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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1536.399727', 'ambient_counter': 399727, 'ambient_order': 1536, 'ambient_tex': 'C_6.D_8^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 256, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1536.399727.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.26844', 'subgroup_hash': 26844, 'subgroup_order': 256, 'subgroup_tex': 'D_{16}:D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1536.399727', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '256.a1', 'complements': ['256.d1', '256.c1'], 'conjugacy_class_count': 4, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.d1', '12.e1', '12.f1', '12.g1', '12.h1', '12.o1', '12.p1', '12.p2', '12.q1'], 'core': '6.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [3603, 5071, 2438, 3935], 'generators': [1, 2, 196, 1152], 'label': '1536.399727.6.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': ['2.e1', '3.a1'], 'normal_contains': ['12.a1', '12.b1', '12.d1', '12.e1', '12.f1', '12.g1', '12.h1'], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': '768.12955', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '256.12955'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [8, 8, 2, 8, 2, 8], 'aut_gens': [[1, 2, 4, 64], [217, 58, 52, 240], [73, 10, 36, 64], [105, 34, 28, 192], [249, 50, 12, 112], [177, 18, 60, 192], [1, 58, 20, 64]], 'aut_group': None, 'aut_hash': 752670059296835666, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 24, 'aut_perms': [604271643510767082193548, 330032121757304641480489, 26495789411355375690233, 270413087534405157996092, 479651935898268629133852, 13021951546770499852450], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 2, 1], [2, 8, 1, 2], [2, 16, 2, 1], [4, 2, 1, 2], [4, 4, 2, 2], [4, 8, 1, 2], [4, 16, 2, 1], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 2, 1], [8, 16, 1, 2], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2.C_2^3.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '128.2194', 'autcentquo_hash': 2194, 'autcentquo_nilpotent': True, 'autcentquo_order': 128, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_4^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 2], [2, 8, 2], [2, 16, 2], [4, 2, 2], [4, 4, 4], [4, 8, 2], [4, 16, 2], [8, 2, 4], [8, 4, 2], [8, 8, 2], [8, 16, 2], [16, 2, 4], [16, 4, 6], [16, 8, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '128.2011', 'commutator_count': 1, 'commutator_label': '16.5', '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', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 26844, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 2], [2, 8, 1, 2], [2, 16, 1, 2], [4, 2, 1, 2], [4, 4, 1, 4], [4, 8, 1, 2], [4, 16, 1, 2], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 1, 2], [8, 16, 1, 2], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 645120, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[4, 0, 8]], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '16.14', 'hash': 26844, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 2, 8, 4], 'inner_gens': [[1, 2, 4, 240], [1, 2, 28, 80], [1, 42, 4, 64], [145, 50, 4, 64]], 'inner_hash': 2011, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'D_4\\times D_8', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 16], [4, 11]], 'label': '256.26844', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 2, 'linQ_dim': 16, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D16:D4', 'ngens': 4, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 53, 'number_conjugacy_classes': 43, 'number_divisions': 32, 'number_normal_subgroups': 105, 'number_subgroup_autclasses': 215, 'number_subgroup_classes': 326, 'number_subgroups': 1015, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 59], [4, 68], [8, 64], [16, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 104, 0], 'outer_gens': [[1, 2, 4, 96], [105, 34, 4, 64], [1, 2, 20, 64]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [120, 5040, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 5], [8, 1], [16, 2]], 'representations': {'PC': {'code': 167454138931776382468421263645601884, 'gens': [1, 2, 3, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 346, 66, 907, 91, 972, 116, 13446, 2254, 166, 10247, 5135]}, 'Perm': {'d': 32, 'gens': [8864346369514948454174359610742, 135955991562369039230941840932864000, 67986860127283896396511282924227143, 67977995780968282257608325225692856, 50973977447395947166374977137321656, 16985047389861003970253793579100937, 25199055155403427461045987627105862, 8231691320578226211046411712681647]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{16}:D_4', 'transitive_degree': 32, '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': '48.