 2, 3, 1, 5, 0], [5, 1, 3, 2, 4, 0]], 
            [[1, 0, 2, 3, 5, 4], [2, 0, 1, 4, 5, 3]], 
            [[0, 2, 1, 4, 3, 5], [1, 2, 0, 4, 5, 3]], 
            [[4, 2, 5, 0, 3, 1], [4, 5, 2, 3, 0, 1]], 
            [[0, 2, 1, 4, 3, 5], [3, 2, 5, 4, 0, 1]], 
            [[1, 0, 2, 3, 5, 4], [1, 2, 0, 4, 5, 3]], 
            [[2, 0, 1, 4, 5, 3], [2, 1, 0, 3, 5, 4]], 
            [[3, 4, 1, 5, 2, 0], [5, 4, 2, 3, 1, 0]], 
            [[3, 2, 4, 5, 1, 0], [5, 1, 4, 3, 2, 0]], 
            [[0, 3, 2, 1, 5, 4], [1, 3, 4, 0, 5, 2]], 
            [[1, 0, 5, 3, 4, 2], [1, 3, 5, 0, 2, 4]], 
            [[4, 2, 3, 1, 5, 0], [5, 2, 1, 3, 4, 0]], 
            [[0, 3, 2, 1, 5, 4], [4, 3, 1, 2, 5, 0]], 
            [[0, 3, 4, 1, 2, 5], [1, 3, 5, 0, 2, 4]], 
            [[0, 3, 4, 1, 2, 5], [1, 3, 4, 0, 5, 2]], 
            [[4, 3, 0, 5, 2, 1], [4, 5, 2, 3, 0, 1]], 
            [[2, 3, 4, 5, 0, 1], [4, 1, 2, 5, 0, 3]], 
            [[3, 0, 5, 1, 2, 4], [3, 1, 4, 0, 2, 5]], 
            [[3, 0, 4, 1, 5, 2], [3, 1, 2, 0, 5, 4]], 
            [[2, 4, 5, 1, 3, 0], [5, 4, 2, 3, 1, 0]], 
            [[2, 3, 5, 4, 1, 0], [2, 4, 0, 3, 1, 5]], 
            [[1, 0, 3, 2, 4, 5], [1, 4, 3, 5, 0, 2]], 
            [[1, 0, 5, 3, 4, 2], [1, 4, 5, 2, 0, 3]], 
            [[0, 4, 2, 5, 1, 3], [5, 4, 1, 0, 2, 3]], 
            [[3, 2, 1, 0, 4, 5], [5, 2, 4, 0, 1, 3]], 
            [[1, 0, 2, 5, 4, 3], [4, 0, 3, 5, 1, 2]], 
            [[1, 0, 5, 3, 4, 2], [4, 0, 5, 2, 1, 3]], 
            [[0, 4, 3, 2, 1, 5], [2, 5, 3, 0, 1, 4]], 
            [[2, 4, 3, 0, 5, 1], [2, 5, 0, 3, 4, 1]], 
            [[1, 0, 2, 5, 4, 3], [1, 4, 3, 5, 0, 2]], 
            [[1, 0, 3, 2, 4, 5], [4, 0, 3, 5, 1, 2]], 
            [[2, 1, 0, 4, 3, 5], [2, 3, 5, 4, 1, 0]], 
            [[2, 3, 0, 1, 4, 5], [2, 4, 5, 1, 3, 0]], 
            [[1, 0, 3, 2, 4, 5], [1, 5, 3, 4, 2, 0]], 
            [[0, 5, 2, 4, 3, 1], [5, 0, 3, 4, 2, 1]], 
            [[3, 2, 5, 4, 0, 1], [4, 2, 1, 3, 0, 5]], 
            [[3, 2, 1, 0, 4, 5], [4, 2, 5, 0, 3, 1]], 
            [[1, 0, 2, 4, 3, 5], [5, 0, 3, 4, 2, 1]], 
            [[1, 5, 3, 4, 2, 0], [5, 1, 2, 4, 3, 0]], 
            [[0, 5, 3, 2, 4, 1], [2, 4, 3, 0, 5, 1]], 
            [[3, 1, 2, 0, 5, 4], [3, 4, 0, 2, 5, 1]], 
            [[1, 0, 2, 4, 3, 5], [1, 5, 3, 4, 2, 0]], 
            [[1, 0, 3, 2, 4, 5], [5, 0, 3, 4, 2, 1]], 
            [[0, 5, 4, 3, 2, 1], [2, 3, 4, 5, 0, 1]], 
            [[2, 3, 0, 1, 4, 5], [4, 3, 0, 5, 2, 1]]
        ]
    },
    "C6_three_cycle_transposition": {
        "size": 6,
        "generators": [
            [[0, 2, 3, 1, 5, 4]],
            [[1, 2, 0, 3, 5, 4]],
            [[1, 3, 2, 0, 5, 4]], 
            [[2, 1, 3, 0, 5, 4]], 
            [[0, 2, 5, 4, 3, 1]], 
            [[1, 2, 0, 4, 3, 5]], 
            [[1, 5, 2, 4, 3, 0]], 
            [[2, 1, 5, 4, 3, 0]], 
            [[0, 2, 1, 4, 5, 3]], 
            [[1, 0, 2, 4, 5, 3]], 
            [[2, 1, 0, 4, 5, 3]], 
            [[0, 2, 4, 5, 1, 3]], 
            [[1, 2, 0, 5, 4, 3]], 
            [[1, 4, 2, 5, 0, 3]], 
            [[2, 1, 4, 5, 0, 3]], 
            [[0, 4, 3, 2, 5, 1]], 
            [[1, 4, 3, 2, 0, 5]], 
            [[1, 5, 3, 2, 4, 0]], 
            [[4, 1, 3, 2, 5, 0]], 
            [[0, 5, 3, 4, 2, 1]], 
            [[1, 0, 3, 4, 2, 5]], 
            [[5, 1, 3, 4, 2, 0]], 
            [[0, 4, 3, 5, 1, 2]], 
            [[1, 0, 3, 5, 4, 2]], 
            [[4, 1, 3, 5, 0, 2]], 
            [[0, 3, 4, 5, 2, 1]], 
            [[1, 3, 4, 0, 2, 5]], 
            [[1, 5, 4, 3, 2, 0]], 
            [[3, 1, 4, 5, 2, 0]], 
            [[0, 3, 4, 1, 5, 2]], 
            [[1, 0, 4, 3, 5, 2]], 
            [[3, 1, 4, 0, 5, 2]], 
            [[0, 3, 5, 4, 1, 2]], 
            [[1, 3, 5, 0, 4, 2]], 
            [[1, 4, 5, 3, 0, 2]], 
            [[3, 1, 5, 4, 0, 2]], 
            [[3, 2, 1, 4, 0, 5]], 
            [[3, 2, 1, 5, 4, 0]], 
            [[4, 2, 1, 3, 5, 0]], 
            [[4, 2, 3, 1, 0, 5]], 
            [[5, 2, 3, 1, 4, 0]], 
            [[3, 2, 4, 0, 1, 5]], 
            [[5, 2, 4, 3, 1, 0]], 
            [[3, 2, 5, 0, 4, 1]], 
            [[4, 2, 5, 3, 0, 1]], 
            [[2, 3, 4, 1, 0, 5]], 
            [[2, 3, 5, 1, 4, 0]], 
            [[4, 3, 2, 1, 5, 0]], 
            [[2, 3, 0, 4, 1, 5]], 
            [[5, 3, 2, 4, 1, 0]], 
            [[2, 3, 0, 5, 4, 1]], 
            [[4, 3, 2, 5, 0, 1]], 
            [[2, 4, 3, 0, 1, 5]], 
            [[2, 4, 5, 3, 1, 0]], 
            [[3, 4, 2, 5, 1, 0]], 
            [[2, 4, 0, 3, 5, 1]], 
            [[3, 4, 2, 0, 5, 1]], 
            [[2, 5, 3, 0, 4, 1]], 
            [[2, 5, 4, 3, 0, 1]], 
            [[3, 5, 2, 4, 0, 1]]
        ]
    },
    "C2xC2xC2_single_double_transposition": {
        "size": 8,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [0, 1, 3, 2, 5, 4], [1, 0, 2, 3, 5, 4]],
            [[0, 2, 1, 3, 4, 5], [0, 2, 1, 3, 5, 4], [3, 2, 1, 0, 4, 5]], 
            [[2, 1, 0, 3, 4, 5], [2, 1, 0, 3, 5, 4], [2, 3, 0, 1, 4, 5]], 
