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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3494', 'ambient_counter': 3494, 'ambient_order': 1296, 'ambient_tex': 'S_3^3:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3494.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1296.3494', 'aut_centralizer_order': 1, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1296.3490', 'aut_weyl_index': 2, 'centralizer': '648.a1.a1', 'complements': ['216.d1.a1', '216.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.b1', '12.i1.b1', '18.i1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5155, 3300, 3599, 5528, 4942, 3636, 4951, 6069], 'generators': [23554882, 23443367, 14409982, 14520385, 23258018, 19254468], 'label': '1296.3494.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.b1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '1296.3494', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [2, 2, 3, 2, 2, 3, 3, 3], 'aut_gens': [[42000, 1, 42744, 97224, 3, 136224], [42000, 1, 42744, 141240, 4, 102240], [42744, 1, 42000, 136224, 3, 97224], [1, 42744, 42000, 136224, 141240, 4], [42000, 1, 42744, 141240, 3, 102240], [42000, 1, 42744, 141240, 4, 136224], [42000, 1, 172320, 97224, 3, 136224], [42000, 5, 42744, 97224, 3, 136224], [178680, 1, 42744, 97224, 3, 136224]], 'aut_group': '1296.3490', 'aut_hash': 3490, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1296, 'aut_permdeg': 9, 'aut_perms': [42888, 258684, 257955, 40710, 42624, 56280, 4467, 510], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 3, 1], [2, 9, 3, 1], [2, 27, 1, 1], [3, 2, 3, 1], [3, 4, 3, 1], [3, 8, 1, 1], [6, 6, 6, 1], [6, 12, 3, 1], [6, 18, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\wr S_3', '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': 36, 'autcentquo_group': '1296.3490', 'autcentquo_hash': 3490, 'autcentquo_nilpotent': False, 'autcentquo_order': 1296, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\wr S_3', 'cc_stats': [[1, 1, 1], [2, 3, 3], [2, 9, 3], [2, 27, 1], [3, 2, 3], [3, 4, 3], [3, 8, 1], [6, 6, 6], [6, 12, 3], [6, 18, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '216.162', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 162, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 3], [2, 9, 1, 3], [2, 27, 1, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [6, 6, 1, 6], [6, 12, 1, 3], [6, 18, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1792, 'exponent': 6, 'exponents_of_order': [3, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '216.162', 'hash': 162, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 2, 3, 3, 3], 'inner_gens': [[42000, 1, 42744, 97224, 3, 102240], [42000, 1, 42744, 97224, 4, 136224], [42000, 1, 42744, 141240, 3, 136224], [42000, 1, 219024, 97224, 3, 136224], [42000, 5, 42744, 97224, 3, 136224], [212664, 1, 42744, 97224, 3, 136224]], 'inner_hash': 162, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'S_3^3', 'inner_used': [1, 2, 3, 4, 5, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 12], [4, 6], [8, 1]], 'label': '216.162', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'S3^3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 27, 'number_divisions': 27, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 54, 'number_subgroup_classes': 162, 'number_subgroups': 904, 'old_label': None, 'order': 216, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 63], [3, 26], [6, 126]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [744, 745], 'outer_gens': [[42744, 1, 42000, 102240, 4, 97224], [1, 42744, 42000, 102240, 97224, 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': 4, '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, 12], [4, 6], [8, 1]], 'representations': {'PC': {'code': 6911122835010325191307, 'gens': [1, 2, 4, 6], 'pres': [6, -2, -2, -3, -2, -3, -3, 121, 31, 146, 729, 69, 730, 455]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101743041088268, 91793126248314737, 125124617495221789]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 26172358, 1305911, 2939606, 14159168, 29360962]}, 'Perm': {'d': 9, 'gens': [42000, 1, 42744, 97224, 3, 136224]}}, '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': 'S_3^3', 'transitive_degree': 12, '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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [6, 6, 2], 'aut_gens': [[23554882, 6249670, 14409982, 14520385, 26213243, 26492364, 28816400, 38436746], [26067759, 33123880, 26101684, 14375417, 14409996, 28214329, 28816400, 41258080], [26067759, 35636757, 37786340, 14519751, 23554248, 23783309, 28816400, 29441733], [26068879, 35635204, 23411696, 14520385, 23554248, 23527069, 28816400, 2030952]], 'aut_group': '2592.cg', 'aut_hash': 1290607906254643219, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2592, 'aut_permdeg': 90, 