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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.3158', 'ambient_counter': 3158, 'ambient_order': 864, 'ambient_tex': 'C_3\\times C_{12}.D_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 2, 'counter': 393, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.3158.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.656', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 656, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2.D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '864.3158', 'aut_centralizer_order': 18432, 'aut_label': '432.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '216.a1.a1', '216.b1.a1', '216.b1.b1', '216.d1.a1', '216.d1.b1', '216.e1.a1', '216.e1.b1'], 'contains': ['864.a1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4417, 5226, 3243, 6538, 6798, 5638, 3439, 6316], 'generators': [432], 'label': '864.3158.432.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.b1.a1', 'normal_contained_in': ['144.d1.a1', '144.f1.a1', '144.e1.a1', '216.a1.a1', '216.b1.a1', '216.b1.b1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '432.656', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.656', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 4, 4, 4, 6, 4, 12], 'aut_gens': [[1, 6, 72], [245, 690, 540], [437, 654, 108], [497, 246, 72], [5, 798, 828], [25, 678, 540], [449, 762, 72], [649, 462, 360], [649, 426, 540]], 'aut_group': None, 'aut_hash': 2220188335685626814, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 18432, 'aut_permdeg': 50, 'aut_perms': [20911083617968080533516139069629638884716211652115879000438716237, 18508494824055297017543905508160915736727655668884271067709000477, 11914176857071255934445776369317772437874953486425686737057689323, 19825683926836886462578647117967869101014976501668056025456038041, 18499958484012668897069245253178824172445883364898328442731415277, 1164062588139929292645745716804021065424738577081444826281476912, 26743958801091766520334498877529124554199065713524723240336787304, 16787915593510866814026196323572706046759685647099981847789681895], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 2, 2, 1], [4, 6, 4, 1], [4, 12, 2, 1], [4, 36, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 2], [6, 2, 2, 4], [6, 2, 4, 2], [6, 4, 1, 1], [6, 4, 2, 2], [6, 4, 4, 1], [12, 2, 4, 2], [12, 2, 8, 1], [12, 4, 2, 1], [12, 4, 4, 2], [12, 4, 8, 1], [12, 6, 8, 2], [12, 6, 16, 1], [12, 12, 4, 2], [12, 12, 8, 1], [12, 36, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6^2.C_2^6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '144.192', 'autcentquo_hash': 192, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 2, 6], [3, 4, 3], [4, 2, 2], [4, 6, 4], [4, 12, 2], [4, 36, 2], [6, 1, 6], [6, 2, 18], [6, 4, 9], [12, 2, 16], [12, 4, 18], [12, 6, 32], [12, 12, 16], [12, 36, 4]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '72.46', 'commutator_count': 1, 'commutator_label': '36.14', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3158, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['288.514', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 2, 1, 2], [4, 6, 1, 4], [4, 12, 1, 2], [4, 36, 1, 2], [6, 1, 2, 3], [6, 2, 1, 6], [6, 2, 2, 6], [6, 4, 1, 3], [6, 4, 2, 3], [12, 2, 2, 4], [12, 2, 4, 2], [12, 4, 1, 2], [12, 4, 2, 4], [12, 4, 4, 2], [12, 6, 2, 8], [12, 6, 4, 4], [12, 12, 2, 8], [12, 36, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8736, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '216.170', 'hash': 3158, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 6], 'inner_gens': [[1, 66, 504], [13, 6, 360], [433, 582, 72]], 'inner_hash': 46, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': False, 'inner_tex': 'S_3\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 90], [4, 30]], 'label': '864.3158', 'linC_count': 256, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 152, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 360, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3*C12.D12', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 144, 'number_divisions': 78, 'number_normal_subgroups': 120, 'number_subgroup_autclasses': 222, 'number_subgroup_classes': 394, 'number_subgroups': 1300, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 124], [6, 78], [12, 632]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 2, 4], 'outer_gen_pows': [0, 0, 216, 