            [[0, 1, 2, 4, 3, 5], [0, 1, 5, 4, 3, 2], [1, 0, 2, 4, 3, 5]], 
            [[5, 1, 2, 3, 4, 0], [5, 1, 2, 4, 3, 0], [5, 2, 1, 3, 4, 0]], 
            [[0, 5, 2, 3, 4, 1], [0, 5, 2, 4, 3, 1], [2, 5, 0, 3, 4, 1]], 
            [[0, 1, 4, 3, 2, 5], [0, 1, 4, 5, 2, 3], [1, 0, 4, 3, 2, 5]], 
            [[0, 1, 2, 5, 4, 3], [0, 2, 1, 5, 4, 3], [4, 1, 2, 5, 0, 3]], 
            [[0, 4, 2, 3, 1, 5], [0, 4, 2, 5, 1, 3], [2, 4, 0, 3, 1, 5]], 
            [[0, 1, 3, 2, 4, 5], [0, 4, 3, 2, 1, 5], [5, 1, 3, 2, 4, 0]], 
            [[0, 1, 3, 2, 4, 5], [0, 5, 3, 2, 4, 1], [4, 1, 3, 2, 0, 5]], 
            [[0, 3, 2, 1, 4, 5], [0, 3, 4, 1, 2, 5], [5, 3, 2, 1, 4, 0]], 
            [[3, 1, 2, 0, 4, 5], [3, 1, 4, 0, 2, 5], [3, 5, 2, 0, 4, 1]], 
            [[0, 1, 5, 3, 4, 2], [0, 3, 5, 1, 4, 2], [4, 1, 5, 3, 0, 2]], 
            [[0, 1, 5, 3, 4, 2], [0, 4, 5, 3, 1, 2], [3, 1, 5, 0, 4, 2]]
        ]
    },
    "C2xC2xC2_single_double_triple_transposition": {
        "size": 8,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [1, 0, 3, 2, 5, 4], [3, 2, 1, 0, 4, 5]],
            [[0, 1, 2, 4, 3, 5], [1, 0, 5, 3, 4, 2], [5, 2, 1, 4, 3, 0]], 
            [[0, 1, 2, 5, 4, 3], [1, 0, 4, 3, 2, 5], [4, 2, 1, 5, 0, 3]], 
            [[0, 1, 3, 2, 4, 5], [1, 0, 3, 2, 5, 4], [5, 4, 2, 3, 1, 0]], 
            [[0, 1, 5, 4, 3, 2], [1, 0, 2, 3, 4, 5], [1, 0, 3, 2, 5, 4]], 
            [[0, 1, 4, 3, 2, 5], [1, 0, 4, 5, 2, 3], [5, 3, 2, 1, 4, 0]], 
            [[0, 1, 5, 3, 4, 2], [1, 0, 2, 4, 3, 5], [4, 3, 5, 1, 0, 2]], 
            [[0, 2, 1, 3, 4, 5], [3, 1, 2, 0, 5, 4], [5, 2, 1, 4, 3, 0]], 
            [[0, 2, 1, 3, 5, 4], [3, 1, 2, 0, 4, 5], [3, 5, 4, 0, 2, 1]], 
            [[0, 4, 3, 2, 1, 5], [5, 1, 2, 3, 4, 0], [5, 2, 1, 4, 3, 0]], 
            [[0, 2, 1, 5, 4, 3], [4, 1, 2, 3, 0, 5], [4, 5, 3, 2, 0, 1]], 
            [[0, 3, 2, 1, 4, 5], [2, 1, 0, 3, 5, 4], [5, 3, 4, 1, 2, 0]], 
            [[0, 5, 2, 4, 3, 1], [2, 1, 0, 3, 4, 5], [2, 3, 0, 1, 5, 4]], 
            [[0, 4, 2, 3, 1, 5], [2, 4, 0, 5, 1, 3], [5, 1, 3, 2, 4, 0]], 
            [[0, 5, 2, 3, 4, 1], [2, 5, 0, 4, 3, 1], [4, 1, 3, 2, 0, 5]]
        ]
    },
    "D4_four_cycle_transposition_transposition": {
        "size": 8,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [1, 0, 4, 5, 3, 2]], 
            [[0, 2, 1, 3, 4, 5], [3, 5, 4, 0, 1, 2]], 
            [[0, 1, 2, 3, 5, 4], [2, 4, 0, 5, 3, 1]], 
            [[1, 0, 2, 3, 4, 5], [5, 4, 3, 2, 0, 1]], 
            [[2, 1, 0, 3, 4, 5], [5, 3, 4, 1, 0, 2]], 
            [[0, 1, 2, 3, 5, 4], [4, 2, 1, 5, 3, 0]], 
            [[0, 1, 2, 4, 3, 5], [1, 0, 4, 2, 5, 3]], 
            [[0, 1, 2, 4, 3, 5], [5, 3, 4, 2, 1, 0]], 
            [[0, 5, 2, 3, 4, 1], [2, 3, 0, 5, 1, 4]], 
            [[0, 1, 2, 4, 3, 5], [3, 4, 5, 1, 0, 2]], 
            [[0, 1, 2, 4, 3, 5], [3, 5, 4, 2, 0, 1]], 
            [[3, 2, 1, 5, 0, 4], [5, 1, 2, 3, 4, 0]], 
            [[0, 1, 2, 5, 4, 3], [1, 0, 3, 4, 5, 2]], 
            [[0, 2, 1, 3, 4, 5], [4, 5, 3, 1, 0, 2]], 
            [[0, 1, 2, 5, 4, 3], [2, 3, 0, 4, 5, 1]], 
            [[1, 0, 2, 3, 4, 5], [5, 3, 4, 0, 2, 1]], 
            [[2, 1, 0, 3, 4, 5], [5, 4, 3, 0, 1, 2]], 
            [[3, 2, 1, 4, 5, 0], [4, 1, 2, 3, 0, 5]], 
            [[0, 1, 3, 2, 4, 5], [5, 3, 1, 4, 2, 0]], 
            [[0, 1, 3, 2, 4, 5], [4, 3, 1, 5, 0, 2]], 
            [[0, 1, 3, 2, 4, 5], [2, 3, 1, 0, 5, 4]], 
            [[0, 1, 3, 2, 4, 5], [3, 4, 0, 5, 1, 2]], 
            [[0, 1, 3, 2, 4, 5], [3, 5, 0, 4, 2, 1]], 
            [[0, 1, 4, 3, 2, 5], [5, 2, 3, 4, 1, 0]], 
            [[0, 5, 2, 3, 4, 1], [3, 2, 5, 0, 1, 4]], 
            [[0, 1, 4, 3, 2, 5], [2, 4, 1, 5, 0, 3]], 
            [[2, 3, 5, 1, 0, 4], [5, 1, 2, 3, 4, 0]], 
            [[0, 1, 4, 3, 2, 5], [2, 5, 3, 4, 0, 1]], 
            [[0, 3, 2, 1, 4, 5], [4, 2, 3, 5, 0, 1]], 
            [[0, 4, 2, 3, 1, 5], [3, 2, 4, 0, 5, 1]], 
            [[1, 0, 2, 3, 4, 5], [5, 2, 0, 4, 3, 1]], 
            [[2, 3, 4, 1, 5, 0], [4, 1, 2, 3, 0, 5]], 
            [[2, 4, 3, 5, 1, 0], [3, 1, 2, 0, 4, 5]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 3, 1, 5, 4]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 4, 5, 1, 3]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 5, 4, 3, 1]], 
            [[0, 3, 2, 1, 4, 5], [1, 2, 3, 0, 5, 4]], 
            [[0, 3, 2, 1, 4, 5], [3, 0, 4, 5, 2, 1]], 
            [[0, 3, 2, 1, 4, 5], [3, 0, 5, 4, 1, 2]], 
            [[1, 5, 3, 2, 0, 4], [5, 1, 2, 3, 4, 0]], 
            [[1, 2, 4, 5, 0, 3], [2, 1, 0, 3, 4, 5]], 
            [[1, 3, 5, 4, 0, 2], [3, 1, 2, 0, 4, 5]], 
            [[0, 5, 2, 3, 4, 1], [5, 0, 3, 2, 1, 4]], 
            [[1, 3, 4, 5, 2, 0], [3, 1, 2, 0, 4, 5]], 
            [[1, 2, 5, 4, 3, 0], [2, 1, 0, 3, 4, 5]]
        ]
    },
    "C4xC2": {
        "size": 8,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [3, 2, 0, 1, 5, 4]],
            [[0, 1, 2, 3, 5, 4], [3, 0, 1, 2, 5, 4]], 
            [[0, 1, 2, 3, 5, 4], [1, 3, 0, 2, 5, 4]], 