'aut_perms': [656565418069998805141857065373903945796016581495414222570829487570530239554645843407825528910542365559595572227903679939861139089623574057, 1387253712756628417114522123109432143591167130942951981218231660960204850242122812086027591125758943711849277571727251626568263237313487977, 1193998947524996125427754446243788912618678744377134624067295794014916918681126975255637043457237535735969023149485525543477066183914939699], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 2, 1], [2, 27, 1, 2], [2, 27, 2, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 36, 2, 1], [6, 6, 1, 1], [6, 8, 1, 1], [6, 12, 1, 1], [6, 18, 4, 1], [6, 36, 2, 2], [6, 54, 1, 2], [6, 108, 4, 1], [9, 72, 2, 1], [18, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3^3:D_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '1296.3490', 'autcentquo_hash': 3490, 'autcentquo_nilpotent': False, 'autcentquo_order': 1296, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\wr S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [2, 27, 4], [3, 6, 1], [3, 8, 1], [3, 12, 1], [3, 36, 2], [6, 6, 1], [6, 8, 1], [6, 12, 1], [6, 18, 4], [6, 36, 4], [6, 54, 2], [6, 108, 4], [9, 72, 2], [18, 72, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '648.705', 'commutator_count': 1, 'commutator_label': '108.40', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3494, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['648.705', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [2, 27, 1, 4], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 36, 2, 1], [6, 6, 1, 1], [6, 8, 1, 1], [6, 12, 1, 1], [6, 18, 1, 4], [6, 36, 1, 2], [6, 36, 2, 1], [6, 54, 1, 2], [6, 108, 2, 2], [9, 72, 2, 1], [18, 72, 2, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 156, 'exponent': 18, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 4], [8, 0, 2], [8, 1, 1], [12, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1296.3494', 'hash': 3494, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [3, 2, 2, 3, 3, 9, 1, 6], 'inner_gens': [[23554882, 2082058, 26067745, 14520385, 26213243, 26493007, 28816400, 35669543], [26068879, 6249670, 14377199, 26211453, 23410554, 16521498, 28816400, 38292409], [26068879, 6282480, 14409982, 14377177, 23410554, 23781537, 28816400, 38293962], [23554882, 13690262, 14376043, 14520385, 26213243, 26524030, 28816400, 35669143], [23554882, 13775547, 23409906, 14520385, 26213243, 26525817, 28816400, 35669543], [23443367, 36883697, 23442719, 14409996, 26211453, 26492364, 28816400, 13689844], [23554882, 6249670, 14409982, 14520385, 26213243, 26492364, 28816400, 38436746], [26068879, 13775547, 23410540, 23409914, 14375417, 23013838, 28816400, 38436746]], 'inner_hash': 705, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': True, 'inner_tex': 'S_3\\wr C_3', 'inner_used': [1, 2, 3, 4, 6], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 12], [3, 4], [6, 8], [8, 6], [12, 4]], 'label': '1296.3494', 'linC_count': 4, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 4, 'linQ_dim': 6, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'S3^3:C6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 34, 'number_divisions': 28, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 170, 'number_subgroup_classes': 268, 'number_subgroups': 4712, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 127], [3, 98], [6, 782], [9, 144], [18, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [14408200, 14408200], 'outer_gens': [[26068879, 6282480, 28817048, 14377177, 23410554, 23781537, 28816400, 38293962], [26068879, 38326748, 14409982, 14520385, 23554248, 23494250, 28816400, 6282880]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [6, 8], [8, 2], [12, 4], [16, 2]], 'representations': {'PC': {'code': 2040168731592704685977758431116653294519473528006018084277293804676445068282189, 'gens': [1, 3, 4, 6, 7], 'pres': [8, 2, 3, 2, 2, 3, 3, 2, 3, 16, 866, 514, 17475, 1259, 339, 91, 40324, 2892, 340, 1157, 24205, 605, 45702, 11438, 11446, 5070, 166, 7687, 16911, 10007, 4639]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [24992906226966221, 80611462333246657]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [23554882, 6249670, 14409982, 14520385, 26213243, 26492364, 28816400, 38436746]}, 'Perm': {'d': 11, 'gens': [128208, 1, 4436886, 126774, 2328, 16014, 1136304, 7747200]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], '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_6', 'transitive_degree': 18, '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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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, 1], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, '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', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], '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': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
