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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.l', 'ambient_counter': 12, 'ambient_order': 5280, 'ambient_tex': 'C_{24}:C_2\\times F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 11, 'counter': 234, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '5280.l.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.781', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 781, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}:D_6', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
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gps_subgroup_data • Show schema
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{'ambient': '5280.l', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10.d1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.b1.a1', '240.b1.b1', '240.c1.a1', '240.d1.a1'], 'contains': ['5280.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1174, 1597, 8512, 1939, 1331, 2245, 8147, 2235], 'generators': [480], 'label': '5280.l.480.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.b1.a1', '240.b1.b1'], 'normal_contains': ['5280.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '5280.l', 'quotient_action_image': '10.2', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '11.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 10, 'aut_gen_orders': [10], 'aut_gens': [[1], [2]], 'aut_group': '10.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 10, 'aut_permdeg': 7, 'aut_perms': [753], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [11, 1, 10, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{10}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', '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], [11, 1, 10]], 'center_label': '11.1', 'center_order': 11, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['11.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [11, 1, 10, 1]], 'element_repr_type': 'PC', 'elementary': 11, 'eulerian_function': 1, 'exponent': 11, 'exponents_of_order': [1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [11], 'faithful_reps': [[1, 0, 10]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '11.1', 'hash': 1, 'hyperelementary': 11, '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': 10, 'irrQ_dim': 10, 'irrR_degree': 2, 'irrep_stats': [[1, 11]], 'label': '11.1', 'linC_count': 10, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 5, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 11, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 11, 'order_factorization_type': 1, 'order_stats': [[1, 1], [11, 10]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [10], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '10.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 10, 'outer_permdeg': 7, 'outer_perms': [753], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{10}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 11, 'pgroup': 11, 'primary_abelian_invariants': [11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [10, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -11]}, 'Lie': [{'d': 1, 'q': 11, 'gens': [4037913], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 11, 'gens': [1343]}, 'Perm': {'d': 11, 'gens': [36288000]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [11], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}', 'transitive_degree': 11, '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 10, 10, 10, 20, 60, 30], 'aut_gens': [[1, 10, 20], [3121, 4250, 4300], [3121, 810, 4660], [1681, 5050, 1700], [1681, 4010, 4060], [4801, 3570, 2020], [3601, 4850, 1220], [3841, 1410, 2540]], 'aut_group': None, 'aut_hash': 5956886757194812668, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 38, 'aut_perms': [334784766771750714765567746750204820611589375, 10212800402108678825526549856042727626254411, 358529843608810321782796320526048808124924089, 482472868688125166741347152976637663836434582, 368890856753190538917988343212023462760358644, 362864636238509311977018059360820296313007280, 336128383470905682413776866880492065784532633], 'aut_phi_ratio': 16.