            [[0, 1, 2, 4, 3, 5], [2, 5, 1, 4, 3, 0]], 
            [[0, 1, 2, 4, 3, 5], [5, 0, 1, 4, 3, 2]], 
            [[0, 1, 2, 4, 3, 5], [1, 5, 0, 4, 3, 2]], 
            [[0, 1, 2, 5, 4, 3], [4, 2, 0, 5, 1, 3]], 
            [[0, 1, 2, 5, 4, 3], [4, 0, 1, 5, 2, 3]], 
            [[0, 1, 2, 5, 4, 3], [1, 4, 0, 5, 2, 3]], 
            [[0, 1, 3, 2, 4, 5], [4, 5, 3, 2, 1, 0]], 
            [[0, 1, 3, 2, 4, 5], [5, 0, 3, 2, 1, 4]], 
            [[0, 1, 3, 2, 4, 5], [4, 0, 3, 2, 5, 1]], 
            [[1, 0, 2, 3, 4, 5], [1, 0, 5, 4, 2, 3]], 
            [[1, 0, 2, 3, 4, 5], [1, 0, 5, 2, 3, 4]], 
            [[1, 0, 2, 3, 4, 5], [1, 0, 4, 2, 5, 3]], 
            [[0, 1, 4, 3, 2, 5], [3, 5, 4, 1, 2, 0]], 
            [[0, 1, 4, 3, 2, 5], [5, 0, 4, 1, 2, 3]], 
            [[0, 1, 4, 3, 2, 5], [1, 5, 4, 0, 2, 3]], 
            [[0, 1, 5, 3, 4, 2], [4, 3, 5, 0, 1, 2]], 
            [[0, 1, 5, 3, 4, 2], [1, 3, 5, 4, 0, 2]], 
            [[0, 1, 5, 3, 4, 2], [3, 0, 5, 4, 1, 2]], 
            [[0, 2, 1, 3, 4, 5], [5, 2, 1, 4, 0, 3]], 
            [[0, 2, 1, 3, 4, 5], [5, 2, 1, 0, 3, 4]], 
            [[0, 2, 1, 3, 4, 5], [4, 2, 1, 0, 5, 3]], 
            [[3, 1, 2, 0, 4, 5], [3, 4, 5, 0, 2, 1]], 
            [[5, 1, 2, 3, 4, 0], [5, 4, 3, 1, 2, 0]], 
            [[4, 1, 2, 3, 0, 5], [4, 5, 3, 1, 0, 2]], 
            [[5, 1, 2, 3, 4, 0], [5, 4, 1, 2, 3, 0]], 
            [[4, 1, 2, 3, 0, 5], [4, 5, 1, 2, 0, 3]], 
            [[5, 1, 2, 3, 4, 0], [5, 3, 1, 4, 2, 0]], 
            [[3, 1, 2, 0, 4, 5], [3, 2, 4, 0, 5, 1]], 
            [[4, 1, 2, 3, 0, 5], [4, 2, 5, 1, 0, 3]], 
            [[3, 1, 2, 0, 4, 5], [3, 4, 1, 0, 5, 2]], 
            [[0, 3, 2, 1, 4, 5], [4, 3, 5, 1, 2, 0]], 
            [[0, 3, 2, 1, 4, 5], [5, 3, 0, 1, 2, 4]], 
            [[0, 3, 2, 1, 4, 5], [4, 3, 0, 1, 5, 2]], 
            [[2, 1, 0, 3, 4, 5], [2, 5, 0, 4, 1, 3]], 
            [[2, 1, 0, 3, 4, 5], [2, 5, 0, 1, 3, 4]], 
            [[2, 1, 0, 3, 4, 5], [2, 4, 0, 1, 5, 3]], 
            [[0, 4, 2, 3, 1, 5], [5, 4, 3, 0, 1, 2]], 
            [[0, 4, 2, 3, 1, 5], [5, 4, 0, 2, 1, 3]], 
            [[0, 4, 2, 3, 1, 5], [2, 4, 5, 0, 1, 3]], 
            [[0, 5, 2, 3, 4, 1], [4, 5, 3, 0, 2, 1]], 
            [[0, 5, 2, 3, 4, 1], [4, 5, 0, 2, 3, 1]], 
            [[0, 5, 2, 3, 4, 1], [3, 5, 0, 4, 2, 1]]
        ]
    },
    "D4_four_cycle_transposition": {
        "size": 8,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [0, 1, 4, 5, 3, 2]], 
            [[0, 2, 1, 3, 4, 5], [0, 5, 4, 3, 1, 2]], 
            [[0, 1, 2, 3, 5, 4], [0, 4, 2, 5, 3, 1]], 
            [[1, 0, 2, 3, 4, 5], [5, 4, 2, 3, 0, 1]], 
            [[2, 1, 0, 3, 4, 5], [5, 1, 4, 3, 0, 2]], 
            [[0, 1, 2, 3, 5, 4], [4, 1, 2, 5, 3, 0]], 
            [[0, 1, 2, 4, 3, 5], [0, 1, 4, 2, 5, 3]], 
            [[0, 1, 2, 4, 3, 5], [0, 3, 4, 2, 1, 5]], 
            [[0, 3, 2, 5, 1, 4], [0, 5, 2, 3, 4, 1]], 
            [[0, 1, 2, 4, 3, 5], [3, 4, 2, 1, 0, 5]], 
            [[0, 1, 2, 4, 3, 5], [3, 1, 4, 2, 0, 5]], 
            [[3, 1, 2, 5, 0, 4], [5, 1, 2, 3, 4, 0]], 
            [[0, 1, 2, 5, 4, 3], [0, 1, 3, 4, 5, 2]], 
            [[0, 2, 1, 3, 4, 5], [0, 5, 3, 1, 4, 2]], 
            [[0, 1, 2, 5, 4, 3], [0, 3, 2, 4, 5, 1]], 
            [[1, 0, 2, 3, 4, 5], [5, 3, 2, 0, 4, 1]], 
            [[2, 1, 0, 3, 4, 5], [5, 1, 3, 0, 4, 2]], 
            [[3, 1, 2, 4, 5, 0], [4, 1, 2, 3, 0, 5]], 
            [[0, 1, 3, 2, 4, 5], [0, 3, 1, 4, 2, 5]], 
            [[0, 1, 3, 2, 4, 5], [0, 3, 1, 5, 4, 2]], 
            [[0, 1, 3, 2, 4, 5], [2, 3, 1, 0, 4, 5]], 
            [[0, 1, 3, 2, 4, 5], [3, 1, 0, 4, 2, 5]], 
            [[0, 1, 3, 2, 4, 5], [3, 1, 0, 5, 4, 2]], 
            [[0, 2, 5, 3, 1, 4], [0, 5, 2, 3, 4, 1]], 
            [[0, 1, 4, 3, 2, 5], [0, 2, 3, 4, 1, 5]], 
            [[0, 1, 4, 3, 2, 5], [2, 4, 1, 3, 0, 5]], 
            [[2, 1, 5, 3, 0, 4], [5, 1, 2, 3, 4, 0]], 
            [[0, 1, 4, 3, 2, 5], [2, 1, 3, 4, 0, 5]], 
            [[0, 2, 4, 3, 5, 1], [0, 4, 2, 3, 1, 5]], 
            [[0, 2, 3, 5, 4, 1], [0, 3, 2, 1, 4, 5]], 
            [[1, 0, 2, 3, 4, 5], [5, 2, 0, 3, 4, 1]], 
            [[2, 1, 4, 3, 5, 0], [4, 1, 2, 3, 0, 5]], 
            [[2, 1, 3, 5, 4, 0], [3, 1, 2, 0, 4, 5]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 3, 1, 4, 5]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 4, 3, 1, 5]], 
            [[0, 2, 1, 3, 4, 5], [2, 0, 5, 3, 4, 1]], 
            [[0, 3, 2, 1, 4, 5], [3, 0, 2, 4, 1, 5]], 
            [[0, 3, 2, 1, 4, 5], [3, 0, 2, 5, 4, 1]], 
            [[0, 3, 2, 1, 4, 5], [1, 2, 3, 0, 4, 5]], 
            [[1, 5, 2, 3, 0, 4], [5, 1, 2, 3, 4, 0]],
            [[1, 3, 2, 4, 0, 5], [3, 1, 2, 0, 4, 5]], 
            [[1, 2, 4, 3, 0, 5], [2, 1, 0, 3, 4, 5]], 
            [[0, 5, 2, 3, 4, 1], [5, 0, 2, 3, 1, 4]],
            [[1, 3, 2, 5, 4, 0], [3, 1, 2, 0, 4, 5]], 
            [[1, 2, 5, 3, 4, 0], [2, 1, 0, 3, 4, 5]]
        ]
    },
    "D4_double_transposition": {
        "size": 8,
