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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2061', 'ambient_counter': 2061, 'ambient_order': 1728, 'ambient_tex': 'C_4.D_8\\times \\He_3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2061.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.2061', 'aut_centralizer_order': 27648, 'aut_label': '72.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 27648, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.a1', '36.e1', '36.f1'], 'contains': ['144.a1', '144.d1', '144.e1', '216.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2351, 5137, 3747, 1741], 'generators': [438, 864, 48, 72], 'label': '1728.2061.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['24.b1', '36.a1'], 'normal_contains': ['144.a1', '144.d1', '144.e1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '144.102', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.14', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2], 'aut_gens': [[1, 2], [13, 2], [1, 23], [1, 10], [1, 14]], 'aut_group': '16.11', 'aut_hash': 11, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 6, 'aut_perms': [288, 6, 127, 126], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [12, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', '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], [3, 1, 2], [4, 1, 4], [6, 1, 6], [12, 1, 8]], 'center_label': '24.9', 'center_order': 24, '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', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 2], [6, 1, 2, 3], [12, 1, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 12, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '12.5', 'hash': 9, '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, 24]], 'label': '24.9', 'linC_count': 96, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 4, 'linQ_dim': 4, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C12', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 24, 'number_divisions': 12, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [12, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[13, 2], [1, 23], [1, 10], [1, 14]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 6, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, '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, 2]], 'representations': {'PC': {'code': 221281, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -3, 21, 34]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931072, 26129103]}, 'GLFp': {'d': 2, 'p': 13, 'gens': [10993, 4396]}, 'Perm': {'d': 9, 'gens': [2400, 40320, 4, 744]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{12}', 'transitive_degree': 24, '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': '72.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 12, 4, 12, 4, 12, 6, 8], 'aut_gens': [[1, 12, 144], [195, 1362, 1084], [275, 930, 216], [1135, 948, 1636], [1185, 1380, 1588], [155, 1386, 1084], [1205, 138, 192], [895, 1380, 1104], [583, 492, 1112]], 'aut_group': None, 'aut_hash': 4876081057154083558, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 110592, 'aut_permdeg': 56, 'aut_perms': [567503747706757134363177163256467232719760790152777699175557240574450771802, 185631710113732410161214722549632458901577447274447763049286649306788222524, 14431482769503354801953855283264834317414974299071160413470120790868188789, 7804746504889371727475473319204490135623802088798572199356100246581108034, 403529416702245746222341605546409229134260666411160313658524467597039259842, 23450489971648623650907765676687371766023806659436998797744705750946873838, 497777128800761934785886143711625906545737146113819829635519177033193958470, 397007243892913005960180520852817311569683911366745874038710789613925912530], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 3, 8, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [6, 1, 2, 3], [6, 3, 8, 3], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 6, 8, 4], [12, 8, 4, 1], [12, 12, 8, 1], [12, 24, 16, 1], [24, 4, 8, 2], [24, 12, 32, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times D_4^2\\times \\AGL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '144.197', 'autcent_hash': 197, 'autcent_nilpotent': True, 'autcent_order': 144, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_6^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '768.1090160', 'autcentquo_hash': 1090160, 'autcentquo_nilpotent': False, 'autcentquo_order': 768, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^4\\times \\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 3, 8], [4, 2, 4], [4, 4, 1], [4, 8, 2], [6, 1, 6], [6, 3, 24], [8, 4, 8], [12, 2, 8], [12, 4, 2], [12, 6, 32], [12, 8, 4], [12, 12, 8], [12, 24, 16], [24, 4, 16], [24, 12, 64]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '144.102', 'commutator_count': 1, 'commutator_label': '24.9', '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': 2061, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['27.3', 1], ['64.