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [2, 12, 1, 1], [2, 132, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 12, 1, 1], [4, 22, 1, 1], [4, 132, 1, 1], [5, 11, 1, 4], [6, 2, 1, 1], [6, 22, 2, 1], [8, 2, 2, 1], [8, 22, 2, 1], [10, 11, 1, 4], [10, 11, 2, 4], [10, 132, 1, 8], [11, 10, 1, 1], [12, 2, 2, 1], [12, 22, 2, 1], [15, 22, 1, 4], [20, 22, 1, 8], [20, 132, 1, 8], [22, 10, 1, 1], [22, 120, 1, 1], [24, 2, 4, 1], [24, 22, 4, 1], [30, 22, 1, 4], [30, 22, 2, 4], [33, 20, 1, 1], [40, 22, 2, 8], [44, 20, 1, 1], [44, 120, 1, 1], [60, 22, 2, 8], [66, 20, 1, 1], [88, 20, 2, 1], [120, 22, 4, 8], [132, 20, 2, 1], [264, 20, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{66}.C_{10}.C_2^5', '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': 330, 'autcentquo_group': None, 'autcentquo_hash': 4845733366138083661, 'autcentquo_nilpotent': False, 'autcentquo_order': 2640, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{11}:(C_2^2\\times C_{10}\\times S_3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [2, 12, 1], [2, 132, 1], [3, 2, 1], [4, 2, 1], [4, 12, 1], [4, 22, 1], [4, 132, 1], [5, 11, 4], [6, 2, 1], [6, 22, 2], [8, 2, 2], [8, 22, 2], [10, 11, 12], [10, 132, 8], [11, 10, 1], [12, 2, 2], [12, 22, 2], [15, 22, 4], [20, 22, 8], [20, 132, 8], [22, 10, 1], [22, 120, 1], [24, 2, 4], [24, 22, 4], [30, 22, 12], [33, 20, 1], [40, 22, 16], [44, 20, 1], [44, 120, 1], [60, 22, 16], [66, 20, 1], [88, 20, 2], [120, 22, 32], [132, 20, 2], [264, 20, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '2640.x', 'commutator_count': 1, 'commutator_label': '132.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['110.1', 1], ['48.6', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [2, 12, 1, 1], [2, 132, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 12, 1, 1], [4, 22, 1, 1], [4, 132, 1, 1], [5, 11, 4, 1], [6, 2, 1, 1], [6, 22, 1, 2], [8, 2, 2, 1], [8, 22, 2, 1], [10, 11, 4, 3], [10, 132, 4, 2], [11, 10, 1, 1], [12, 2, 2, 1], [12, 22, 2, 1], [15, 22, 4, 1], [20, 22, 4, 2], [20, 132, 4, 2], [22, 10, 1, 1], [22, 120, 1, 1], [24, 2, 4, 1], [24, 22, 4, 1], [30, 22, 4, 3], [33, 20, 1, 1], [40, 22, 8, 2], [44, 20, 1, 1], [44, 120, 1, 1], [60, 22, 8, 2], [66, 20, 1, 1], [88, 20, 2, 1], [120, 22, 16, 2], [132, 20, 2, 1], [264, 20, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1999872, 'exponent': 1320, 'exponents_of_order': [5, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[20, 0, 4]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '1320.142', 'hash': 3340380322487147873, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 660, 'inner_gen_orders': [10, 2, 132], 'inner_gens': [[1, 1450, 3860], [3841, 10, 2620], [1441, 2690, 20]], 'inner_hash': 1114821233248874711, 'inner_nilpotent': False, 'inner_order': 2640, 'inner_split': True, 'inner_tex': 'D_{12}\\times F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 20, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 40, 'irrep_stats': [[1, 40], [2, 110], [10, 4], [20, 11]], 'label': '5280.l', 'linC_count': 160, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 32, 'linQ_dim': 16, 'linQ_dim_count': 32, 'linR_count': 80, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24:C2*F11', '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, 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': 100, 'number_characteristic_subgroups': 69, 'number_conjugacy_classes': 165, 'number_divisions': 50, 'number_normal_subgroups': 77, 'number_subgroup_autclasses': 256, 'number_subgroup_classes': 272, 'number_subgroups': 4136, 'old_label': None, 'order': 5280, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 167], [3, 2], [4, 168], [5, 44], [6, 46], [8, 48], [10, 1188], [11, 10], [12, 48], [15, 88], [20, 1232], [22, 130], [24, 96], [30, 264], [33, 20], [40, 352], [44, 140], [60, 352], [66, 20], [88, 40], [120, 704], [132, 40], [264, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 490, 2180], [2641, 490, 4820], [1, 490, 1300]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 12], [8, 8], [10, 4], [16, 4], [20, 3], [32, 2], [40, 2], [80, 1]], 'representations': {'PC': {'code': '46322998854108250826595521280476493151650528079774433168774427595788748881483859469375884103000019', 'gens': [1, 3, 4], 'pres': [8, -2, -5, -2, -2, -2, -2, -3, -11, 16, 34802, 57730, 123523, 8011, 8403, 91, 97604, 20012, 20980, 116, 234245, 48013, 24981, 141, 250886, 112014, 28694, 222, 184327, 46095, 30743]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [31471887339564514, 