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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47887', 'ambient_counter': 47887, 'ambient_order': 1728, 'ambient_tex': 'D_6^2:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 4, 'counter': 387, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1728.47887.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '432.741', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 741, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^3:C_2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.47887', 'aut_centralizer_order': 55296, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 55296, 'centralizer': '1.a1', 'complements': ['4.k1'], 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.s1', '144.t1', '216.k1', '216.l1', '216.m1', '216.n1', '216.o1'], 'contains': ['864.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8703, 9771, 8515, 9894], 'generators': [16, 7], 'label': '1728.47887.432.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '432.a1', 'normal_contained_in': ['48.c1', '144.b1'], 'normal_contains': ['864.a1'], 'normalizer': '1.a1', 'old_label': '432.a1', 'projective_image': '432.741', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.741', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [12, 6, 24, 8, 12], 'aut_gens': [[362887, 486984960, 127, 7, 16, 11652480, 840, 83825280, 1089043200], [123742096, 486984960, 1560, 7, 23, 1078116480, 840, 83825280, 1089043200], [11289616, 1520507527, 736, 16, 23, 131362560, 840, 2435328000, 1089043200], [1520507527, 11289607, 743, 16, 23, 131362560, 840, 2554715520, 123379200], [1520507527, 997920023, 127, 7, 16, 1037836800, 840, 1049489280, 83825280], [1607598727, 2438956800, 127, 23, 7, 2522419200, 1440, 2515484160, 83825280]], 'aut_group': None, 'aut_hash': 4618254056760348283, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 60, 'aut_perms': [6225660698933531137801464931402414354640963393391331380856491951112675320942231856, 7386100241072175180498420285727339866163393747650368981841048487880251189729460369, 8289729471512072658489551602031562963019611869365666722384840378000285646261714613, 2992355622483418469503920048129531518736094933398423098836368281845466020766106039, 1109213467067641415755695794701606012671933418291032862024665362967486648581907628], 'aut_phi_ratio': 576.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 4, 1], [2, 6, 8, 1], [2, 9, 1, 1], [2, 9, 3, 1], [2, 18, 8, 1], [2, 27, 4, 1], [3, 2, 1, 1], [3, 4, 2, 1], [3, 8, 2, 1], [4, 18, 4, 1], [4, 54, 4, 1], [6, 2, 3, 1], [6, 4, 6, 1], [6, 8, 6, 1], [6, 12, 8, 3], [6, 18, 1, 1], [6, 18, 3, 1], [6, 24, 8, 1], [6, 36, 8, 1], [12, 36, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_2^4:C_3.C_4.C_2^3\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '384.20164', 'autcent_hash': 20164, 'autcent_nilpotent': False, 'autcent_order': 384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.4662', 'autcentquo_hash': 4662, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 6, 8], [2, 9, 4], [2, 18, 8], [2, 27, 4], [3, 2, 1], [3, 4, 2], [3, 8, 2], [4, 18, 4], [4, 54, 4], [6, 2, 3], [6, 4, 6], [6, 8, 6], [6, 12, 24], [6, 18, 4], [6, 24, 8], [6, 36, 8], [12, 36, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '432.741', 'commutator_count': 1, 'commutator_label': '54.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 47887, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['6.1', 1], ['72.40', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 6, 1, 8], [2, 9, 1, 4], [2, 18, 1, 8], [2, 27, 1, 4], [3, 2, 1, 1], [3, 4, 1, 2], [3, 8, 1, 2], [4, 18, 1, 4], [4, 54, 1, 4], [6, 2, 1, 3], [6, 4, 1, 6], [6, 8, 1, 6], [6, 12, 1, 24], [6, 18, 1, 4], [6, 24, 1, 8], [6, 36, 1, 8], [12, 36, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 13665792000, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1728.47887', 'hash': 47887, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 1, 1, 2, 3, 3, 3], 'inner_gens': [[362887, 482670720, 127, 7, 16, 11652480, 840, 123379200, 1049489280], [11289607, 486984960, 127, 7, 16, 11652480, 840, 2435328000, 1089043200], [362887, 486984960, 127, 7, 16, 11652480, 1440, 83825280, 1089043200], [362887, 486984960, 127, 7, 16, 11652480, 840, 83825280, 1089043200], [362887, 486984960, 127, 7, 16, 11652480, 840, 83825280, 1089043200], [362887, 486984960, 127, 7, 16, 11652480, 840, 123379200, 2515484160], [362887, 486984960, 1567, 7, 16, 11652480, 840, 83825280, 1089043200], [123742087, 1520507520, 127, 7, 16, 131362560, 840, 83825280, 1089043200], [83462407, 486984960, 127, 7, 16, 2522419200, 840, 83825280, 1089043200]], 'inner_hash': 741, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': False, 'inner_tex': 'S_3^3:C_2', 'inner_used': [1, 2, 3, 7, 8], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 24], [4, 36], [8, 16]], 'label': '1728.47887', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, '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': 'D6^2:D6', 'ngens': 9, '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': 24, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 108, 'number_divisions': 108, 'number_normal_subgroups': 524, 'number_subgroup_autclasses': 414, 'number_subgroup_classes': 4488, 'number_subgroups': 48776, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 351], [3, 26], [4, 288], [6, 918], [12, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 11652480, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[362887, 486984960, 127, 23, 16, 