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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4135', 'ambient_counter': 4135, 'ambient_order': 1344, 'ambient_tex': 'D_{84}.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4135.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.64', 'subgroup_hash': 64, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.4135', 'aut_centralizer_order': 24, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '112.c1.a1', 'complements': ['336.l1.a1', '336.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.v1.a1', '12.c1.a1', '28.i1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [992, 3675, 7118, 6759, 4049, 3823, 8434, 5143], 'generators': [6, 192, 448, 344, 336, 672], 'label': '1344.4135.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '672.716', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.29'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 2, 2, 6, 28], 'aut_gens': [[1, 4], [1, 116], [3, 4], [1, 172], [1, 124], [325, 4]], 'aut_group': '1344.11434', 'aut_hash': 11434, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1344, 'aut_permdeg': 58, 'aut_perms': [44112101040, 330006797574848558418396986469743355577451989511382572826947564474221583252400, 65475462328490265990823613057227565670844974235809284938941532672684806, 1828576021971420295879971921266764212983700503954280305853656140158001740969, 308301989074160818067810561335169293942704237457314240043425437056103329751046], 'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [7, 2, 3, 1], [8, 14, 4, 1], [12, 1, 4, 1], [12, 2, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [21, 2, 6, 1], [24, 14, 8, 1], [28, 2, 6, 2], [42, 2, 6, 1], [42, 2, 12, 1], [84, 2, 12, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times D_4\\times F_7', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [3, 1, 2], [4, 1, 2], [4, 2, 1], [6, 1, 2], [6, 2, 2], [7, 2, 3], [8, 14, 4], [12, 1, 4], [12, 2, 2], [14, 2, 9], [21, 2, 6], [24, 14, 8], [28, 2, 12], [42, 2, 18], [84, 2, 24]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '28.3', 'commutator_count': 1, 'commutator_label': '14.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 64, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['112.9', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [7, 2, 3, 1], [8, 14, 2, 2], [12, 1, 4, 1], [12, 2, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [21, 2, 6, 1], [24, 14, 4, 2], [28, 2, 6, 2], [42, 2, 6, 1], [42, 2, 12, 1], [84, 2, 12, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 168, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[2, 0, 24]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '84.12', 'hash': 64, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 14], 'inner_gens': [[1, 220], [121, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 28, 'inner_split': True, 'inner_tex': 'D_{14}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 4, 'irrep_stats': [[1, 24], [2, 78]], 'label': '336.64', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 16, 'linQ_dim': 12, 'linQ_dim_count': 8, 'linR_count': 12, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C21:OD16', 'ngens': 6, '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': 22, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 102, 'number_divisions': 24, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 40, 'number_subgroups': 80, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [7, 6], [8, 56], [12, 8], [14, 18], [21, 12], [24, 112], [28, 24], [42, 36], [84, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 172], [3, 4], [1, 116], [85, 76]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [24, 3628800, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 3], [6, 4], [8, 1], [12, 4], [24, 1], [48, 1]], 'representations': {'PC': {'code': 39831444146142160693064678605259, 'gens': [1, 3], 'pres': [6, -2, -2, -2, -2, -3, -7, 12, 1015, 3962, 50, 2499, 69, 6244, 118, 10373]}, 'GLFp': {'d': 2, 'p': 337, 'gens': [202874, 6621186419, 11328735115]}, 'Perm': {'d': 18, 'gens': [21010447186983, 2309, 3991680, 13294, 17764, 397707843456000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{21}:\\OD_{16}', 'transitive_degree': 168, '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': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 12, 84, 4, 6, 12, 6, 6], 'aut_gens': [[1, 2, 4, 16], [1, 242, 4, 592], [1017, 1282, 564, 176], [1, 82, 572, 16], [1, 530, 4, 656], [673, 898, 900, 976], [1017, 946, 900, 976], [345, 786, 1132, 880], [1, 130, 908, 880]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 84, 