44892999667169041, 15858444949379930, 26934596962789267, 29311048591218838, 9794019781044287, 32390444358457867, 41772741070013040]}, 'Perm': {'d': 22, 'gens': [10463720175840647544, 61328800643894784000, 112805267711768755200, 158145787614360268803, 216657398669661348000, 270067105113437238506, 104885904124511604024, 3719544]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:C_2\\times F_{11}', 'transitive_degree': 264, '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 4, 4, 12, 4, 12, 2], 'aut_gens': [[1, 2, 4], [243, 242, 166], [241, 2, 246], [281, 242, 356], [361, 242, 268], [401, 2, 54], [243, 242, 390], [203, 2, 244], [283, 242, 356]], 'aut_group': None, 'aut_hash': 8810918569713110060, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 36, 'aut_perms': [10622321338897468774444418259490098496535, 95743914216904934974882323197813174164294, 242821220515740931399374064797153123574085, 30709468908519970097870779497528994316999, 86287783443809311505081252607009834938855, 30706837113537532399770967001508107389895, 339152445377233597690130284954325908095288, 338850104862211974855440262806008467960941], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 12, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 2, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [8, 2, 4, 1], [10, 1, 4, 1], [10, 1, 8, 1], [10, 12, 8, 1], [12, 2, 2, 2], [15, 2, 4, 1], [20, 2, 4, 2], [20, 12, 8, 1], [24, 2, 8, 1], [30, 2, 4, 1], [30, 2, 8, 1], [40, 2, 16, 1], [60, 2, 8, 2], [120, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^5.C_2^5)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1031', 'autcent_hash': 1031, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3.C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 12, 2], [3, 2, 1], [4, 2, 2], [4, 12, 2], [5, 1, 4], [6, 2, 3], [8, 2, 4], [10, 1, 12], [10, 12, 8], [12, 2, 4], [15, 2, 4], [20, 2, 8], [20, 12, 8], [24, 2, 8], [30, 2, 12], [40, 2, 16], [60, 2, 16], [120, 2, 32]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '24.6', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 781, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['48.6', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 1, 2], [5, 1, 4, 1], [6, 2, 1, 3], [8, 2, 2, 2], [10, 1, 4, 3], [10, 12, 4, 2], [12, 2, 2, 2], [15, 2, 4, 1], [20, 2, 4, 2], [20, 12, 4, 2], [24, 2, 4, 2], [30, 2, 4, 3], [40, 2, 8, 2], [60, 2, 8, 2], [120, 2, 16, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10416, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '120.45', 'hash': 781, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 12], 'inner_gens': [[1, 2, 44], [1, 2, 4], [441, 2, 4]], 'inner_hash': 6, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'D_{12}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 110]], 'label': '480.781', 'linC_count': 768, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 48, 'linQ_dim': 10, 'linQ_dim_count': 48, 'linR_count': 64, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C40:D6', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 150, 'number_divisions': 40, 'number_normal_subgroups': 66, 'number_subgroup_autclasses': 92, 'number_subgroup_classes': 136, 'number_subgroups': 388, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 27], [3, 2], [4, 28], [5, 4], [6, 6], [8, 8], [10, 108], [12, 8], [15, 8], [20, 112], [24, 16], [30, 24], [40, 32], [60, 32], [120, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 196], [1, 2, 6], [3, 2, 364], [3, 2, 388], [1, 242, 438]], 'outer_group': '128.2154', 'outer_hash': 2154, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [40285008, 127375920, 40279681, 361, 87454369], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 12], [8, 8], [16, 4], [32, 2]], 'representations': {'PC': {'code': 103575408747352717435545311969287, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -5, 926, 58, 2467, 80, 6164, 102, 14789, 166]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1554040531, 228508994, 1755695563, 1346180548, 857494092, 1714988184, 1080409187]}, 'Perm': {'d': 18, 'gens': [5511392410320, 358477173694080, 777033561427200, 33, 1156090040582400, 358477173331200, 5760]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{40}:D_6', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