11652480, 840, 83825280, 1089043200], [486984960, 362887, 127, 7, 16, 11652480, 840, 2554715520, 2435328000], [362887, 486984960, 127, 16, 23, 11652480, 840, 83825280, 1089043200], [362887, 486984960, 120, 7, 16, 11652480, 840, 83825280, 1089043200], [362887, 486984960, 143, 7, 16, 11652480, 840, 83825280, 1089043200], [362887, 486984967, 120, 7, 16, 11652480, 840, 83825280, 1089043200], [362887, 486984976, 143, 7, 16, 11652480, 840, 83825280, 1089043200], [362880, 486984967, 127, 7, 16, 11652480, 840, 83825280, 1089043200], [362903, 486984976, 127, 7, 16, 11652480, 840, 83825280, 1089043200]], 'outer_group': '768.1090070', 'outer_hash': 1090070, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [11291165, 135732240, 4395723, 7, 16, 85800, 127440, 40723320, 90842400], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5:S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 24], [4, 36], [8, 16]], 'representations': {'PC': {'code': 341934734845687005736713618016567599462075741384627401668787783291925, 'gens': [1, 2, 4, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 109, 46, 22179, 11100, 381, 102, 53284, 26653, 382, 1652, 158, 1545, 10960, 25945, 214, 24641, 23354]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101743041089724, 125101729074815868, 24992906222183252, 108378800778157813, 91793130888343612]}, 'Perm': {'d': 13, 'gens': [362887, 486984960, 127, 7, 16, 11652480, 840, 83825280, 1089043200]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6^2:D_6', 'transitive_degree': 48, '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': 3, 'aut_exponent': 24, 'aut_gen_orders': [4, 3, 6, 3, 3, 2, 4, 2], 'aut_gens': [[1, 41064, 264, 1680, 11064, 87240, 3], [1, 10800, 138240, 177960, 103080, 92400, 3], [1, 212664, 10800, 11520, 11064, 87240, 3], [1, 212664, 85680, 100944, 166440, 20904, 4], [5, 41064, 10800, 90720, 11064, 87240, 3], [1, 41064, 10800, 90720, 11064, 87240, 3], [1, 41064, 264, 1680, 20904, 166440, 4], [1, 85680, 224184, 85944, 181440, 103080, 3], [1, 138240, 10800, 177960, 20904, 166440, 3]], 'aut_group': '864.4662', 'aut_hash': 4662, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 864, 'aut_permdeg': 15, 'aut_perms': [1059121783805, 4843213248, 501652445308, 171935260431, 171571981407, 84408625643, 384318281547, 1230171637857], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 2, 1], [2, 9, 1, 1], [2, 18, 2, 1], [2, 27, 1, 1], [3, 2, 1, 1], [3, 4, 2, 1], [3, 8, 2, 1], [4, 18, 1, 1], [4, 54, 1, 1], [6, 12, 2, 3], [6, 18, 1, 1], [6, 24, 2, 1], [6, 36, 2, 1], [12, 36, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_9:D_6', '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': '864.4662', 'autcentquo_hash': 4662, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 6, 2], [2, 9, 1], [2, 18, 2], [2, 27, 1], [3, 2, 1], [3, 4, 2], [3, 8, 2], [4, 18, 1], [4, 54, 1], [6, 12, 6], [6, 18, 1], [6, 24, 2], [6, 36, 2], [12, 36, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '432.741', 'commutator_count': 1, 'commutator_label': '54.13', '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': 741, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['6.1', 1], ['72.40', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 9, 1, 1], [2, 18, 1, 2], [2, 27, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 8, 1, 2], [4, 18, 1, 1], [4, 54, 1, 1], [6, 12, 1, 6], [6, 18, 1, 1], [6, 24, 1, 2], [6, 36, 1, 2], [12, 36, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 26880, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '432.741', 'hash': 741, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 2, 3, 3, 3], 'inner_gens': [[1, 41064, 264, 1680, 11064, 87240, 4], [1, 41064, 1560, 1680, 87240, 11064, 3], [1, 42744, 264, 1680, 20904, 87240, 3], [1, 41064, 264, 1680, 20904, 166440, 3], [1, 138240, 21024, 22584, 11064, 87240, 3], [1, 212664, 264, 167280, 11064, 87240, 3], [5, 41064, 264, 1680, 11064, 87240, 3]], 'inner_hash': 741, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': False, 'inner_tex': 'S_3^3:C_2', 'inner_used': [1, 2, 3, 5, 7], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 6], [4, 9], [8, 4]], 'label': '432.741', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 32, 'linQ_dim': 6, 'linQ_dim_count': 32, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'S3^3:C2', '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': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 27, 'number_divisions': 27, 'number_normal_subgroups': 28, 'number_subgroup_autclasses': 118, 'number_subgroup_classes': 192, 'number_subgroups': 1720, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 87], [3, 26], [4, 72], [6, 210], [12, 36]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [1680], 'outer_gens': [[1, 264, 41064, 1680, 176664, 181440, 3]], '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': 5, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 9], [8, 4]], 'representations': {'PC': {'code': 3916244387391620486288320144628893191, 'gens': [1, 2, 3, 6, 7], 'pres': [7, -2, -2, -2, -2, -3, -3, 3, 422, 303, 58, 1123, 80, 1124, 2539, 530, 9421, 2372, 1791]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101736038818732, 125124605862489321, 58301506734280708]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [1305911, 16002800, 16262215, 13129115, 29655964, 42892023, 13131383]}, 'Perm': {'d': 9, 'gens': [1, 41064, 264, 1680, 11064, 87240, 3]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3^3:C_2', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
