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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1679616.is', 'ambient_counter': 227, 'ambient_order': 1679616, 'ambient_tex': 'C_3^6.S_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1296, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1679616.is.18.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '93312.fs', 'subgroup_hash': 7692347811128442539, 'subgroup_order': 93312, 'subgroup_tex': 'C_6^4.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1679616.is', 'aut_centralizer_order': None, 'aut_label': '18.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1474, -1, 2020, -1], 'generators': [2354, 16808572352701911923372409, 3776, 36543, 241525335571641070310150630, 237182770174237525569292630, 14072318322978746839760, 140248369684386911255172480, 109543852335007595270719, 430867701484346649600, 5611221138701837664230400, 26581, 39393930302280423031680], 'label': '1679616.is.18.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.X', 'old_label': '18.x1', 'projective_image': '1679616.is', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.X', 'subgroup_fusion': None, 'weyl_group': '93312.fs'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 24, 9], 'aut_gens': [[32888271271095440859860885, 16833246703680637935498393], [189524970332637388171008292, 175803080774983496484640727], [133064172219573886329935296, 87235185485155208537039293], [31643178013307604502890933, 23075757345440851553814819]], 'aut_group': None, 'aut_hash': 2531344867876645364, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 279936, 'aut_permdeg': 540, 'aut_perms': 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'aut_phi_ratio': 9.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 216, 1, 1], [2, 324, 1, 2], [2, 972, 1, 1], [3, 4, 1, 2], [3, 12, 1, 1], [3, 18, 1, 2], [3, 24, 1, 1], [3, 144, 3, 1], [3, 288, 3, 1], [4, 324, 1, 2], [4, 648, 1, 2], [4, 972, 1, 1], [4, 3888, 1, 1], [6, 12, 1, 3], [6, 18, 1, 2], [6, 24, 1, 5], [6, 36, 1, 8], [6, 72, 1, 10], [6, 144, 3, 1], [6, 288, 3, 4], [6, 432, 1, 1], [6, 648, 1, 5], [6, 1296, 1, 1], [6, 1944, 1, 1], [6, 2592, 3, 1], [8, 3888, 1, 1], [9, 1728, 1, 3], [12, 648, 1, 5], [12, 1296, 1, 8], [12, 1944, 1, 1], [12, 2592, 3, 1], [12, 3888, 1, 2], [18, 5184, 1, 3], [24, 3888, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.A_4^2.C_6^2.C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 2531344867876645364, 'autcentquo_nilpotent': False, 'autcentquo_order': 279936, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.A_4^2.C_6^2.C_2', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 216, 1], [2, 324, 2], [2, 972, 1], [3, 4, 2], [3, 12, 1], [3, 18, 2], [3, 24, 1], [3, 144, 3], [3, 288, 3], [4, 324, 2], [4, 648, 2], [4, 972, 1], [4, 3888, 1], [6, 12, 3], [6, 18, 2], [6, 24, 5], [6, 36, 8], [6, 72, 10], [6, 144, 3], [6, 288, 12], [6, 432, 1], [6, 648, 5], [6, 1296, 1], [6, 1944, 1], [6, 2592, 3], [8, 3888, 1], [9, 1728, 3], [12, 648, 5], [12, 1296, 8], [12, 1944, 1], [12, 2592, 3], [12, 3888, 2], [18, 5184, 3], [24, 3888, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '93312.fs', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 149, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 216, 1, 1], [2, 324, 1, 2], [2, 972, 1, 1], [3, 4, 1, 2], [3, 12, 1, 1], [3, 18, 1, 2], [3, 24, 1, 1], [3, 144, 1, 3], [3, 288, 1, 3], [4, 324, 1, 2], [4, 