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 16, 'aut_gen_orders': [8, 8, 16, 4, 4, 16], 'aut_gens': [[1, 2, 4, 64], [809, 411, 972, 888], [1361, 1199, 1348, 1488], [585, 1398, 4, 64], [961, 1207, 252, 1128], [193, 238, 28, 1504], [241, 1191, 1004, 336]], 'aut_group': None, 'aut_hash': 7438266653881424873, 'aut_nilpotency_class': 7, 'aut_nilpotent': True, 'aut_order': 32768, 'aut_permdeg': 34, 'aut_perms': [110148197315375908861218829978726328574, 147680573749554454293255282752909024470, 213791052512518628682402430430626176241, 218796269739803869745261516150469796297, 146589209788153723146630833001258263522, 91579428912733989932131101780219270449], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 4, 1], [2, 32, 2, 1], [3, 1, 2, 1], [4, 2, 2, 1], [4, 4, 2, 1], [4, 8, 4, 1], [4, 32, 2, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 8, 8, 1], [6, 32, 4, 1], [8, 2, 4, 1], [8, 4, 2, 1], [8, 4, 8, 1], [8, 16, 4, 1], [12, 2, 4, 1], [12, 4, 4, 1], [12, 8, 8, 1], [12, 32, 4, 1], [16, 2, 8, 1], [16, 4, 4, 1], [16, 4, 8, 1], [16, 16, 8, 1], [24, 2, 8, 1], [24, 4, 4, 1], [24, 4, 16, 1], [24, 16, 8, 1], [48, 2, 16, 1], [48, 4, 8, 1], [48, 4, 16, 1], [48, 16, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_4^2.C_2^3.C_2^3.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': '1024.dge', 'autcentquo_hash': 5549096759936920733, 'autcentquo_nilpotent': True, 'autcentquo_order': 1024, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '(C_2^2\\times D_4^2):C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 8, 4], [2, 32, 2], [3, 1, 2], [4, 2, 2], [4, 4, 2], [4, 8, 4], [4, 32, 2], [6, 1, 2], [6, 2, 2], [6, 8, 8], [6, 32, 4], [8, 2, 4], [8, 4, 10], [8, 16, 4], [12, 2, 4], [12, 4, 4], [12, 8, 8], [12, 32, 4], [16, 2, 8], [16, 4, 12], [16, 16, 8], [24, 2, 8], [24, 4, 20], [24, 16, 8], [48, 2, 16], [48, 4, 24], [48, 16, 16]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '256.12955', 'commutator_count': 1, 'commutator_label': '32.3', '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', '2.1', '2.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 399727, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['512.399727', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 1, 4], [2, 32, 1, 2], [3, 1, 2, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 8, 1, 4], [4, 32, 1, 2], [6, 1, 2, 1], [6, 2, 2, 1], [6, 8, 2, 4], [6, 32, 2, 2], [8, 2, 2, 2], [8, 4, 1, 2], [8, 4, 2, 4], [8, 16, 1, 4], [12, 2, 2, 2], [12, 4, 2, 2], [12, 8, 2, 4], [12, 32, 2, 2], [16, 2, 4, 2], [16, 4, 2, 2], [16, 4, 4, 2], [16, 16, 2, 4], [24, 2, 4, 2], [24, 4, 2, 2], [24, 4, 4, 4], [24, 16, 2, 4], [48, 2, 8, 2], [48, 4, 4, 2], [48, 4, 8, 2], [48, 16, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 51609600, 'exponent': 48, 'exponents_of_order': [9, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 32]], 'familial': False, 'frattini_label': '32.3', 'frattini_quotient': '48.52', 'hash': 399727, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 2, 8, 8], 'inner_gens': [[1, 786, 28, 448], [817, 2, 4, 504], [41, 2, 4, 64], [1153, 1162, 4, 64]], 'inner_hash': 12955, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': False, 'inner_tex': 'D_8^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 48], [2, 72], [4, 75]], 'label': '1536.399727', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.D8^2', 'ngens': 10, 'nilpotency_class': 4, 'nilpotent': True, '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': 24, 'number_conjugacy_classes': 195, 'number_divisions': 82, 'number_normal_subgroups': 240, 'number_subgroup_autclasses': 322, 'number_subgroup_classes': 970, 'number_subgroups': 4452, 'old_label': None, 'order': 1536, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 99], [3, 2], [4, 108], [6, 198], [8, 112], [12, 216], [16, 192], [24, 224], [48, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [576, 768, 0, 0, 0], 'outer_gens': [[1345, 582, 4, 64], [385, 427, 1380, 1472], [1, 2, 4, 1088], [1, 2, 20, 1104], [817, 786, 52, 832]], 'outer_group': '128.1631', 'outer_hash': 1631, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [7, 40723336, 135732256, 243135376, 261314640], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 17], [8, 13], [16, 8], [32, 4]], 'representations': {'PC': {'code': '277264960037630017614857629024146245086890983019632813078106888696833', 'gens': [1, 2, 3, 7], 'pres': [10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 320, 15721, 842, 82, 2243, 113, 2404, 144, 31366, 17656, 206, 71687, 37777, 237, 12978, 268]}, 'Perm': {'d': 35, 'gens': [8203834037372317903337152573272976278480, 4867003915917157903011986831009513472000, 2433765636981401278502450527660445359224, 2433501957955223350312217691907885290984, 1512246359709604079851808643739219127784, 1824845245492297365078063716259105387840, 608095912649138604967346333632388236584, 903065845799780519864142501070727825760, 295496195434689904216526716510628258664, 4]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.D_8^2', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