        "generators": [
            [[0, 1, 4, 5, 2, 3], [1, 0, 2, 3, 5, 4]],
            [[0, 1, 4, 5, 2, 3], [1, 0, 2, 4, 3, 5]], 
            [[0, 1, 3, 2, 5, 4], [1, 0, 2, 5, 4, 3]], 
            [[0, 1, 3, 2, 5, 4], [2, 3, 0, 1, 4, 5]], 
            [[1, 0, 3, 2, 4, 5], [4, 5, 2, 3, 0, 1]], 
            [[0, 1, 4, 5, 2, 3], [2, 4, 0, 3, 1, 5]], 
            [[1, 0, 4, 3, 2, 5], [3, 5, 2, 0, 4, 1]], 
            [[1, 0, 2, 4, 3, 5], [2, 5, 0, 3, 4, 1]], 
            [[0, 1, 5, 4, 3, 2], [3, 4, 2, 0, 1, 5]], 
            [[0, 4, 5, 3, 1, 2], [3, 2, 1, 0, 4, 5]], 
            [[0, 4, 5, 3, 1, 2], [3, 5, 2, 0, 4, 1]], 
            [[0, 5, 4, 3, 2, 1], [3, 4, 2, 0, 1, 5]], 
            [[0, 2, 1, 3, 5, 4], [2, 3, 0, 1, 4, 5]], 
            [[0, 2, 1, 3, 5, 4], [4, 1, 2, 5, 0, 3]], 
            [[0, 3, 4, 1, 2, 5], [5, 1, 2, 4, 3, 0]], 
            [[0, 3, 4, 1, 2, 5], [5, 1, 3, 2, 4, 0]], 
            [[0, 2, 1, 4, 3, 5], [5, 1, 4, 3, 2, 0]], 
            [[0, 2, 1, 4, 3, 5], [2, 5, 0, 3, 4, 1]], 
            [[4, 1, 2, 5, 0, 3], [5, 2, 1, 3, 4, 0]], 
            [[0, 3, 5, 1, 4, 2], [4, 2, 1, 3, 0, 5]], 
            [[0, 3, 5, 1, 4, 2], [4, 1, 3, 2, 0, 5]], 
            [[0, 5, 3, 2, 4, 1], [4, 3, 2, 1, 0, 5]], 
            [[0, 2, 1, 5, 4, 3], [2, 4, 0, 3, 1, 5]], 
            [[4, 2, 1, 3, 0, 5], [5, 1, 2, 4, 3, 0]], 
            [[0, 4, 2, 5, 1, 3], [2, 1, 0, 3, 5, 4]], 
            [[0, 4, 2, 5, 1, 3], [2, 5, 0, 3, 4, 1]], 
            [[0, 3, 2, 1, 5, 4], [2, 1, 0, 5, 4, 3]], 
            [[0, 3, 2, 1, 5, 4], [1, 0, 3, 2, 4, 5]], 
            [[2, 3, 0, 1, 4, 5], [4, 1, 5, 3, 0, 2]], 
            [[0, 3, 4, 1, 2, 5], [3, 5, 2, 0, 4, 1]], 
            [[4, 1, 5, 3, 0, 2], [5, 3, 2, 1, 4, 0]], 
            [[0, 3, 5, 1, 4, 2], [3, 4, 2, 0, 1, 5]], 
            [[4, 3, 2, 1, 0, 5], [5, 1, 4, 3, 2, 0]], 
            [[2, 1, 0, 5, 4, 3], [4, 2, 1, 3, 0, 5]], 
            [[2, 4, 0, 3, 1, 5], [3, 1, 5, 0, 4, 2]], 
            [[4, 5, 2, 3, 0, 1], [5, 1, 3, 2, 4, 0]], 
            [[0, 4, 3, 2, 1, 5], [3, 1, 5, 0, 4, 2]], 
            [[3, 1, 5, 0, 4, 2], [4, 3, 2, 1, 0, 5]], 
            [[3, 4, 2, 0, 1, 5], [5, 1, 3, 2, 4, 0]], 
            [[2, 1, 0, 4, 3, 5], [5, 2, 1, 3, 4, 0]], 
            [[0, 5, 2, 4, 3, 1], [3, 1, 4, 0, 2, 5]], 
            [[0, 5, 3, 2, 4, 1], [5, 4, 2, 3, 1, 0]], 
            [[0, 5, 3, 2, 4, 1], [3, 1, 4, 0, 2, 5]], 
            [[3, 1, 4, 0, 2, 5], [5, 3, 2, 1, 4, 0]], 
            [[0, 5, 4, 3, 2, 1], [2, 1, 0, 4, 3, 5]]
        ]
    },
    "D4_double_transposition_four_cycle": {
        "size": 8,
        "generators": [
            [[0, 1, 4, 5, 3, 2], [1, 0, 2, 3, 5, 4]],
            [[0, 1, 3, 2, 5, 4], [2, 3, 1, 0, 4, 5]], 
            [[1, 0, 3, 2, 4, 5], [5, 4, 2, 3, 0, 1]], 
            [[0, 1, 3, 4, 5, 2], [1, 0, 2, 5, 4, 3]], 
            [[0, 1, 4, 2, 5, 3], [1, 0, 2, 4, 3, 5]], 
            [[0, 1, 4, 5, 2, 3], [2, 4, 1, 3, 0, 5]], 
            [[1, 0, 4, 3, 2, 5], [5, 3, 2, 0, 4, 1]], 
            [[1, 0, 2, 4, 3, 5], [5, 2, 0, 3, 4, 1]], 
            [[0, 1, 5, 4, 3, 2], [3, 4, 2, 1, 0, 5]], 
            [[0, 5, 4, 3, 1, 2], [3, 2, 1, 0, 4, 5]], 
            [[0, 2, 1, 3, 5, 4], [2, 0, 3, 1, 4, 5]], 
            [[0, 2, 1, 3, 5, 4], [4, 1, 2, 5, 3, 0]], 
            [[0, 3, 4, 2, 1, 5], [5, 1, 2, 4, 3, 0]], 
            [[0, 2, 1, 4, 3, 5], [2, 0, 5, 3, 4, 1]], 
            [[3, 1, 2, 5, 0, 4], [5, 2, 1, 3, 4, 0]], 
            [[0, 5, 3, 1, 4, 2], [4, 2, 1, 3, 0, 5]], 
            [[0, 2, 1, 5, 4, 3], [2, 0, 4, 3, 1, 5]], 
            [[3, 1, 2, 4, 5, 0], [4, 2, 1, 3, 0, 5]], 
            [[0, 2, 3, 4, 1, 5], [5, 1, 4, 3, 2, 0]], 
            [[0, 2, 3, 5, 4, 1], [4, 3, 2, 1, 0, 5]], 
            [[0, 3, 1, 4, 2, 5], [5, 1, 3, 2, 4, 0]], 
            [[0, 2, 4, 3, 5, 1], [3, 4, 2, 0, 1, 5]], 
            [[0, 3, 1, 5, 4, 2], [4, 1, 3, 2, 0, 5]], 
            [[0, 2, 5, 3, 1, 4], [3, 5, 2, 0, 4, 1]], 
            [[0, 4, 2, 5, 3, 1], [2, 1, 0, 3, 5, 4]], 
            [[0, 3, 2, 1, 5, 4], [1, 2, 3, 0, 4, 5]], 
            [[2, 3, 0, 1, 4, 5], [5, 1, 4, 3, 0, 2]], 
            [[0, 3, 2, 4, 5, 1], [2, 1, 0, 5, 4, 3]], 
            [[0, 3, 2, 5, 1, 4], [2, 5, 0, 3, 4, 1]], 
            [[0, 3, 4, 1, 2, 5], [3, 0, 2, 5, 4, 1]], 
            [[2, 1, 5, 3, 0, 4], [5, 3, 2, 1, 4, 0]], 
            [[0, 3, 5, 1, 4, 2], [3, 0, 2, 4, 1, 5]], 
            [[2, 1, 4, 3, 5, 0], [4, 3, 2, 1, 0, 5]], 
            [[1, 2, 4, 3, 0, 5], [2, 1, 0, 5, 4, 3]], 
            [[2, 4, 0, 3, 1, 5], [5, 1, 3, 0, 4, 2]], 
            [[1, 5, 2, 3, 0, 4], [5, 1, 3, 2, 4, 0]], 
            [[0, 4, 3, 2, 1, 5], [3, 1, 0, 5, 4, 2]], 
            [[1, 3, 2, 4, 0, 5], [3, 1, 5, 0, 4, 2]], 
            [[2, 1, 3, 5, 4, 0], [3, 4, 2, 0, 1, 5]], 
            [[1, 2, 5, 3, 4, 0], [2, 1, 0, 4, 3, 5]], 
            [[0, 5, 2, 4, 3, 1], [3, 1, 4, 2, 0, 5]], 
            [[0, 5, 3, 2, 4, 1], [5, 0, 2, 3, 1, 4]], 
            [[0, 5, 3, 2, 4, 1], [3, 1, 0, 4, 2, 5]], 