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 3, 2, 4], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [6, 1, 2, 3], [6, 3, 2, 12], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 6, 2, 16], [12, 8, 2, 2], [12, 12, 2, 4], [12, 24, 2, 8], [24, 4, 8, 2], [24, 12, 8, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 24, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '48.20', 'frattini_quotient': '36.14', 'hash': 2061, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [12, 2, 6], 'inner_gens': [[1, 1380, 168], [505, 12, 1008], [121, 876, 144]], 'inner_hash': 102, 'inner_nilpotent': True, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'C_6^2:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 72], [2, 90], [3, 16], [4, 9], [6, 20], [12, 2]], 'label': '1728.2061', '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': 'C4.D8*He3', 'ngens': 9, 'nilpotency_class': 3, 'nilpotent': True, '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': 36, 'number_characteristic_subgroups': 51, 'number_conjugacy_classes': 209, 'number_divisions': 78, 'number_normal_subgroups': 133, 'number_subgroup_autclasses': 145, 'number_subgroup_classes': 352, 'number_subgroups': 1083, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 28], [6, 78], [8, 32], [12, 728], [24, 832]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 6, 4, 4, 2, 2, 2], 'outer_gen_pows': [1160, 6, 0, 0, 0, 0, 0], 'outer_gens': [[893, 60, 152], [1153, 954, 556], [413, 12, 152], [585, 12, 1352], [943, 12, 1080], [1, 876, 144], [865, 876, 144]], 'outer_group': '768.1090160', 'outer_hash': 1090160, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 16, 'outer_perms': [19679361967, 13499136007, 8396067415680, 2796019793280, 5160, 16, 11520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4\\times \\GL(2,3)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 20], [4, 21], [6, 4], [8, 20], [12, 4], [24, 5]], 'representations': {'PC': {'code': 682248891032104514082966922489967281679955867603957126500814147215902228041, 'gens': [1, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 18, 46, 6338, 49683, 17076, 102, 130, 10590, 6063, 3804, 5325, 186, 24199, 13840, 6073, 214, 54440, 25289, 13634]}, 'Perm': {'d': 25, 'gens': [82154478324727430899200, 677928144599712397036800, 1320859237105390232275200, 45968909011200, 1969256573772393185280000, 1969256573840829584505600, 138838, 276480, 80884]}}, 'schur_multiplier': [3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4.D_8\\times \\He_3', 'transitive_degree': 576, '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': '36.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 3, 2, 2, 2, 4, 4, 2], 'aut_gens': [[1, 6], [63, 56], [29, 56], [37, 6], [7, 66], [41, 30], [11, 10], [59, 30], [23, 66]], 'aut_group': '384.17972', 'aut_hash': 17972, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 12, 'aut_perms': [127019656, 128995200, 16, 806543, 40284856, 175800378, 18, 7], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [3, 1, 8, 1], [4, 2, 1, 1], [6, 1, 8, 1], [6, 2, 16, 1], [12, 2, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '192.1475', 'autcent_hash': 1475, 'autcent_nilpotent': False, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^2\\times \\GL(2,3)', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [3, 1, 8], [4, 2, 1], [6, 1, 8], [6, 2, 16], [12, 2, 8]], 'center_label': '18.5', 'center_order': 18, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 37, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 2], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [3, 1, 2, 4], [4, 2, 1, 1], [6, 1, 2, 4], [6, 2, 2, 8], [12, 2, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 12, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '36.14', 'hash': 37, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 42], [37, 6]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 36], [2, 9]], 'label': '72.37', 'linC_count': 192, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 144, 'linQ_dim': 6, 'linQ_dim_count': 144, 'linR_count': 144, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D4*C3^2', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 45, 'number_divisions': 25, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 48, 'number_subgroups': 60, 'old_label': None, 'order': 72, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 5], [3, 8], [4, 2], [6, 40], [12, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [3, 2, 2, 2, 4, 4], 'outer_gen_pows': [0, 0, 6, 6, 0, 0], 'outer_gens': [[27, 32], [27, 58], [19, 6], [23, 30], [43, 34], [29, 10]], 'outer_group': '96.189', 'outer_hash': 189, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 10, 'outer_perms': [23040, 363168, 368047, 1, 1641001, 2442654], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 17], [4, 4]], 'representations': {'PC': {'code': 785595237801, 'gens': [1, 3], 'pres': [5, -2, -3, -2, -2, -3, 10, 632, 42, 58]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101746527870476, 41624325034614139]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [34649835, 5774458, 17383742, 5779409, 23068812]}, 'Perm': {'d': 10, 'gens': [806400, 5040, 240, 4, 367920]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 6], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4\\times C_3^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