0, 0, 0], 'outer_gens': [[5, 438, 72], [433, 42, 72], [221, 6, 72], [5, 678, 72], [1, 30, 72], [689, 66, 108]], 'outer_group': '256.27633', 'outer_hash': 27633, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 14, 'outer_perms': [6266937601, 6266942640, 13412412721, 19679794254, 6267305646, 13451966760], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 22], [4, 32], [8, 14], [16, 2]], 'representations': {'PC': {'code': 1525665957954070241576155013426977748085877206857, 'gens': [1, 3, 6], 'pres': [8, -2, -3, -2, -2, -3, -2, -2, -3, 16, 3465, 1586, 66, 1923, 91, 1924, 24197, 2901, 141, 6742, 166, 6167]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1166425, 793169, 985713, 1372111, 1614733, 1197961, 532321, 473246]}, 'Perm': {'d': 21, 'gens': [249692575006925304, 2560950789965568000, 8448744, 3, 5109094217170944000, 12541704, 22230464256000, 6706022400]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{12}.D_{12}', 'transitive_degree': 96, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 6, 12, 2, 6, 6, 2], 'aut_gens': [[1, 6, 72], [37, 282, 108], [25, 390, 72], [5, 114, 108], [13, 318, 396], [29, 186, 72], [269, 258, 360], [13, 30, 72]], 'aut_group': None, 'aut_hash': 8142848205473677161, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2304, 'aut_permdeg': 26, 'aut_perms': [196860533720901685151935352, 2515258693556483882215439, 530945821627064109220250, 240345314731180084867106349, 77736912152298522939625096, 97439727930265472931925075, 240556576587829282165235904], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 18, 2, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 6, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 2], [6, 2, 2, 4], [6, 2, 4, 2], [6, 4, 1, 1], [6, 4, 2, 2], [6, 4, 4, 1], [6, 6, 4, 2], [6, 6, 8, 1], [6, 18, 4, 1], [12, 6, 4, 2], [12, 6, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6^2.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '36.10', 'autcentquo_hash': 10, 'autcentquo_nilpotent': False, 'autcentquo_order': 36, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 18, 2], [3, 1, 2], [3, 2, 6], [3, 4, 3], [4, 6, 2], [6, 1, 6], [6, 2, 18], [6, 4, 9], [6, 6, 16], [6, 18, 4], [12, 6, 16]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '36.10', 'commutator_count': 1, 'commutator_label': '18.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 656, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['72.23', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 18, 1, 2], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 6, 1, 2], [6, 1, 2, 3], [6, 2, 1, 6], [6, 2, 2, 6], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 2, 8], [6, 18, 2, 2], [12, 6, 2, 4], [12, 6, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8736, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '216.170', 'hash': 656, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 3], 'inner_gens': [[1, 66, 72], [13, 6, 360], [1, 150, 72]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': True, 'inner_tex': 'S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 54], [4, 12]], 'label': '432.656', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 16, 'linQ_dim': 6, 'linQ_dim_count': 16, 'linR_count': 136, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.D6', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 90, 'number_divisions': 54, 'number_normal_subgroups': 80, 'number_subgroup_autclasses': 180, 'number_subgroup_classes': 306, 'number_subgroups': 1120, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 51], [3, 26], [4, 12], [6, 246], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[221, 222, 360], [217, 6, 72], [5, 6, 72], [1, 30, 360], [221, 6, 108]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [766096, 23, 806520, 806407, 1174342], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 22], [8, 6]], 'representations': {'PC': {'code': 20936774360428536126890953528997, 'gens': [1, 3, 6], 'pres': [7, -2, -3, -2, -2, -3, -2, -3, 14, 1388, 58, 1683, 80, 1684, 2539, 124, 2372]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101736038821652, 24992906222180337, 41624323485457081]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [99161, 68839, 40831, 6083, 5941, 5995, 42997]}, 'Perm': {'d': 15, 'gens': [41064, 1465, 39916800, 93405312000, 2424, 3, 403200]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.D_6', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