            [[1, 3, 2, 5, 4, 0], [3, 1, 4, 0, 2, 5]], 
            [[0, 5, 4, 3, 2, 1], [2, 1, 3, 4, 0, 5]]
        ]
    },
    "C3xC3": {
        "size": 9,
        "generators": [
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            [[0, 1, 5, 3, 4, 2], [0, 3, 2, 1, 4, 5], [3, 0, 2, 4, 1, 5]], 
            [[0, 3, 2, 1, 4, 5], [2, 1, 4, 3, 5, 0], [4, 1, 2, 3, 0, 5]], 
            [[0, 1, 5, 3, 4, 2], [1, 3, 2, 4, 0, 5], [3, 1, 2, 0, 4, 5]], 
            [[0, 4, 2, 3, 1, 5], [2, 1, 3, 5, 4, 0], [3, 1, 2, 0, 4, 5]]
        ]
    }, 
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        "size": 18,
        "generators": [
            [[0, 2, 1, 3, 5, 4], [2, 0, 1, 3, 4, 5], [2, 0, 1, 4, 5, 3]],
            [[5, 1, 2, 3, 0, 4], [5, 1, 3, 2, 4, 0], [5, 2, 3, 1, 0, 4]],
            [[0, 5, 2, 3, 1, 4], [0, 5, 3, 2, 4, 1], [2, 5, 3, 0, 1, 4]],
            [[1, 0, 2, 4, 3, 5], [5, 0, 2, 3, 4, 1], [5, 0, 3, 4, 2, 1]],
            [[0, 1, 5, 2, 4, 3], [1, 0, 2, 5, 4, 3], [1, 4, 5, 2, 0, 3]],
            [[0, 3, 2, 1, 5, 4], [3, 0, 2, 1, 4, 5], [3, 0, 4, 1, 5, 2]],
            [[0, 4, 1, 3, 2, 5], [3, 4, 1, 5, 2, 0], [5, 1, 4, 3, 2, 0]],
            [[0, 5, 4, 3, 2, 1], [4, 1, 0, 3, 2, 5], [4, 3, 0, 5, 2, 1]],
            [[0, 2, 1, 4, 3, 5], [0, 5, 1, 3, 4, 2], [3, 5, 1, 4, 0, 2]],
            [[2, 1, 0, 4, 3, 5], [5, 1, 0, 3, 4, 2], [5, 3, 0, 4, 1, 2]]
        ]
    },
    "C3xS3_triple_transposition_three_cycle": {
        "size": 18,
        "generators": [
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            [[1, 2, 0, 3, 4, 5], [4, 3, 5, 1, 0, 2]],
            [[3, 4, 5, 0, 1, 2], [5, 0, 2, 3, 4, 1]], 
            [[1, 5, 2, 3, 4, 0], [4, 3, 5, 1, 0, 2]], 
            [[0, 1, 5, 2, 4, 3], [3, 5, 4, 0, 2, 1]], 
            [[0, 1, 5, 2, 4, 3], [5, 3, 4, 1, 2, 0]], 
            [[2, 4, 0, 5, 1, 3], [3, 0, 2, 1, 4, 5]], 
            [[1, 3, 2, 0, 4, 5], [4, 2, 1, 5, 0, 3]], 
            [[3, 4, 5, 0, 1, 2], [5, 1, 2, 3, 0, 4]], 
            [[0, 2, 3, 1, 4, 5], [3, 5, 4, 0, 2, 1]], 
            [[0, 4, 1, 3, 2, 5], [4, 3, 5, 1, 0, 2]], 
            [[0, 2, 4, 3, 1, 5], [4, 5, 3, 2, 0, 1]], 
            [[0, 5, 1, 3, 4, 2], [5, 3, 4, 1, 2, 0]], 
            [[1, 0, 4, 5, 2, 3], [3, 1, 2, 4, 0, 5]], 
            [[3, 5, 4, 0, 2, 1], [5, 1, 0, 3, 4, 2]], 
            [[0, 3, 2, 4, 1, 5], [1, 0, 4, 5, 2, 3]], 
            [[3, 4, 5, 0, 1, 2], [4, 1, 0, 3, 2, 5]], 
            [[2, 1, 4, 3, 0, 5], [5, 4, 3, 2, 1, 0]], 
            [[0, 5, 2, 3, 1, 4], [4, 3, 5, 1, 0, 2]], 
            [[2, 1, 3, 0, 4, 5], [5, 3, 4, 1, 2, 0]]
        ]
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    "C3xS3_transposition_three_cycle_double_three_cycle": {
        "size": 18,
        "generators": [
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            [[0, 1, 2, 3, 5, 4], [3, 0, 2, 1, 4, 5], [3, 0, 4, 1, 5, 2]],
            [[0, 3, 1, 2, 4, 5], [4, 3, 1, 2, 5, 0], [5, 1, 2, 3, 4, 0]],
            [[0, 5, 2, 3, 4, 1], [3, 1, 0, 2, 4, 5], [3, 4, 0, 2, 5, 1]],
            [[0, 1, 2, 4, 3, 5], [5, 0, 2, 3, 4, 1], [5, 0, 3, 4, 2, 1]],
            [[0, 1, 2, 4, 3, 5], [0, 5, 1, 3, 4, 2], [3, 5, 1, 4, 0, 2]],
            [[0, 1, 2, 4, 3, 5], [5, 1, 0, 3, 4, 2], [5, 3, 0, 4, 1, 2]],
            [[0, 1, 2, 5, 3, 4], [0, 2, 1, 3, 4, 5], [1, 2, 0, 5, 3, 4]],
            [[0, 1, 2, 5, 4, 3], [4, 0, 2, 3, 1, 5], [4, 0, 3, 5, 1, 2]],
            [[0, 4, 1, 3, 2, 5], [3, 4, 1, 5, 2, 0], [5, 1, 2, 3, 4, 0]],
            [[0, 5, 2, 3, 4, 1], [4, 1, 0, 3, 2, 5], [4, 3, 0, 5, 2, 1]],
            [[0, 1, 3, 2, 4, 5], [5, 1, 2, 3, 0, 4], [5, 2, 3, 1, 0, 4]],
            [[0, 1, 3, 2, 4, 5], [0, 5, 2, 3, 1, 4], [2, 5, 3, 0, 1, 4]],
            [[0, 1, 4, 2, 3, 5], [1, 0, 2, 3, 4, 5], [1, 5, 4, 2, 3, 0]],
            [[0, 1, 5, 2, 4, 3], [1, 0, 2, 3, 4, 5], [1, 4, 5, 2, 0, 3]],
            [[0, 1, 4, 3, 2, 5], [5, 1, 2, 0, 4, 3], [5, 2, 4, 0, 1, 3]],
            [[0, 5, 2, 1, 4, 3], [2, 1, 0, 3, 4, 5], [2, 5, 4, 1, 0, 3]],
            [[0, 1, 5, 3, 2, 4], [0, 3, 2, 1, 4, 5], [1, 3, 5, 0, 2, 4]],
            [[0, 2, 1, 3, 4, 5], [4, 1, 2, 0, 3, 5], [4, 2, 5, 0, 3, 1]],
            [[0, 4, 2, 1, 3, 5], [2, 1, 0, 3, 4, 5], [2, 4, 5, 1, 3, 0]]
        ]
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        "size": 20, 
        "generators": [
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            [[0, 3, 1, 4, 5, 2], [0, 4, 2, 1, 5, 3]], 
            [[5, 1, 2, 0, 3, 4], [5, 1, 3, 4, 0, 2]], 
            [[3, 1, 0, 4, 5, 2], [4, 1, 2, 0, 5, 3]], 
            [[0, 3, 4, 2, 5, 1], [0, 4, 5, 3, 2, 1]], 
            [[0, 1, 5, 2, 3, 4], [0, 2, 3, 5, 1, 4]], 
            [[3, 1, 4, 2, 5, 0], [4, 1, 5, 3, 2, 0]], 
            [[2, 1, 3, 5, 0, 4], [4, 1, 3, 0, 2, 5]], 
            [[0, 2, 4, 5, 3, 1], [0, 2, 5, 1, 4, 3]], 
            [[0, 1, 4, 2, 5, 3], [0, 2, 3, 4, 5, 1]],
            [[2, 1, 4, 5, 3, 0], [2, 1, 5, 0, 4, 3]],
            [[2, 1, 3, 4, 5, 0], [4, 1, 2, 5, 3, 0]],
