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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.767', 'ambient_counter': 767, 'ambient_order': 480, 'ambient_tex': 'C_{60}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 240, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.767.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.165', 'subgroup_hash': 165, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}:Q_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '480.767', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.f1.a1', '4.f1.b1', '6.d1.a1', '10.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7282, 5170, 3978, 4340, 3413, 3643, 3370, 5716], 'generators': [1, 8, 240, 96, 6, 12], 'label': '480.767.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '10.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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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, 6, 4, 4, 2], 'aut_gens': [[1, 2, 4], [1, 2, 29], [1, 2, 164], [1, 22, 124], [1, 182, 197], [121, 123, 4], [1, 2, 124]], 'aut_group': '1536.194556563', 'aut_hash': 1637901404035917049, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 15, 'aut_perms': [193157758089, 193158121080, 561960324000, 561959959680, 348872832000, 124104960], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 6, 4, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 1, 4, 1], [10, 1, 8, 1], [12, 2, 4, 1], [15, 2, 4, 1], [20, 2, 8, 1], [20, 6, 16, 1], [30, 2, 4, 1], [30, 2, 8, 1], [60, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': '(D_6\\times C_4^2):D_4', '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': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 6, 4], [5, 1, 4], [6, 2, 3], [10, 1, 12], [12, 2, 4], [15, 2, 4], [20, 2, 8], [20, 6, 16], [30, 2, 12], [60, 2, 16]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 165, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.4', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 1, 4], [5, 1, 4, 1], [6, 2, 1, 3], [10, 1, 4, 3], [12, 2, 2, 2], [15, 2, 4, 1], [20, 2, 4, 2], [20, 6, 4, 4], [30, 2, 4, 3], [60, 2, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2604, 'exponent': 60, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '120.45', 'hash': 165, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 6], 'inner_gens': [[1, 2, 4], [1, 2, 44], [1, 202, 4]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 50]], 'label': '240.165', 'linC_count': 384, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 56, 'linQ_dim': 10, 'linQ_dim_count': 52, 'linR_count': 32, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C30:Q8', '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': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 90, 'number_divisions': 32, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 76, 'number_subgroups': 120, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [5, 4], [6, 6], [10, 12], [12, 8], [15, 8], [20, 112], [30, 24], [60, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [0, 12, 0, 0, 0], 'outer_gens': [[121, 2, 124], [1, 62, 196], [1, 123, 4], [1, 2, 148], [121, 2, 5]], 'outer_group': '128.1031', 'outer_hash': 1031, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [367927, 806400, 262897920, 40284862, 127019640], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^4', '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, 10], [8, 6], [16, 2]], 'representations': {'PC': {'code': 6604223689737096648581127, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -5, 727, 404, 50, 1065, 69, 2650, 118]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1547864562, 106922612, 296010408, 632568400, 297800445, 2143735230]}, 'Perm': {'d': 18, 'gens': [379574279925120, 774405718732801, 1156178136960000, 870, 774405718732800, 403200]}}, '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_{30}:Q_8', 'transitive_degree': 240, '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': [6, 4, 4, 4, 4, 6, 2, 4], 'aut_gens': [[1, 2, 24], [249, 362, 264], [241, 130, 24], [253, 134, 216], [253, 370, 180], [261, 22, 168], [257, 2, 228], [5, 142, 264], [13, 10, 84]], 'aut_group': None, 'aut_hash': 2284238130320887519, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 24, 'aut_perms': [472409903639566669439594, 556294550498731827994376, 271043657979142337572822, 482304577644600278440639, 353661702568810240632036, 4326279247330568306146, 283133213706249923238416, 12275681751636533566196], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 2, 1], [4, 4, 2, 1], [4, 6, 2, 2], [4, 12, 2, 1], [5, 1, 4, 1], [6, 2, 1, 3], [10, 1, 4, 3], [12, 4, 2, 1], [12, 4, 4, 1], [15, 2, 4, 1], [20, 2, 8, 1], [20, 4, 8, 1], [20, 6, 8, 2], [20, 12, 8, 1], [30, 2, 4, 3], [60, 4, 8, 1], [60, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^5.C_2^5)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '256.56082', 'autcent_hash': 56082, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 4, 2], [4, 6, 4], [4, 12, 2], [5, 1, 4], [6, 2, 3], [10, 1, 12], [12, 4, 6], [15, 2, 4], [20, 2, 8], [20, 4, 8], [20, 6, 16], [20, 12, 8], [30, 2, 12], [60, 4, 24]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '12.5', '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': 767, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['96.95', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 6, 1, 4], [4, 12, 1, 2], [5, 1, 4, 1], [6, 2, 1, 3], [10, 1, 4, 3], [12, 4, 1, 2], [12, 4, 2, 2], [15, 2, 4, 1], [20, 2, 4, 2], [20, 4, 4, 2], [20, 6, 4, 4], [20, 12, 4, 2], [30, 2, 4, 3], [60, 4, 4, 2], [60, 4, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10416, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.45', 'hash': 767, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 2], 'inner_gens': [[1, 22, 24], [5, 2, 264], [1, 242, 24]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 70], [4, 10]], 'label': '480.767', 'linC_count': 384, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 512, 'linQ_dim': 12, 'linQ_dim_count': 324, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C60:Q8', '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': 30, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 120, 'number_divisions': 44, 'number_normal_subgroups': 74, 'number_subgroup_autclasses': 88, 'number_subgroup_classes': 136, 'number_subgroups': 276, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 60], [5, 4], [6, 6], [10, 12], [12, 24], [15, 8], [20, 240], [30, 24], [60, 96]], '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': [[13, 2, 24], [13, 2, 36], [241, 2, 24], [13, 14, 408], [13, 134, 36]], 'outer_group': '128.2154', 'outer_hash': 2154, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [5167, 87091327, 40284846, 408, 87459246], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 12], [8, 10], [16, 4]], 'representations': {'PC': {'code': 43636101896632587599116402450874435, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -3, -2, -2, -5, 84, 309, 36, 422, 58, 451, 4631, 102, 124]}, 'GLZN': {'d': 2, 'p': 33, 'gens': [898450, 826574, 359380, 428131, 48302, 1010002, 265522]}, 'Perm': {'d': 20, 'gens': [135936679844005200, 87454080, 263295183970022400, 33, 392327162440012800, 40279680, 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_{60}:Q_8', 'transitive_degree': 480, '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': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
