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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.5071', 'ambient_counter': 5071, 'ambient_order': 576, 'ambient_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '576.5071.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5071', 'subgroup_hash': 5071, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '576.5071', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1.a1', 'complements': ['576.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1', '4.d1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3928, 3743, 4256, 3883, 2868, 4774, 2747, 4774], 'generators': [3200423, 742666, 597409, 43332947, 7705165, 892585, 25782667, 7960177], 'label': '576.5071.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '288.857', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '288.857'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 6, 3, 2, 4, 2, 3, 2], 'aut_gens': [[3200423, 43332947, 742666, 25782667, 894937], [1546550, 6287162, 13489309, 892585, 25785019], [3200423, 43332947, 25932628, 25782667, 894937], [26440160, 31180772, 25639804, 892585, 25492195], [5017088, 17128268, 25932628, 892585, 25487491], [15941774, 6287162, 1042546, 892585, 25492195], [40835384, 17128268, 38379391, 892585, 25787371], [13698725, 18439421, 13189429, 25782667, 25487491], [28094033, 39949133, 25639804, 25782667, 890233], [3200423, 43335299, 742666, 25782667, 894937], [28094033, 18439421, 1042546, 25782667, 894937]], 'aut_group': '2304.oh', 'aut_hash': 2462485762897143514, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2304, 'aut_permdeg': 36, 'aut_perms': [281678708700761784033851316078973722304483, 7094715076678273814979312277162417236074, 164766717635159300004832916399066340896656, 274584548678427508589910551618717553623324, 318574305899986135450956862116046508353804, 180789426888854019196624224968676551796907, 91548962896463427493588979509741093036906, 120776977109714650740872639369784733669503, 152632331731493222767904773587926823270, 113968815377718309548266843803864839297867], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 24, 2, 2], [12, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '576.8659', 'autcentquo_hash': 8659, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2:D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 2, 1], [4, 6, 1], [4, 12, 1], [4, 24, 2], [4, 36, 1], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 16, 1], [8, 36, 4], [12, 4, 1], [12, 12, 1], [12, 16, 3], [12, 24, 4], [12, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '288.857', 'commutator_count': 2, 'commutator_label': '144.155', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5071, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 24, 2, 2], [12, 48, 2, 1]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, -1, 1]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '144.183', 'hash': 5071, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3, 2, 6], 'inner_gens': [[3200423, 29280443, 13489309, 25782667, 25492195], [17762051, 43332947, 13489309, 25782667, 25487491], [3054011, 43779239, 742666, 25489843, 25785019], [3200423, 43332947, 25932628, 25782667, 894937], [28094033, 18441773, 1042546, 25782667, 894937]], 'inner_hash': 857, 'inner_nilpotent': False, 'inner_order': 288, 'inner_split': True, 'inner_tex': 'D_6:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 11], [3, 4], [4, 6], [6, 7], [12, 1]], 'label': '576.5071', 'linC_count': 44, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 4, 'linQ_dim': 11, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6.GL(2,Z/4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 33, 'number_divisions': 27, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 144, 'number_subgroup_classes': 148, 'number_subgroups': 856, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 26], [4, 104], [6, 38], [8, 144], [12, 256]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [592705, 592705, 592705], 'outer_gens': [[3200423, 15055523, 742666, 25782667, 894937], [3200423, 43332947, 742666, 25782667, 890233], [3200423, 43332947, 13489309, 25782667, 25492195]], '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': 5, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [3, 4], [4, 7], [6, 3], [8, 1], [12, 3]], 'representations': {'PC': {'code': 117398145343420738176562054097031600381741090569, 'gens': [1, 2, 5, 6, 7], 'pres': [8, -2, -2, -2, -2, -3, -2, 