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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9861', 'ambient_counter': 9861, 'ambient_order': 1600, 'ambient_tex': 'D_{10}^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9861.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1034', 'subgroup_hash': 1034, 'subgroup_order': 800, 'subgroup_tex': 'C_{10}^2:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1600.9861', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3200.jb', 'aut_weyl_index': 4, 'centralizer': '800.a1.a1', 'complements': ['800.c1.a1', '800.d1.b1', '800.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.m1.a1', '4.n1.a1', '4.p1.b1', '4.q1.b1', '10.b1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [81, 1312, 800, 452, 2, 320, 8], 'label': '1600.9861.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.n1.a1', '4.m1.a1', '4.q1.b1', '4.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [4, 2, 4, 5, 5, 4, 4, 4], 'aut_gens': [[1, 2, 8, 80], [193, 386, 8, 616], [41, 42, 8, 80], [385, 698, 56, 296], [385, 690, 8, 80], [1, 34, 8, 80], [1, 18, 24, 128], [69, 354, 648, 768], [1, 50, 56, 104]], 'aut_group': '6400.ff', 'aut_hash': 3099174978056470494, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6400, 'aut_permdeg': 72, 'aut_perms': [35924145755678479449669441937697056514102553187004904899867044097930035185671116126702813694355104812338, 24153714473901388043605153864845385875214264041683965754173604337158372301966596825330290204260494087101, 5989857581579479415910004378781485928554236404455903001987278551626839236415529032245507272821558851394, 6145473631783523042842158987631031786247837363845135769689303378307912773507488009235720746808895521559, 452715666089771414330659760975729833008057614436877602136497627832910912946562111793823320983335326029, 3424959477158953306297489768355521922821093437340053859194613310865955949535924294299402339400165091, 3672409132922041108320124399601718475357729751725855251844661346222422754619918880755671208661624298573, 346049101190733545976161018891213177452375969370130970258504850448993518667462996592107274355727810], 'aut_phi_ratio': 20.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 10, 2, 1], [2, 25, 1, 2], [2, 50, 1, 1], [4, 10, 2, 1], [4, 25, 2, 2], [4, 50, 1, 2], [4, 50, 2, 2], [5, 4, 2, 1], [5, 8, 2, 1], [10, 4, 2, 1], [10, 8, 2, 2], [10, 8, 4, 1], [10, 40, 2, 1], [20, 40, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5^2:C_2^4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '800.1191', 'autcentquo_hash': 1191, 'autcentquo_nilpotent': False, 'autcentquo_order': 800, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 10, 2], [2, 25, 2], [2, 50, 1], [4, 10, 2], [4, 25, 4], [4, 50, 6], [5, 4, 2], [5, 8, 2], [10, 4, 2], [10, 8, 8], [10, 40, 2], [20, 40, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '400.210', 'commutator_count': 1, 'commutator_label': '50.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1034, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 10, 1, 2], [2, 25, 1, 2], [2, 50, 1, 1], [4, 10, 1, 2], [4, 25, 2, 2], [4, 50, 2, 3], [5, 4, 1, 2], [5, 8, 1, 2], [10, 4, 1, 2], [10, 8, 1, 8], [10, 40, 1, 2], [20, 40, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24192, 'exponent': 20, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 1, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '400.210', 'hash': 1034, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 5, 10], 'inner_gens': [[1, 2, 8, 728], [1, 2, 56, 560], [1, 34, 8, 80], [233, 322, 8, 80]], 'inner_hash': 210, 'inner_nilpotent': False, 'inner_order': 400, 'inner_split': False, 'inner_tex': 'D_{10}:F_5', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 4], [4, 8], [8, 10]], 'label': '800.1034', 'linC_count': 4, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C10^2:(C2*C4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 38, 'number_divisions': 33, 'number_normal_subgroups': 47, 'number_subgroup_autclasses': 140, 'number_subgroup_classes': 242, 'number_subgroups': 2292, 'old_label': None, 'order': 800, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 123], [4, 420], [5, 24], [10, 152], [20, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [6, 4, 0, 0], 'outer_gens': [[5, 42, 232, 128], [5, 2, 536, 240], [41, 42, 8, 80], [1, 2, 8, 768]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [24, 289, 1, 414], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 9], [8, 10]], 'representations': {'PC': {'code': 454109856348755919564457228893355780597495791667, 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 2, 2, 5, 2, 5, 36, 794, 521, 80, 571, 578, 30581, 11772, 7579, 124, 32150, 7853, 7860]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [106564013487, 122109387504, 22500562501, 75598583751, 119191223885, 40783109528, 71529966879]}, 'Perm': {'d': 14, 'gens': [522588249, 1037837520, 90720, 1037836816, 41040, 7743859200, 46]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}^2:(C_2\\times C_4)', 'transitive_degree': 20, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 8, 16, 160], [5, 2, 8, 656, 1440], [9, 2, 8, 48, 480], [1, 10, 8, 784, 1440], [1, 2, 8, 340, 864], [1, 2, 8, 792, 1440], [1, 2, 8, 1072, 1128], [563, 802, 8, 176, 1120], [1, 2, 8, 48, 480], [353, 962, 8, 976, 160], [1, 1314, 8, 656, 160]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 12800, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 20, 2, 2], [2, 25, 1, 2], [2, 50, 1, 1], [4, 20, 2, 1], [4, 50, 2, 2], [4, 100, 1, 2], [4, 100, 2, 2], [5, 8, 1, 1], [5, 8, 2, 1], [10, 8, 1, 1], [10, 8, 2, 2], [10, 16, 2, 1], [10, 40, 4, 1], [10, 80, 2, 1], [20, 80, 2, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 20, 4], [2, 25, 2], [2, 50, 1], [4, 20, 2], [4, 50, 4], [4, 100, 6], [5, 8, 3], [10, 8, 5], [10, 16, 2], [10, 40, 4], [10, 80, 2], [20, 80, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '800.1194', 'commutator_count': 1, 'commutator_label': '100.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9861, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 20, 1, 4], [2, 25, 1, 2], [2, 50, 1, 1], [4, 20, 1, 2], [4, 50, 2, 2], [4, 100, 1, 6], [5, 8, 1, 3], [10, 8, 1, 5], [10, 16, 1, 2], [10, 40, 2, 2], [10, 80, 1, 2], [20, 80, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 157489920, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 1, 4], [16, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '800.1194', 'hash': 9861, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 800, 'inner_split': None, 'inner_tex': 'D_5^2.C_2^3', 'inner_used': None, 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 4], [4, 2], [8, 16], [16, 2]], 'label': '1600.9861', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'D10^2.C2^2', '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': 24, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 40, 'number_divisions': 36, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 245, 'number_subgroup_classes': 410, 'number_subgroups': 6574, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 183], [4, 840], [5, 24], [10, 392], [20, 160]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '16.3', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 16, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^2:C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [4, 4], [8, 12], [16, 4]], 'representations': {'PC': {'code': 12471901926054474554415184722043486563112684103122868671697573249075, 'gens': [1, 2, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 5, 2, 5, 41, 14884, 13932, 11060, 116, 61445, 2317, 1557, 48838, 13454, 20182, 5078, 166, 8199, 30735, 20503, 5159]}, 'Perm': {'d': 18, 'gens': [360158552773119, 1677071699722, 361205054796341, 13075, 6994022131342, 19342, 777213746225280, 1159043607993600]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}^2.C_2^2', 'transitive_degree': 40, '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}