'aut_perms': [2677739078108393814816345070188290856478561616022066779489036545486103302805928990939977855528798843433557932296606572501665747, 1035610925777756332574153344512798722179633759599700373831944666917262380600755147944695676226105260842804545273333796754033277, 1389086311979106995200159380714444819511322699754878325974361161216046003661841255267052728014096793223015057927396311847913027, 2113360648837743589239582024693347285232360052232628319069927840799804878181512945599755823596129740217742685838580667757853099, 1129354403411297271196962859805053924653428240761863527982814689110752991535444375483656812122403756010012636513582879813745213, 1393364521179949417705641319616508088960407434780219626635388838688287201087857288458458554791765789361497816957076841847785806, 1515294691860069897896194577945373605037415740437115530822575490388878925036655321240223719367404808290149667791912925433753259, 687334268038415257231306135473843118207481005204465576847416865517969397928639394752960399004712717872086516302454544055353406], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 84, 1, 1], [2, 84, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 12, 2, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 8, 1, 1], [7, 2, 3, 1], [8, 24, 1, 1], [8, 56, 1, 1], [12, 4, 1, 2], [12, 8, 1, 1], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 3, 1], [21, 4, 3, 1], [24, 56, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 8, 3, 1], [28, 12, 12, 1], [42, 4, 3, 1], [42, 8, 3, 1], [42, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [84, 8, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 6896085666905541017, 'autcentquo_nilpotent': False, 'autcentquo_order': 4032, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 84, 3], [3, 2, 1], [4, 2, 2], [4, 4, 1], [4, 12, 2], [4, 56, 1], [4, 84, 1], [6, 2, 1], [6, 4, 1], [6, 8, 1], [7, 2, 3], [8, 24, 1], [8, 56, 1], [12, 4, 2], [12, 8, 1], [12, 56, 2], [14, 2, 3], [14, 4, 3], [14, 8, 3], [21, 4, 3], [24, 56, 2], [28, 2, 6], [28, 4, 3], [28, 8, 3], [28, 12, 12], [42, 4, 3], [42, 8, 9], [56, 24, 6], [84, 4, 6], [84, 8, 9]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.716', 'commutator_count': 2, 'commutator_label': '168.39', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4135, '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, 1], [2, 84, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 12, 2, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 8, 1, 1], [7, 2, 3, 1], [8, 24, 1, 1], [8, 56, 1, 1], [12, 4, 1, 2], [12, 8, 1, 1], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 3, 1], [21, 4, 3, 1], [24, 56, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 8, 3, 1], [28, 12, 12, 1], [42, 4, 3, 1], [42, 8, 3, 1], [42, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [84, 8, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 4135, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 4, 42], 'inner_gens': [[1, 2, 348, 16], [1, 2, 340, 1328], [1017, 1010, 4, 464], [1, 34, 900, 16]], 'inner_hash': 716, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 38], [4, 46], [8, 7]], 'label': '1344.4135', 'linC_count': 96, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 16, 'linQ_dim_count': 16, 'linR_count': 6, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D84.D4', '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': 39, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 99, 'number_divisions': 40, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': 260, 'number_subgroup_classes': 304, 'number_subgroups': 3684, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 259], [3, 2], [4, 172], [6, 14], [7, 6], [8, 80], [12, 128], [14, 42], [21, 12], [24, 112], [28, 192], [42, 84], [56, 144], [84, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 1016, 0], 'outer_gens': [[1, 2, 4, 464], [1, 2, 676, 16], [345, 2, 4, 16], [1, 2, 4, 976]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [744, 3628800, 40320, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [6, 4], [8, 2], [12, 8], [24, 2], [48, 2]], 'representations': {'PC': {'code': 32639098440752706938142447961932465854551402367030580775744523, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 8354, 4090, 66, 21763, 10891, 26572, 4660, 116, 31501, 11157, 141, 35854, 7190, 222, 36879]}, 'Perm': {'d': 26, 'gens': [621574835364785858272100, 358855046710913, 4577091886668, 5976703744631, 7371371332511, 8785582767242, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{84}.D_4', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
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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}
