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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.29', 'ambient_counter': 29, 'ambient_order': 1320, 'ambient_tex': 'C_{132}:C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': True, 'core_order': 660, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1320.29.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.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': '660.18', 'subgroup_hash': 18, 'subgroup_order': 660, 'subgroup_tex': 'C_{66}:C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1320.29', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 2, 'centralizer': '330.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.b1.a1', '10.a1.a1', '22.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3870, 3116, 3284, 3329, 2751, 1959, 3683, 2697], 'generators': [5, 2, 880, 660, 120], 'label': '1320.29.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.b1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '660.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [2, 10, 66], 'aut_gens': [[1, 10], [331, 230], [331, 610], [11, 10]], 'aut_group': '1320.142', 'aut_hash': 142, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1320, 'aut_permdeg': 17, 'aut_perms': [792835169070, 121264337885270, 27226629342999], 'aut_phi_ratio': 8.25, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [5, 11, 1, 4], [6, 2, 1, 1], [10, 11, 1, 4], [10, 33, 2, 4], [11, 5, 2, 1], [15, 22, 1, 4], [22, 5, 2, 1], [22, 15, 4, 1], [30, 22, 1, 4], [33, 10, 2, 1], [66, 10, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6\\times F_{11}', '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': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [5, 11, 4], [6, 2, 1], [10, 11, 4], [10, 33, 8], [11, 5, 2], [15, 22, 4], [22, 5, 2], [22, 15, 4], [30, 22, 4], [33, 10, 2], [66, 10, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '330.2', 'commutator_count': 1, 'commutator_label': '33.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 18, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['55.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [5, 11, 4, 1], [6, 2, 1, 1], [10, 11, 4, 1], [10, 33, 4, 2], [11, 5, 2, 1], [15, 22, 4, 1], [22, 5, 2, 1], [22, 15, 2, 2], [30, 22, 4, 1], [33, 10, 2, 1], [66, 10, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 330, 'exponents_of_order': [2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '660.18', 'hash': 18, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [10, 33], 'inner_gens': [[1, 590], [81, 10]], 'inner_hash': 2, 'inner_nilpotent': False, 'inner_order': 330, 'inner_split': True, 'inner_tex': 'C_{33}:C_{10}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 20], [2, 10], [5, 8], [10, 4]], 'label': '660.18', 'linC_count': 60, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 6, 'linQ_dim': 12, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C66:C10', 'ngens': 5, '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': 15, 'number_conjugacy_classes': 42, 'number_divisions': 18, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 40, 'number_subgroups': 224, 'old_label': None, 'order': 660, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 7], [3, 2], [5, 44], [6, 2], [10, 308], [11, 10], [15, 88], [22, 70], [30, 88], [33, 20], [66, 20]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 110], 'outer_gens': [[331, 430], [441, 430]], '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': 2, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [8, 2], [10, 4], [20, 2]], 'representations': {'PC': {'code': 236404182472859997731104561303019, 'gens': [1, 3], 'pres': [5, -2, -5, -2, -3, -11, 10, 8852, 3682, 42, 10403, 3208, 78, 6004, 3759]}, 'GLZN': {'d': 2, 'p': 22, 'gens': [10693, 133343, 10891, 10653, 223629]}, 'Perm': {'d': 16, 'gens': [7, 1, 100724642640, 30, 1496093004000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{66}:C_{10}', 'transitive_degree': 66, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [10, 10, 10, 10, 10], 'aut_gens': [[1, 10], [401, 1010], [1261, 1070], [241, 910], [161, 350], [701, 590]], 'aut_group': None, 'aut_hash': 4845733366138083661, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2640, 'aut_permdeg': 19, 'aut_perms': [100348364696369126, 102567173273711315, 107574602362093254, 5113207551993976, 4055670212855244], 'aut_phi_ratio': 8.25, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [5, 11, 1, 4], [6, 2, 1, 1], [10, 11, 1, 4], [10, 33, 2, 4], [11, 5, 2, 1], [12, 2, 2, 1], [15, 22, 1, 4], [20, 11, 2, 4], [20, 33, 2, 4], [22, 5, 2, 1], [22, 15, 4, 1], [30, 22, 1, 4], [33, 10, 2, 1], [44, 5, 4, 1], [44, 15, 4, 1], [60, 22, 2, 4], [66, 10, 2, 1], [132, 10, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{11}:(C_2^2\\times C_{10}\\times S_3)', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [4, 1, 2], [4, 3, 2], [5, 11, 4], [6, 2, 1], [10, 11, 4], [10, 33, 8], [11, 5, 2], [12, 2, 2], [15, 22, 4], [20, 11, 8], [20, 33, 8], [22, 5, 2], [22, 15, 4], [30, 22, 4], [33, 10, 2], [44, 5, 4], [44, 15, 4], [60, 22, 8], [66, 10, 2], [132, 10, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '330.2', 'commutator_count': 1, 'commutator_label': '33.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 29, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['55.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [5, 11, 4, 1], [6, 2, 1, 1], [10, 11, 4, 1], [10, 33, 4, 2], [11, 5, 2, 1], [12, 2, 2, 1], [15, 22, 4, 1], [20, 11, 8, 1], [20, 33, 8, 1], [22, 5, 2, 1], [22, 15, 2, 2], [30, 22, 4, 1], [33, 10, 2, 1], [44, 5, 4, 1], [44, 15, 4, 1], [60, 22, 8, 1], [66, 10, 2, 1], [132, 10, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 660, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '660.18', 'hash': 29, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [10, 33], 'inner_gens': [[1, 50], [1281, 10]], 'inner_hash': 2, 'inner_nilpotent': False, 'inner_order': 330, 'inner_split': True, 'inner_tex': 'C_{33}:C_{10}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 20, 'irrep_stats': [[1, 40], [2, 20], [5, 16], [10, 8]], 'label': '1320.29', 'linC_count': 240, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 20, 'linQ_dim': 14, 'linQ_dim_count': 20, 'linR_count': 8, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C132:C10', '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, 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': 48, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 84, 'number_divisions': 27, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 64, 'number_subgroups': 364, 'old_label': None, 'order': 1320, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [5, 44], [6, 2], [10, 308], [11, 10], [12, 4], [15, 88], [20, 352], [22, 70], [30, 88], [33, 20], [44, 80], [60, 176], [66, 20], [132, 40]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 550], 'outer_gens': [[1, 430], [661, 1090], [881, 1090]], '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': 2, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 5], [8, 4], [10, 4], [16, 1], [20, 4], [40, 1]], 'representations': {'PC': {'code': 44592077204886695310830089968484972773341030019, 'gens': [1, 3], 'pres': [6, -2, -5, -2, -2, -3, -11, 12, 902, 2258, 50, 2403, 6009, 69, 6004, 15010, 118, 21605, 6491]}, 'GLZN': {'d': 2, 'p': 55, 'gens': [166651, 3826648, 166391, 167619, 3961541, 5656784]}, 'Perm': {'d': 18, 'gens': [120, 9, 23819883050880, 16, 840, 401650985393280]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{132}:C_{10}', 'transitive_degree': 132, '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}