            [[2, 0, 5, 3, 1, 4], [2, 4, 1, 3, 0, 5]],
            [[2, 0, 4, 3, 5, 1], [2, 5, 1, 3, 4, 0]],
            [[0, 4, 3, 1, 2, 5], [4, 2, 3, 0, 1, 5]],
            [[2, 0, 3, 4, 1, 5], [3, 1, 0, 4, 2, 5]],
            [[0, 5, 3, 1, 4, 2], [5, 2, 3, 0, 4, 1]],
            [[1, 2, 3, 0, 4, 5], [2, 0, 3, 5, 4, 1]],
            [[0, 2, 3, 4, 1, 5], [2, 3, 1, 4, 0, 5]],
            [[0, 4, 1, 2, 3, 5], [1, 2, 4, 0, 3, 5]],
            [[1, 3, 0, 2, 4, 5], [2, 3, 1, 5, 4, 0]],
            [[1, 2, 5, 0, 4, 3], [3, 2, 0, 1, 4, 5]],
            [[0, 2, 4, 1, 3, 5], [1, 3, 4, 2, 0, 5]],
            [[0, 3, 1, 4, 2, 5], [1, 2, 3, 4, 0, 5]],
            [[2, 4, 1, 3, 5, 0], [5, 0, 1, 3, 4, 2]],
            [[1, 2, 5, 3, 0, 4], [4, 2, 0, 3, 1, 5]],
            [[1, 3, 5, 2, 4, 0], [3, 0, 1, 2, 4, 5]],
            [[1, 2, 3, 5, 4, 0], [2, 0, 3, 1, 4, 5]],
            [[1, 4, 5, 3, 2, 0], [1, 5, 0, 3, 4, 2]],
            [[1, 2, 4, 3, 5, 0], [5, 2, 0, 3, 4, 1]],
            [[3, 0, 2, 5, 1, 4], [3, 4, 2, 1, 0, 5]],
            [[3, 0, 2, 4, 5, 1], [5, 0, 2, 3, 1, 4]],
            [[3, 4, 2, 1, 5, 0], [4, 5, 2, 3, 1, 0]],
            [[1, 3, 2, 5, 0, 4], [4, 3, 2, 0, 1, 5]],
            [[1, 4, 2, 5, 3, 0], [1, 5, 2, 0, 4, 3]],
            [[1, 3, 2, 4, 5, 0], [1, 5, 2, 3, 0, 4]]
        ]
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        "size": 24,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [2, 3, 4, 5, 1, 0]],
            [[0, 2, 1, 3, 4, 5], [4, 3, 0, 5, 1, 2]],
            [[2, 1, 0, 3, 4, 5], [3, 4, 1, 5, 0, 2]],
            [[0, 1, 2, 4, 3, 5], [3, 4, 0, 5, 2, 1]],
            [[1, 3, 4, 5, 0, 2], [5, 1, 2, 3, 4, 0]],
            [[0, 5, 2, 3, 4, 1], [3, 0, 4, 5, 1, 2]],
            [[0, 1, 4, 3, 2, 5], [2, 4, 5, 0, 3, 1]],
            [[0, 1, 2, 5, 4, 3], [2, 3, 5, 0, 1, 4]],
            [[0, 4, 2, 3, 1, 5], [1, 5, 4, 0, 3, 2]],
            [[0, 1, 3, 2, 4, 5], [3, 5, 4, 1, 0, 2]],
            [[0, 1, 3, 2, 4, 5], [5, 3, 4, 0, 1, 2]],
            [[0, 3, 2, 1, 4, 5], [3, 4, 5, 2, 0, 1]],
            [[3, 1, 2, 0, 4, 5], [4, 3, 5, 2, 1, 0]],
            [[0, 1, 5, 3, 4, 2], [3, 2, 0, 5, 1, 4]],
            [[0, 1, 5, 3, 4, 2], [2, 3, 1, 5, 0, 4]]
        ]
    }, 
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        "size": 24,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [1, 3, 2, 0, 4, 5], [2, 0, 1, 3, 4, 5]],
            [[0, 1, 2, 4, 3, 5], [2, 1, 5, 3, 4, 0], [5, 0, 2, 3, 4, 1]],
            [[0, 1, 3, 5, 4, 2], [0, 1, 4, 2, 3, 5], [1, 0, 2, 3, 4, 5]], 
            [[0, 1, 2, 5, 3, 4], [0, 2, 1, 3, 4, 5], [3, 1, 2, 4, 0, 5]], 
            [[0, 3, 2, 5, 4, 1], [0, 4, 2, 1, 3, 5], [2, 1, 0, 3, 4, 5]],
            [[0, 1, 2, 5, 4, 3], [2, 1, 4, 3, 0, 5], [4, 0, 2, 3, 1, 5]],
            [[0, 1, 3, 2, 4, 5], [0, 4, 2, 3, 5, 1], [5, 1, 2, 3, 0, 4]],
            [[0, 2, 4, 3, 1, 5], [0, 3, 1, 2, 4, 5], [5, 1, 2, 3, 4, 0]],
            [[0, 5, 2, 3, 4, 1], [2, 1, 4, 3, 0, 5], [3, 1, 0, 2, 4, 5]],
            [[0, 3, 2, 5, 4, 1], [0, 5, 1, 3, 4, 2], [4, 1, 2, 3, 0, 5]],
            [[0, 1, 3, 5, 4, 2], [0, 4, 2, 3, 1, 5], [5, 1, 2, 0, 4, 3]],
            [[0, 1, 4, 3, 2, 5], [0, 3, 2, 5, 4, 1], [5, 1, 2, 0, 4, 3]],
            [[0, 1, 5, 3, 2, 4], [0, 2, 4, 3, 1, 5], [3, 1, 2, 0, 4, 5]],
            [[0, 1, 5, 3, 2, 4], [0, 3, 2, 1, 4, 5], [2, 1, 4, 3, 0, 5]],
            [[0, 1, 5, 3, 4, 2], [3, 1, 2, 4, 0, 5], [4, 0, 2, 3, 1, 5]]
        ]
    },
    "S4_four_cycle_transposition_double_transposition": {
        "size": 24,
        "generators": [
            [[1, 0, 3, 2, 4, 5], [1, 0, 3, 4, 5, 2]],
            [[0, 2, 1, 4, 3, 5], [3, 2, 1, 4, 5, 0]],
            [[2, 3, 0, 1, 4, 5], [2, 3, 0, 4, 5, 1]],
            [[1, 0, 2, 3, 5, 4], [1, 2, 3, 0, 5, 4]],
            [[0, 1, 3, 2, 5, 4], [1, 4, 3, 2, 5, 0]],
            [[5, 2, 1, 3, 4, 0], [5, 2, 3, 4, 1, 0]],
            [[2, 5, 0, 3, 4, 1], [2, 5, 3, 4, 0, 1]],
            [[4, 2, 3, 5, 0, 1], [4, 5, 2, 3, 0, 1]],
            [[0, 4, 2, 5, 1, 3], [2, 4, 3, 5, 1, 0]],
            [[3, 1, 4, 0, 2, 5], [3, 2, 4, 0, 5, 1]],
            [[0, 3, 4, 1, 2, 5], [2, 3, 4, 1, 5, 0]],
            [[1, 2, 4, 5, 0, 3], [4, 1, 2, 5, 0, 3]],
            [[0, 1, 4, 5, 2, 3], [1, 3, 4, 5, 2, 0]],
            [[1, 2, 5, 4, 3, 0], [5, 1, 2, 4, 3, 0]],
            [[1, 3, 5, 4, 0, 2], [4, 1, 5, 3, 0, 2]]
        ]
    },
    "S4_double_three_cycle_double_transposition": {
        "size": 24,
        "generators": [
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            [[3, 4, 0, 2, 5, 1], [3, 4, 2, 0, 1, 5], [4, 3, 0, 5, 2, 1]],
            [[2, 4, 0, 3, 1, 5], [2, 4, 3, 0, 5, 1], [4, 2, 5, 0, 3, 1]],
            [[2, 1, 0, 5, 4, 3], [2, 3, 4, 5, 0, 1], [5, 3, 1, 2, 0, 4]],
            [[2, 3, 5, 4, 1, 0], [4, 0, 5, 2, 1, 3], [5, 3, 2, 1, 4, 0]],
            [[0, 4, 5, 3, 1, 2], [4, 0, 3, 5, 1, 2], [4, 3, 0, 5, 2, 1]],
            [[2, 5, 4, 1, 0, 3], [3, 1, 5, 0, 4, 2], [3, 5, 1, 4, 0, 2]],
