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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.od', 'ambient_counter': 368, 'ambient_order': 5832, 'ambient_tex': '\\He_3^2:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.od.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5832.od', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': ['324.br1', '324.bq1', '324.bs1', '324.df1', '324.db1', '324.dd1', '324.de1', '324.ee1', '324.ed1', '324.eh1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.c1', '9.g1'], 'contains': ['36.d1', '36.f1', '54.cd1', '54.ce1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8145, 1561, 7586, 9667], 'generators': [10825, 122424, 153460181145600, 2535581637388800, 800409278592000, 51867], 'label': '5832.od.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.b1', '6.c1'], 'normal_contains': ['36.d1', '36.f1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '5832.od', 'quotient_action_image': '18.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '5832.od'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 48, 'aut_gen_orders': [6, 4, 8], 'aut_gens': [[24577758, 15477644, 24507118, 2939606, 36731395, 14159168], [2721277, 16002766, 43014227, 6973453, 11495158, 4228509], [24507118, 16002766, 20201582, 42578137, 2939606, 34612436], [11225629, 8567290, 24577758, 6973453, 7138662, 29204454]], 'aut_group': '373248.b', 'aut_hash': 4345101132123987080, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 373248, 'aut_permdeg': 18, 'aut_perms': [4842285684641954, 3553553159135111, 5268177583354101], 'aut_phi_ratio': 3456.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 2, 1], [2, 81, 1, 1], [3, 2, 8, 1], [3, 4, 16, 1], [6, 18, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:\\GL(2,3)\\wr 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': 48, 'autcentquo_group': '373248.b', 'autcentquo_hash': 4345101132123987080, 'autcentquo_nilpotent': False, 'autcentquo_order': 373248, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GL(2,3)\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [3, 2, 8], [3, 4, 16], [6, 18, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '324.169', 'commutator_count': 1, 'commutator_label': '81.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 169, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 2, 1, 8], [3, 4, 1, 16], [6, 18, 1, 8]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 21, 'exponent': 6, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '324.169', 'hash': 169, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 2, 3, 3, 3, 2], 'inner_gens': [[24577758, 24033196, 24507118, 2939606, 36731395, 8188666], [20201582, 15477644, 24507118, 32864349, 36731395, 34924766], [24577758, 15477644, 24507118, 2939606, 36731395, 8314856], [24577758, 2414724, 24507118, 2939606, 36731395, 39300942], [24577758, 15477644, 24507118, 2939606, 36731395, 17350487], [20201582, 38113169, 20254942, 32864349, 11225629, 14159168]], 'inner_hash': 169, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': False, 'inner_tex': 'C_3^2:S_3^2', 'inner_used': [1, 2, 3, 4, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 16], [4, 16]], 'label': '324.169', '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': 'C3^2:S3^2', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 6, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 36, 'number_divisions': 36, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 35, 'number_subgroup_classes': 356, 'number_subgroups': 3412, 'old_label': None, 'order': 324, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 99], [3, 80], [6, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 3, 3, 2, 2, 2, 2], 'outer_gen_pows': [14408200, 17072210, 14408200, 14408200, 17072210, 15477644, 15477644, 16002766, 16002766], 'outer_gens': [[43014227, 15477644, 24507118, 32864349, 36731395, 14159168], [32479219, 16002766, 32864349, 24507118, 7138662, 38864855], [43014227, 15477644, 24507118, 32864349, 2721277, 14159168], [43014227, 15477644, 24507118, 2939606, 36731395, 25627762], [37043725, 15477644, 20254942, 32864349, 6973453, 8188666], [11495158, 15477644, 24507118, 43014227, 36731395, 21271266], [7138662, 15477644, 24507118, 11495158, 36731395, 29131384], [24577758, 15477644, 11225629, 2939606, 24507118, 14159168], [24577758, 15477644, 6973453, 2939606, 2721277, 14159168]], 'outer_group': '1152.157849', 'outer_hash': 5496387407741636925, 'outer_nilpotent': False, 'outer_order': 1152, 'outer_permdeg': 8, 'outer_perms': [15960, 31892, 15962, 15240, 6966, 5064, 17520, 514, 635], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4\\wr C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 16], [4, 16]], 'representations': {'PC': {'code': 241849281311649315095, 'gens': [1, 2, 3, 5, 6], 'pres': [6, -2, -3, -2, -3, -3, -3, 49, 542, 50, 579, 376, 1313]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 15477644, 24507118, 2939606, 36731395, 14159168]}, 'Perm': {'d': 12, 'gens': [3633840, 25, 147, 240, 43590960, 43626240]}}, 'schur_multiplier': [3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:S_3^2', 'transitive_degree': 18, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [4, 6, 6], 'aut_gens': [[64426274048275, 43352558825490, 10825, 99090, 52560, 123124, 800409278691090, 357014781446400], [753239636161464, 737635164856491, 1492144191014400, 737635164537600, 507659391187200, 2197173157804800, 737635164660724, 40349], [127300024152265, 43352558942854, 42625, 216454, 121683, 123124, 2197173158021254, 1492144191014400], [732496954387200, 2155160403114366, 2870613562118400, 2155160402841600, 507659391187200, 800409278592000, 2155160402964724, 11525]], 'aut_group': '23328.o', 'aut_hash': 4677685659119495630, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23328, 'aut_permdeg': 99, 'aut_perms': [846379947101589063154896018529489475091637935306675213172873442755749696321552652203223858932575913753500507260430688614857590013275043926890652065529669749, 892317769115462398778467747555647691139600914456374495080092111470374884398271539378523602240340804879860415888031978406614608553209732972170465290079119716, 