648, 1, 2], [4, 972, 1, 1], [4, 3888, 1, 1], [6, 12, 1, 3], [6, 18, 1, 2], [6, 24, 1, 3], [6, 24, 2, 1], [6, 36, 1, 6], [6, 36, 2, 1], [6, 72, 1, 8], [6, 72, 2, 1], [6, 144, 1, 3], [6, 288, 1, 12], [6, 432, 1, 1], [6, 648, 1, 3], [6, 648, 2, 1], [6, 1296, 1, 1], [6, 1944, 1, 1], [6, 2592, 1, 3], [8, 3888, 1, 1], [9, 1728, 1, 1], [9, 1728, 2, 1], [12, 648, 1, 3], [12, 648, 2, 1], [12, 1296, 1, 6], [12, 1296, 2, 1], [12, 1944, 1, 1], [12, 2592, 1, 3], [12, 3888, 2, 1], [18, 5184, 1, 1], [18, 5184, 2, 1], [24, 3888, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [7, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 6], [24, 1, 12], [36, 0, 4], [36, 1, 6], [72, 0, 4], [72, 1, 7]], 'familial': False, 'frattini_label': '27.5', 'frattini_quotient': '3456.da', 'hash': 7692347811128442539, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [2, 24], 'inner_gens': [[32888271271095440859860885, 146538548916327473799375294], [2513623910609778012780200, 16833246703680637935498393]], 'inner_hash': 7692347811128442539, 'inner_nilpotent': False, 'inner_order': 93312, 'inner_split': True, 'inner_tex': 'C_6^4.\\SOPlus(4,2)', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 5], [4, 8], [6, 8], [8, 1], [9, 4], [12, 24], [18, 9], [24, 19], [36, 14], [72, 11]], 'label': '93312.fs', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C6^4.SO+(4,2)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 89, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 107, 'number_divisions': 97, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 4808, 'number_subgroup_classes': 6236, 'number_subgroups': 1367914, 'old_label': None, 'order': 93312, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1851], [3, 1376], [4, 6804], [6, 19776], [8, 3888], [9, 5184], [12, 31104], [18, 15552], [24, 7776]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 3, 'outer_gen_orders': [3], 'outer_gen_pows': [0], 'outer_gens': [[32888271271095440859860885, 24926305958918107273923993]], 'outer_group': '3.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 3, 'outer_permdeg': 3, 'outer_perms': [3], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 5], [6, 6], [8, 3], [9, 4], [12, 25], [18, 5], [24, 19], [36, 12], [72, 9], [144, 2]], 'representations': {'PC': {'code': '671989764071074044513394503061920584257971264704498636148889021689545379754044233844615147073053886983023916571023927276404956865976671358124622392069982251720801787183814144554002696476212730590774786094701472161029641763366771771865804384672333718634022553044', 'gens': [1, 2, 4, 6, 8, 10, 12, 13], 'pres': [13, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 2, 1222053, 66, 3125618, 227476, 1567179, 1025560, 660065, 146, 5648764, 2809577, 1295610, 42176, 2697557, 1117602, 953347, 290204, 100677, 304, 1415238, 19675, 3321, 1190599, 4279412, 350110, 366035, 132984, 306, 2148128, 105347, 8484, 27451, 7862409, 3538102, 926688, 221191, 112394, 386, 61786, 1111991, 11220779, 1061474, 315963, 155920, 985633, 848769, 95887, 136967]}, 'Perm': {'d': 26, 'gens': [32888271271095440859860885, 16833246703680637935498393]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 243, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^4.