            [[1, 4, 5, 2, 0, 3], [3, 2, 5, 4, 0, 1], [3, 5, 2, 0, 4, 1]],
            [[1, 3, 4, 0, 5, 2], [2, 3, 4, 5, 0, 1], [4, 1, 2, 5, 0, 3]],
            [[0, 3, 5, 1, 4, 2], [5, 2, 4, 0, 1, 3], [5, 3, 0, 4, 1, 2]],
            [[0, 2, 1, 5, 4, 3], [3, 2, 4, 5, 1, 0], [3, 5, 0, 2, 1, 4]],
            [[0, 3, 5, 1, 4, 2], [2, 3, 5, 4, 1, 0], [2, 5, 3, 0, 1, 4]],
            [[1, 4, 3, 5, 0, 2], [3, 4, 1, 5, 2, 0], [4, 1, 5, 3, 0, 2]],
            [[1, 0, 4, 3, 2, 5], [1, 3, 4, 0, 5, 2], [4, 5, 1, 0, 3, 2]],
            [[0, 4, 2, 5, 1, 3], [3, 0, 4, 1, 5, 2], [3, 2, 4, 5, 1, 0]]
        ]
    },
    "S4_exceptional": {
        "size": 24,
        "generators": [
            [[2, 3, 5, 4, 1, 0], [3, 2, 0, 1, 4, 5]],
            [[3, 5, 2, 1, 4, 0], [4, 2, 5, 0, 3, 1]],
            [[2, 5, 1, 3, 4, 0], [4, 3, 0, 5, 2, 1]],
            [[4, 3, 0, 5, 2, 1], [5, 1, 2, 4, 0, 3]],
            [[0, 4, 3, 1, 2, 5], [1, 3, 4, 0, 5, 2]],
            [[1, 4, 0, 3, 2, 5], [2, 5, 3, 0, 1, 4]],
            [[1, 4, 5, 2, 0, 3], [4, 1, 0, 3, 5, 2]],
            [[1, 4, 2, 0, 3, 5], [3, 5, 0, 2, 1, 4]],
            [[2, 5, 4, 1, 0, 3], [4, 0, 2, 3, 5, 1]],
            [[4, 0, 2, 1, 3, 5], [5, 3, 1, 2, 0, 4]],
            [[1, 4, 2, 3, 5, 0], [5, 2, 4, 0, 1, 3]],
            [[0, 4, 1, 3, 5, 2], [4, 0, 5, 2, 1, 3]],
            [[0, 5, 2, 4, 1, 3], [3, 4, 1, 5, 2, 0]],
            [[3, 1, 5, 2, 4, 0], [4, 5, 1, 0, 3, 2]],
            [[3, 0, 4, 1, 5, 2], [4, 1, 3, 0, 2, 5]]
        ]
    },
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        "size": 24,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [0, 1, 3, 4, 5, 2]], 
            [[0, 1, 2, 3, 5, 4], [0, 3, 2, 4, 5, 1]],
            [[3, 1, 2, 4, 5, 0], [5, 1, 2, 3, 4, 0]], 
            [[0, 2, 4, 3, 5, 1], [0, 5, 2, 3, 4, 1]], 
            [[2, 1, 4, 3, 5, 0], [5, 1, 2, 3, 4, 0]], 
            [[1, 0, 2, 3, 4, 5], [1, 4, 2, 3, 5, 0]], 
            [[0, 1, 2, 4, 3, 5], [0, 2, 3, 4, 1, 5]], 
            [[0, 1, 2, 4, 3, 5], [2, 1, 3, 4, 0, 5]], 
            [[0, 3, 2, 1, 4, 5], [1, 3, 2, 4, 0, 5]], 
            [[0, 1, 3, 2, 4, 5], [0, 2, 3, 5, 4, 1]], 
            [[2, 1, 0, 3, 4, 5], [2, 1, 3, 5, 4, 0]], 
            [[1, 0, 2, 3, 4, 5], [1, 3, 2, 5, 4, 0]], 
            [[0, 1, 3, 2, 4, 5], [1, 2, 3, 0, 4, 5]], 
            [[0, 2, 1, 3, 4, 5], [1, 2, 4, 3, 0, 5]], 
            [[0, 2, 1, 3, 4, 5], [1, 2, 5, 3, 4, 0]]
        ]
    },
    "S3xS3_transpositions_double_three_cycle": {
        "size": 36,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [1, 0, 2, 3, 4, 5], [2, 0, 1, 4, 5, 3]],
            [[0, 1, 2, 3, 5, 4], [0, 1, 3, 2, 4, 5], [5, 2, 3, 1, 0, 4]],
            [[0, 1, 2, 3, 5, 4], [0, 1, 3, 2, 4, 5], [2, 5, 3, 0, 1, 4]],
            [[0, 1, 2, 3, 5, 4], [1, 0, 2, 3, 4, 5], [3, 0, 4, 1, 5, 2]],
            [[0, 1, 2, 4, 3, 5], [5, 0, 3, 4, 2, 1], [5, 1, 2, 3, 4, 0]],
            [[0, 1, 2, 4, 3, 5], [0, 5, 2, 3, 4, 1], [3, 5, 1, 4, 0, 2]],
            [[0, 1, 2, 4, 3, 5], [5, 1, 2, 3, 4, 0], [5, 3, 0, 4, 1, 2]],
            [[0, 1, 3, 2, 4, 5], [1, 0, 2, 3, 4, 5], [1, 4, 5, 2, 0, 3]],
            [[0, 2, 1, 3, 4, 5], [3, 4, 1, 5, 2, 0], [5, 1, 2, 3, 4, 0]],
            [[0, 5, 2, 3, 4, 1], [2, 1, 0, 3, 4, 5], [4, 3, 0, 5, 2, 1]]
        ]
    },
    "S3xS3_six_cycles_three_cycle": {
        "size": 36,
        "generators": [
            [[2, 0, 1, 3, 4, 5], [3, 4, 5, 1, 2, 0], [4, 3, 5, 0, 2, 1]],
            [[3, 4, 0, 5, 2, 1], [3, 5, 0, 4, 1, 2], [5, 1, 2, 3, 0, 4]],
            [[0, 5, 2, 3, 1, 4], [4, 3, 1, 5, 2, 0], [5, 3, 1, 4, 0, 2]],
            [[2, 4, 5, 1, 0, 3], [3, 4, 0, 1, 5, 2], [5, 0, 2, 3, 4, 1]],
            [[0, 1, 5, 2, 4, 3], [5, 2, 4, 0, 3, 1], [5, 3, 0, 4, 2, 1]],
            [[2, 4, 1, 5, 3, 0], [3, 0, 2, 1, 4, 5], [4, 2, 0, 5, 3, 1]],
            [[0, 4, 1, 3, 2, 5], [1, 3, 5, 2, 0, 4], [2, 5, 3, 1, 0, 4]],
            [[3, 0, 5, 2, 1, 4], [4, 1, 0, 3, 2, 5], [5, 2, 3, 0, 1, 4]],
            [[0, 5, 1, 3, 4, 2], [1, 3, 4, 2, 5, 0], [5, 0, 4, 2, 1, 3]],
            [[1, 5, 4, 2, 0, 3], [3, 0, 4, 2, 5, 1], [5, 1, 0, 3, 4, 2]]
        ]
    },
    "(C3xC3):C4": {
        "size": 36,
        "generators": [
            [[2, 0, 1, 3, 4, 5], [5, 3, 4, 1, 0, 2]],
            [[2, 5, 4, 0, 3, 1], [5, 1, 2, 3, 0, 4]], 
            [[0, 5, 2, 3, 1, 4], [5, 2, 4, 1, 3, 0]], 
            [[2, 3, 0, 5, 1, 4], [5, 0, 2, 3, 4, 1]], 
            [[0, 1, 5, 2, 4, 3], [2, 5, 1, 4, 3, 0]], 
            [[3, 0, 2, 1, 4, 5], [5, 2, 1, 4, 0, 3]], 
            [[0, 4, 1, 3, 2, 5], [4, 0, 3, 2, 5, 1]], 
            [[1, 4, 3, 2, 5, 0], [4, 1, 0, 3, 2, 5]], 
            [[0, 5, 1, 3, 4, 2], [1, 0, 3, 5, 2, 4]], 
            [[1, 0, 3, 5, 2, 4], [5, 1, 0, 3, 4, 2]]
        ]
    },
    "C2xS4": {
        "size": 48,
        "generators": [
            [[0, 1, 2, 3, 5, 4], [2, 3, 4, 5, 1, 0], [3, 2, 0, 1, 4, 5]],
            [[0, 2, 1, 3, 4, 5], [4, 3, 0, 5, 1, 2], [5, 1, 2, 4, 0, 3]], 