2, -3, 64, 225, 41, 290, 66, 1284, 652, 1045, 8070, 14798, 1550, 166, 12303]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [7705165, 17400613, 1042546, 892585, 595057, 25782667, 637573, 3200423]}, 'Perm': {'d': 23, 'gens': [1292878671028637817720, 2460805174576459025282, 3644911634129794062720, 4823231579504271763200, 3, 840, 7, 16]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 144, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 6, 3, 2, 4, 2, 3, 2], 'aut_gens': [[3200423, 43332947, 742666, 25782667, 894937], [1546550, 6287162, 13489309, 892585, 25785019], [3200423, 43332947, 25932628, 25782667, 894937], [26440160, 31180772, 25639804, 892585, 25492195], [5017088, 17128268, 25932628, 892585, 25487491], [15941774, 6287162, 1042546, 892585, 25492195], [40835384, 17128268, 38379391, 892585, 25787371], [13698725, 18439421, 13189429, 25782667, 25487491], [28094033, 39949133, 25639804, 25782667, 890233], [3200423, 43335299, 742666, 25782667, 894937], [28094033, 18439421, 1042546, 25782667, 894937]], 'aut_group': '2304.oh', 'aut_hash': 2462485762897143514, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2304, 'aut_permdeg': 36, 'aut_perms': [281678708700761784033851316078973722304483, 7094715076678273814979312277162417236074, 164766717635159300004832916399066340896656, 274584548678427508589910551618717553623324, 318574305899986135450956862116046508353804, 180789426888854019196624224968676551796907, 91548962896463427493588979509741093036906, 120776977109714650740872639369784733669503, 152632331731493222767904773587926823270, 113968815377718309548266843803864839297867], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 24, 2, 2], [12, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '576.8659', 'autcentquo_hash': 8659, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2:D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 2, 1], [4, 6, 1], [4, 12, 1], [4, 24, 2], [4, 36, 1], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 16, 1], [8, 36, 4], [12, 4, 1], [12, 12, 1], [12, 16, 3], [12, 24, 4], [12, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '288.857', 'commutator_count': 2, 'commutator_label': '144.155', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5071, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 24, 2, 2], [12, 48, 2, 1]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, -1, 1]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '144.183', 'hash': 5071, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3, 2, 6], 'inner_gens': [[3200423, 29280443, 13489309, 25782667, 25492195], [17762051, 43332947, 13489309, 25782667, 25487491], [3054011, 43779239, 742666, 25489843, 25785019], [3200423, 43332947, 25932628, 25782667, 894937], [28094033, 18441773, 1042546, 25782667, 894937]], 'inner_hash': 857, 'inner_nilpotent': False, 'inner_order': 288, 'inner_split': True, 'inner_tex': 'D_6:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 11], [3, 4], [4, 6], [6, 7], [12, 1]], 'label': '576.5071', 'linC_count': 44, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 4, 'linQ_dim': 11, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6.GL(2,Z/4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 33, 'number_divisions': 27, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 144, 'number_subgroup_classes': 148, 'number_subgroups': 856, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 26], [4, 104], [6, 38], [8, 144], [12, 256]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [592705, 592705, 592705], 'outer_gens': [[3200423, 15055523, 742666, 25782667, 894937], [3200423, 43332947, 742666, 25782667, 890233], [3200423, 43332947, 13489309, 25782667, 25492195]], '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': 5, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [3, 4], [4, 7], [6, 3], [8, 1], [12, 3]], 'representations': {'PC': {'code': 117398145343420738176562054097031600381741090569, 'gens': [1, 2, 5, 6, 7], 'pres': [8, -2, -2, -2, -2, -3, -2, 2, -3, 64, 225, 41, 290, 66, 1284, 652, 1045, 8070, 14798, 1550, 166, 12303]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [7705165, 17400613, 1042546, 892585, 595057, 25782667, 637573, 3200423]}, 'Perm': {'d': 23, 'gens': [1292878671028637817720, 2460805174576459025282, 3644911634129794062720, 4823231579504271763200, 3, 840, 7, 16]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 144, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
