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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.484', 'ambient_counter': 484, 'ambient_order': 480, 'ambient_tex': '(C_6\\times D_{20}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 240, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.484.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.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': '240.26', 'subgroup_hash': 26, 'subgroup_order': 240, 'subgroup_tex': 'C_6.D_{20}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '480.484', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.236168', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['240.e1.a1', '240.d1.a1', '240.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1', '6.f1.a1', '10.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2436, 6202, 5161, 3221, 4444, 5723, 5103, 1168], 'generators': [9, 16, 4, 240, 42, 160], 'label': '480.484.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '120.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [4, 10, 6, 2, 2, 2], 'aut_gens': [[1, 4, 24], [1, 4, 72], [1, 68, 24], [19, 4, 24], [121, 4, 24], [121, 6, 24], [1, 124, 24]], 'aut_group': '1920.236168', 'aut_hash': 3337138837734452234, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 16, 'aut_perms': [261538542727, 1407310370040, 7984807, 3669136, 23, 7], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 2, 1], [3, 2, 1, 1], [4, 6, 2, 1], [4, 30, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 10, 4, 1], [10, 2, 2, 3], [15, 4, 2, 1], [20, 6, 8, 1], [30, 4, 2, 3]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times D_6\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 10, 2], [3, 2, 1], [4, 6, 2], [4, 30, 2], [5, 2, 2], [6, 2, 3], [6, 10, 4], [10, 2, 6], [15, 4, 2], [20, 6, 8], [30, 4, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '60.8', 'commutator_count': 1, 'commutator_label': '30.4', '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': 26, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 1, 2], [3, 2, 1, 1], [4, 6, 2, 1], [4, 30, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 10, 2, 2], [10, 2, 2, 3], [15, 4, 2, 1], [20, 6, 8, 1], [30, 4, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 60, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '60.8', 'hash': 26, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 6, 5], 'inner_gens': [[1, 140, 24], [129, 4, 216], [1, 52, 24]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'S_3\\times D_5', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 26], [4, 8]], 'label': '240.26', 'linC_count': 48, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 10, 'linQ_dim_count': 40, 'linR_count': 42, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.D20', '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': 21, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 42, 'number_divisions': 23, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 68, 'number_subgroups': 272, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 72], [5, 4], [6, 46], [10, 12], [15, 8], [20, 48], [30, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 20, 24], [3, 4, 24], [1, 6, 24], [1, 4, 168]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [5040, 362880, 120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 4], [8, 7]], 'representations': {'PC': {'code': 2476166880185825775931411, 'gens': [1, 3, 5], 'pres': [6, -2, -2, -2, -3, -2, -5, 12, 2522, 50, 387, 1636, 88, 1745]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [110203, 92049, 72009, 8081, 130311, 152019]}, 'Perm': {'d': 16, 'gens': [87660961927, 766217, 7, 7983360, 840, 1482509952000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.D_{20}', 'transitive_degree': 120, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [12, 6, 4, 6, 4, 2, 6, 2, 2], 'aut_gens': [[1, 2, 8, 80], [17, 2, 136, 80], [241, 6, 156, 80], [309, 6, 380, 400], [49, 242, 396, 80], [257, 242, 268, 80], [5, 2, 88, 400], [5, 246, 328, 80], [277, 242, 312, 400], [241, 242, 248, 80]], 'aut_group': None, 'aut_hash': 814302305876374217, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7680, 'aut_permdeg': 36, 'aut_perms': [134888629105910558810065709047867532942500, 250920661230868836926830891797767402066978, 168085790595560023935516687896486540768682, 223406082470214341834583734940464733375173, 182134941874548645938735814774430950062724, 289834233676043450656339500049078341608752, 173819873990651570305124454672514428336653, 295985058684435462163843850242171397755608, 6208843725544583882340148457810968881840], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 2, 1], [2, 12, 1, 1], [2, 20, 1, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 6, 2, 1], [4, 30, 2, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 20, 2, 2], [10, 2, 2, 3], [10, 12, 4, 1], [12, 4, 2, 1], [15, 4, 2, 1], [20, 4, 4, 1], [20, 12, 4, 1], [30, 4, 2, 3], [60, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times S_3\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 10, 2], [2, 12, 1], [2, 20, 1], [3, 2, 1], [4, 4, 1], [4, 6, 2], [4, 30, 2], [4, 60, 1], [5, 2, 2], [6, 2, 3], [6, 20, 4], [10, 2, 6], [10, 12, 4], [12, 4, 2], [15, 4, 2], [20, 4, 4], [20, 12, 4], [30, 4, 6], [60, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '120.42', 'commutator_count': 1, 'commutator_label': '60.13', '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': 484, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 1, 2], [2, 12, 1, 1], [2, 20, 1, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 6, 2, 1], [4, 30, 1, 2], [4, 60, 1, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 20, 1, 2], [6, 20, 2, 1], [10, 2, 2, 3], [10, 12, 4, 1], [12, 4, 2, 1], [15, 4, 2, 1], [20, 4, 4, 1], [20, 12, 4, 1], [30, 4, 2, 3], [60, 4, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4032, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.42', 'hash': 484, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 2, 10, 3], 'inner_gens': [[1, 6, 76, 80], [5, 2, 248, 80], [21, 242, 8, 400], [1, 2, 168, 80]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'S_3\\times D_{10}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 30], [4, 22]], 'label': '480.484', 'linC_count': 32, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 104, 'linQ_dim': 10, 'linQ_dim_count': 88, 'linR_count': 306, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C6*D20):C2', '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': 44, 'number_conjugacy_classes': 60, 'number_divisions': 33, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 160, 'number_subgroup_classes': 188, 'number_subgroups': 1052, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 55], [3, 2], [4, 136], [5, 4], [6, 86], [10, 60], [12, 8], [15, 8], [20, 64], [30, 24], [60, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 8, 400], [5, 2, 8, 80], [241, 2, 8, 80], [1, 6, 8, 80], [1, 2, 56, 80]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [5040, 39916800, 362880, 127, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 9], [8, 4], [16, 4]], 'representations': {'PC': {'code': 6222617437373997911386739892191281, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -2, 2, -5, -2, -3, 85, 36, 2131, 3482, 80, 2244, 2126, 124, 1987]}, 'GLZN': {'d': 2, 'p': 60, 'gens': [216721, 2124639, 5385324, 4215421, 6858916, 8856041, 5275524]}, 'Perm': {'d': 16, 'gens': [87657297967, 368057, 10216, 7, 16687, 3991680, 1482509952000]}}, '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': '(C_6\\times D_{20}):C_2', 'transitive_degree': 240, '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}