\\SOPlus(4,2)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [12, 12, 6, 24], 'aut_gens': [[2591145499384530926975722, 16808572718369597977868409, 32993114507303845598335158], [49175249239298054686838790, 191759646647973187259061670, 54611826069805800785351819], [38132262902224579798509318, 20563136813527199239242380, 133404858441103239759690491], [99957967333531781150035862, 219184960343512052025571587, 240336571420636208909796263], [98858482957421628810537593, 176242572965079230066563604, 37434346105318601534295515]], 'aut_group': None, 'aut_hash': 447151837324768108, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10077696, 'aut_permdeg': 1404, 'aut_perms': 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15552, 1, 1], [18, 15552, 2, 1], [18, 93312, 2, 1], [24, 69984, 2, 1], [36, 15552, 1, 1], [36, 15552, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^4.C_3^4.(C_6\\times D_4).C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 447151837324768108, 'autcentquo_nilpotent': False, 'autcentquo_order': 10077696, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^4.C_3^4.C_2.C_6.C_2^3', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 108, 1], [2, 324, 2], [2, 648, 2], [2, 729, 1], [2, 972, 1], [2, 2916, 2], [2, 4374, 1], [2, 6561, 1], [3, 4, 2], [3, 12, 4], [3, 18, 2], [3, 24, 4], [3, 36, 3], [3, 72, 6], [3, 144, 1], [3, 288, 1], [3, 864, 4], [3, 5184, 1], [4, 108, 1], [4, 324, 2], [4, 648, 1], [4, 972, 1], [4, 1944, 2], [4, 2916, 2], [4, 5832, 1], [4, 34992, 2], [6, 12, 6], [6, 18, 2], [6, 24, 9], [6, 36, 15], [6, 48, 4], [6, 72, 57], [6, 144, 40], [6, 216, 2], [6, 432, 2], [6, 648, 14], [6, 864, 5], [6, 1296, 29], [6, 1728, 4], [6, 1944, 4], [6, 2592, 6], [6, 3888, 8], [6, 5832, 6], [6, 7776, 2], [6, 11664, 2], [6, 15552, 5], [6, 34992, 1], [6, 46656, 3], [8, 34992, 2], [9, 288, 1], [9, 576, 1], [9, 864, 2], [9, 1728, 3], [9, 10368, 2], [9, 20736, 1], [12, 216, 2], [12, 432, 1], [12, 648, 14], [12, 1296, 35], [12, 1944, 4], [12, 2592, 22], [12, 3888, 10], [12, 5832, 6], [12, 7776, 10], [12, 11664, 5], [12, 15552, 5], [12, 69984, 2], [18, 864, 3], [18, 1728, 12], [18, 15552, 3], [18, 93312, 2], [24, 69984, 2], [36, 15552, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1679616.is', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 227, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 108, 1, 1], [2, 324, 1, 2], [2, 648, 1, 2], [2, 729, 1, 1], [2, 972, 1, 1], [2, 2916, 1, 2], [2, 4374, 1, 1], [2, 6561, 1, 1], [3, 4, 1, 2], [3, 12, 1, 4], [3, 18, 1, 2], [3, 24, 1, 4], [3, 36, 1, 3], [3, 72, 1, 6], [3, 144, 1, 1], [3, 288, 1, 1], [3, 864, 1, 4], [3, 5184, 1, 1], [4, 108, 1, 1], [4, 324, 1, 2], [4, 648, 1, 1], [4, 972, 1, 1], [4, 1944, 1, 2], [4, 2916, 1, 2], [4, 5832, 1, 1], [4, 34992, 1, 2], [6, 12, 1, 6], [6, 18, 1, 2], [6, 24, 1, 9], [6, 36, 1, 15], [6, 48, 1, 4], [6, 72, 1, 57], [6, 144, 1, 40], [6, 216, 1, 2], [6, 432, 1, 2], [6, 648, 1, 14], [6, 864, 1, 5], [6, 1296, 1, 29], [6, 1728, 1, 4], [6, 1944, 1, 4], [6, 2592, 1, 6], [6, 3888, 1, 8], [6, 5832, 1, 6], [6, 7776, 1, 2], [6, 11664, 1, 2], [6, 15552, 1, 5], [6, 34992, 1, 1], [6, 46656, 1, 3], [8, 34992, 1, 2], [9, 288, 1, 1], [9, 576, 1, 1], [9, 864, 2, 1], [9, 1728, 1, 3], [9, 10368, 1, 2], [9, 20736, 1, 1], [12, 216, 1, 2], [12, 432, 1, 1], [12, 648, 1, 14], [12, 1296, 1, 35], [12, 1944, 1, 4], [12, 2592, 1, 22], [12, 3888, 1, 10], [12, 5832, 1, 6], [12, 7776, 1, 10], [12, 11664, 1, 5], [12, 15552, 1, 5], [12, 69984, 1, 2], [18, 864, 1, 1], [18, 864, 2, 1], [18, 1728, 1, 4], [18, 1728, 2, 4], [18, 15552, 1, 1], [18, 15552, 2, 1], [18, 93312, 