            [[0, 5, 2, 4, 1, 3], [2, 1, 0, 3, 4, 5], [3, 4, 1, 5, 0, 2]], 
            [[0, 1, 2, 4, 3, 5], [2, 5, 1, 3, 4, 0], [3, 4, 0, 5, 2, 1]], 
            [[0, 4, 3, 1, 2, 5], [1, 3, 4, 5, 0, 2], [5, 1, 2, 3, 4, 0]], 
            [[0, 5, 2, 3, 4, 1], [3, 0, 4, 5, 1, 2], [4, 1, 3, 0, 2, 5]], 
            [[0, 1, 4, 3, 2, 5], [2, 4, 5, 0, 3, 1], [3, 5, 2, 1, 4, 0]], 
            [[0, 1, 2, 5, 4, 3], [1, 4, 0, 3, 2, 5], [2, 3, 5, 0, 1, 4]],
            [[0, 4, 2, 3, 1, 5], [1, 5, 4, 0, 3, 2], [3, 1, 5, 2, 4, 0]],
            [[0, 1, 3, 2, 4, 5], [3, 5, 4, 1, 0, 2], [4, 0, 2, 3, 5, 1]],
            [[0, 1, 3, 2, 4, 5], [1, 4, 2, 3, 5, 0], [5, 3, 4, 0, 1, 2]],
            [[0, 4, 1, 3, 5, 2], [3, 1, 2, 0, 4, 5], [4, 3, 5, 2, 1, 0]],
            [[0, 3, 2, 1, 4, 5], [3, 4, 5, 2, 0, 1], [4, 1, 0, 3, 5, 2]],
            [[0, 1, 5, 3, 4, 2], [2, 3, 1, 5, 0, 4], [4, 0, 2, 1, 3, 5]],
            [[0, 1, 5, 3, 4, 2], [1, 4, 2, 0, 3, 5], [3, 2, 0, 5, 1, 4]]
        ]
    },
    "C2xS4_exceptional": {
        "size": 48,
        "generators": [
            [[0, 1, 2, 5, 3, 4], [0, 1, 2, 5, 4, 3], [0, 1, 4, 2, 3, 5], [1, 0, 2, 3, 4, 5]],
            [[0, 1, 2, 5, 3, 4], [0, 2, 1, 3, 4, 5], [4, 1, 2, 3, 0, 5], [5, 1, 2, 3, 0, 4]],
            [[0, 1, 2, 5, 3, 4], [0, 1, 2, 5, 4, 3], [0, 4, 2, 1, 3, 5], [2, 1, 0, 3, 4, 5]],
            [[0, 1, 2, 3, 5, 4], [0, 3, 1, 2, 4, 5], [0, 3, 2, 1, 4, 5], [2, 0, 1, 3, 4, 5]],
            [[0, 1, 3, 2, 4, 5], [0, 5, 2, 3, 4, 1], [5, 0, 2, 3, 4, 1], [5, 1, 2, 3, 0, 4]],
            [[0, 1, 5, 3, 2, 4], [0, 4, 2, 3, 1, 5], [0, 5, 2, 3, 1, 4], [3, 1, 2, 0, 4, 5]],
            [[0, 1, 5, 3, 2, 4], [0, 3, 2, 1, 4, 5], [4, 1, 2, 3, 0, 5], [5, 1, 2, 3, 0, 4]],
            [[0, 1, 4, 2, 3, 5], [0, 1, 4, 3, 2, 5], [0, 3, 1, 2, 4, 5], [5, 1, 2, 3, 4, 0]],
            [[0, 1, 4, 2, 3, 5], [0, 1, 4, 3, 2, 5], [0, 5, 2, 3, 4, 1], [3, 1, 0, 2, 4, 5]],
            [[0, 1, 2, 4, 3, 5], [2, 0, 1, 3, 4, 5], [2, 1, 0, 3, 4, 5], [5, 0, 2, 3, 4, 1]],
            [[0, 1, 5, 3, 4, 2], [3, 0, 2, 1, 4, 5], [3, 1, 2, 0, 4, 5], [4, 0, 2, 3, 1, 5]],
            [[0, 3, 1, 2, 4, 5], [0, 3, 2, 1, 4, 5], [0, 5, 1, 3, 4, 2], [4, 1, 2, 3, 0, 5]],
            [[0, 1, 5, 3, 4, 2], [0, 4, 2, 3, 1, 5], [5, 1, 0, 3, 4, 2], [5, 1, 2, 0, 4, 3]],
            [[0, 1, 2, 5, 4, 3], [2, 0, 1, 3, 4, 5], [2, 1, 0, 3, 4, 5], [4, 0, 2, 3, 1, 5]],
            [[0, 1, 4, 3, 2, 5], [0, 5, 2, 3, 4, 1], [5, 0, 2, 3, 4, 1], [5, 1, 2, 0, 4, 3]]
        ]
    },
    "A5": {
        "size": 60,
        "generators": [
            [[0, 1, 4, 2, 3, 5], [0, 1, 5, 2, 4, 3], [0, 2, 3, 1, 4, 5]], 
            [[0, 1, 2, 5, 3, 4], [0, 1, 3, 4, 2, 5], [4, 1, 2, 0, 3, 5]], 
            [[0, 1, 2, 4, 5, 3], [0, 5, 2, 3, 1, 4], [5, 1, 2, 3, 0, 4]],
            [[0, 3, 1, 2, 4, 5], [0, 4, 1, 3, 2, 5], [1, 2, 0, 3, 4, 5]],
            [[1, 5, 2, 3, 4, 0], [2, 0, 1, 3, 4, 5], [3, 0, 2, 1, 4, 5]],
            [[4, 1, 2, 3, 5, 0], [5, 0, 2, 3, 4, 1], [5, 1, 0, 3, 4, 2]]
        ]
    },
    "A5_exceptional": {
        "size": 60,
        "generators": [
            [[2, 5, 1, 3, 0, 4], [3, 2, 4, 5, 1, 0]],
            [[2, 3, 4, 5, 0, 1], [5, 2, 0, 3, 1, 4]],
            [[3, 2, 4, 5, 1, 0], [5, 0, 2, 1, 3, 4]], 
            [[1, 5, 2, 0, 3, 4], [2, 3, 4, 5, 0, 1]],
            [[1, 3, 4, 0, 5, 2], [5, 1, 0, 2, 3, 4]],
            [[0, 5, 1, 2, 3, 4], [2, 3, 5, 4, 1, 0]]
        ]
    },
    "(S3xS3):C2": {
        "size": 72,
        "generators": [
            [[1, 0, 2, 3, 4, 5], [4, 3, 5, 0, 2, 1]],
            [[0, 1, 2, 3, 5, 4], [3, 4, 0, 5, 2, 1]],
            [[0, 1, 2, 3, 5, 4], [4, 3, 1, 5, 2, 0]],
            [[1, 0, 2, 3, 4, 5], [4, 2, 0, 5, 3, 1]], 
            [[2, 4, 5, 1, 0, 3], [5, 1, 2, 3, 4, 0]], 
            [[0, 5, 2, 3, 4, 1], [5, 0, 4, 2, 1, 3]], 
            [[1, 5, 4, 2, 0, 3], [5, 1, 2, 3, 4, 0]], 
            [[0, 1, 3, 2, 4, 5], [5, 3, 0, 4, 2, 1]], 
            [[0, 2, 1, 3, 4, 5], [2, 5, 3, 1, 0, 4]], 
            [[2, 1, 0, 3, 4, 5], [5, 2, 3, 0, 1, 4]]
        ]
    },
    "S5": {
        "size": 120,
        "generators": [
            [[0, 1, 3, 4, 5, 2], [0, 5, 2, 3, 4, 1]],
            [[2, 1, 0, 3, 4, 5], [3, 1, 2, 4, 5, 0]],
            [[0, 3, 2, 1, 4, 5], [1, 4, 2, 3, 5, 0]],
            [[0, 1, 4, 3, 2, 5], [1, 2, 5, 3, 4, 0]],
            [[0, 2, 3, 4, 1, 5], [4, 1, 2, 3, 0, 5]],
            [[0, 1, 2, 5, 4, 3], [1, 2, 3, 0, 4, 5]]
        ]
    },
    "S5_exceptional": {
        "size": 120,
        "generators": [
            [[2, 1, 3, 4, 0, 5], [4, 2, 1, 5, 0, 3]],
            [[0, 2, 3, 4, 1, 5], [2, 4, 0, 5, 1, 3]],
            [[2, 0, 3, 1, 4, 5], [5, 3, 4, 1, 2, 0]],
            [[1, 2, 3, 0, 4, 5], [3, 5, 4, 0, 2, 1]],
            [[0, 1, 4, 2, 5, 3], [4, 2, 1, 5, 0, 3]],
            [[0, 3, 1, 4, 2, 5], [1, 0, 4, 5, 2, 3]]
        ]
    },
    "A6": {
        "size": 360,
        "generators": [
            [[0, 2, 1, 4, 3, 5], [1, 2, 4, 5, 0, 3]]
        ]
    }
}