421591734543339627348871863148317351622669499519170970625883834959259601430271883066301276181080287912635389562386476184868192288322925411144591634551828902], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 2, 1], [2, 81, 1, 3], [2, 81, 2, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 6, 2, 2], [3, 12, 2, 3], [3, 18, 2, 1], [3, 24, 2, 1], [3, 36, 1, 1], [3, 36, 2, 1], [3, 36, 4, 1], [3, 72, 2, 2], [6, 18, 2, 2], [6, 36, 2, 1], [6, 54, 2, 2], [6, 54, 4, 1], [6, 108, 2, 2], [6, 108, 4, 1], [6, 162, 2, 6], [6, 324, 1, 2], [6, 324, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:D_6\\wr 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': 12, 'autcentquo_group': '23328.o', 'autcentquo_hash': 4677685659119495630, 'autcentquo_nilpotent': False, 'autcentquo_order': 23328, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:D_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 5], [3, 2, 2], [3, 4, 1], [3, 6, 4], [3, 12, 6], [3, 18, 2], [3, 24, 2], [3, 36, 7], [3, 72, 4], [6, 18, 4], [6, 36, 2], [6, 54, 8], [6, 108, 8], [6, 162, 12], [6, 324, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5832.od', 'commutator_count': 1, 'commutator_label': '729.453', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 368, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 5], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 4], [3, 12, 1, 6], [3, 18, 1, 2], [3, 24, 1, 2], [3, 36, 1, 7], [3, 72, 1, 4], [6, 18, 1, 4], [6, 36, 1, 2], [6, 54, 1, 8], [6, 108, 1, 8], [6, 162, 1, 12], [6, 324, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1306368, 'exponent': 6, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[36, 1, 2]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '648.732', 'hash': 2043999697674719391, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 2, 3, 3, 3, 3, 2], 'inner_gens': [[64426274048275, 85017558800766, 10825, 272766, 121683, 51867, 800409278864766, 1492144191014400], [127300024330555, 43352558825490, 10825, 99090, 1588, 123124, 800409278691090, 1176932321913600], [64426274048275, 43352558825490, 10825, 99090, 122424, 51867, 800409278691090, 357014781446400], [64426274314555, 43352558825490, 10825, 99090, 1588, 123124, 800409278691090, 357014781446400], [64426274165639, 43352558911797, 127441, 185397, 52560, 123124, 800409278777397, 357014781446400], [64426274079332, 43352558825490, 41882, 99090, 52560, 123124, 800409278691090, 357014781446400], [64426274314555, 43352558825490, 10825, 99090, 1588, 123124, 800409278691090, 1176932321913600], [2514838952115475, 737635164636690, 10825, 99090, 52560, 123124, 2197173157903890, 357014781446400]], 'inner_hash': 2043999697674719391, 'inner_nilpotent': False, 'inner_order': 5832, 'inner_split': False, 'inner_tex': '\\He_3^2:C_2^3', 'inner_used': [1, 2, 3, 4, 5, 7, 8], 'irrC_degree': 36, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 36, 'irrep_stats': [[1, 8], [2, 24], [4, 18], [6, 8], [8, 4], [12, 8], [24, 2], [36, 2]], 'label': '5832.od', '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': True, 'name': 'He3^2:C2^3', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 74, 'number_divisions': 74, 'number_normal_subgroups': 91, 'number_subgroup_autclasses': 973, 'number_subgroup_classes': 2110, 'number_subgroups': 78280, 'old_label': None, 'order': 5832, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 423], [3, 728], [6, 4680]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 5511392510665], 'outer_gens': [[127300024064275, 85017558627090, 10825, 99090, 52560, 123124, 2197173157903890, 357014781446400], [89121125592690, 43352558999166, 153460181145600, 43352558726400, 2853794339020800, 800409278592000, 43352558778267, 127441]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 24], [4, 18], [6, 8], [8, 4], [12, 8], [24, 2], [36, 2]], 'representations': {'PC': {'code': '16597436444236989042796985809208377612318165984759996457749006770298561647', 'gens': [1, 2, 4, 5, 7, 8, 9], 'pres': [9, -2, -2, -3, -3, -2, -3, -3, -3, -3, 35173, 46, 218, 35436, 17625, 81823, 22297, 130, 126374, 53483, 34035, 3066, 1374, 2635, 314936, 157481]}, 'Perm': {'d': 18, 'gens': [64426274048275, 43352558825490, 10825, 99090, 52560, 123124, 800409278691090, 357014781446400]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\He_3^2:C_2^3', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 3], 'aut_gens': [[25, 3, 144], [25, 3, 243], [25, 147, 144], [122, 3, 144]], 'aut_group': '432.734', 'aut_hash': 734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 432, 'aut_permdeg': 9, 'aut_perms': [42648, 223305, 287216], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)', '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': 24, 'autcentquo_group': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 2, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '18.4', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 7, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '18.4', 'hash': 4, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3], 'inner_gens': [[25, 4, 240], [29, 3, 144], [265, 3, 144]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': False, 'inner_tex': 'C_3:S_3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [2, 4]], 'label': '18.4', 'linC_count': 6, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 6, 'linQ_dim': 4, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:S3', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 6, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 12, 'number_subgroups': 28, 'old_label': None, 'order': 18, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 9], [3, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [0, 0, 25, 25], 'outer_gens': [[25, 3, 243], [25, 240, 243], [25, 243, 244], [25, 240, 3]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 4]], 'representations': {'PC': {'code': 5475, 'gens': [1, 2, 3], 'pres': [3, -2, -3, -3, 25, 110]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26483560, 35931151, 16858733]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [11017, 8101, 13933]}, 'Perm': {'d': 6, 'gens': [25, 3, 144]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:S_3', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