1, 2], [24, 69984, 1, 2], [36, 15552, 1, 1], [36, 15552, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [8, 8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 12], [24, 1, 18], [36, 1, 36], [48, 0, 6], [48, 1, 9], [72, 1, 96], [144, 1, 39]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '20736.dj', 'hash': 7494867631108739006, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [18, 24, 12], 'inner_gens': [[2591145499384530926975722, 82785016570167076178380030, 96454351560332667867812633], [32037807361722215780155793, 16808572718369597977868409, 33176432629824933508413908], [126637091768629788759741827, 225959365856760377647297266, 32993114507303845598335158]], 'inner_hash': 7494867631108739006, 'inner_nilpotent': False, 'inner_order': 1679616, 'inner_split': True, 'inner_tex': 'C_3^6.S_4^2:C_2^2', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 2], [4, 16], [6, 8], [8, 8], [9, 8], [12, 44], [16, 2], [18, 18], [24, 54], [36, 76], [48, 23], [72, 126], [144, 40]], 'label': '1679616.is', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.S4^2:C2^2', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 210, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 433, 'number_divisions': 425, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1679616, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 20535], [3, 9800], [4, 87912], [6, 451128], [8, 69984], [9, 49248], [12, 547776], [18, 256608], [24, 139968], [36, 46656]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[268114092672099176837471928, 191369555134990672347905280, 102382438354545880304159346]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 2], [4, 16], [6, 8], [8, 8], [9, 8], [12, 44], [16, 2], [18, 18], [24, 46], [36, 76], [48, 19], [72, 126], [96, 4], [144, 40]], 'representations': {'PC': {'code': '639482164253231392493268707694163493283960760868565205550944830649041885151823758532827550837056918646026699041541609082582764901291614078355404929296251954697730950908111328563733215521563632079483272883750426053178790246164327469727943022530994369242787063187103906640754069443317199493598350850670295780258856700516863138907696440166565970058343934589383385530908447350276198043688404486095901232962334319798141192933136403811768501996962802954344535712100287161911192047511082989849804782261722090736789804980390764896428946986170780335', 'gens': [1, 2, 4, 6, 8, 10, 12, 14, 15, 16], 'pres': [16, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 685056, 47678657, 81, 12802754, 14631010, 5827075, 9639699, 23156643, 179, 36282884, 66487060, 14327716, 68120069, 58807317, 17026597, 8515061, 4257285, 277, 21510, 39674902, 5414, 2742, 157532167, 50465815, 23136807, 7955767, 5546183, 375, 102131720, 73838616, 1969960, 14753720, 6335784, 177256, 5283849, 3386905, 1520681, 798777, 382153, 21241, 9257, 473, 625162, 64171034, 154234, 39146, 133042187, 668187, 33260587, 28408379, 14826315, 823803, 231115, 571, 247283724, 369436, 61820972, 17881404, 9479884, 526780, 429452, 255510541, 109541405, 64253997, 18004285, 8129933, 454397, 502797, 343388174, 181647390, 66355246, 32973182, 20580558, 1146366, 581902, 170778639, 56635423, 71884847, 36056127, 9068623]}, 'Perm': {'d': 26, 'gens': [2591145499384530926975722, 16808572718369597977868409, 32993114507303845598335158]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.S_4^2:C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
