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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '900.149', 'ambient_counter': 149, 'ambient_order': 900, 'ambient_tex': 'C_{15}:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 450, 'characteristic': False, 'core_order': 150, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '900.149.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '150.13', 'subgroup_hash': 13, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times C_{30}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '900.149', 'aut_centralizer_order': 2700, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 10800, 'centralizer': '2.a1', 'complements': ['150.b1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '18.a1', '30.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7100, 2870, 6791, 6762], 'generators': [450, 6, 180, 20], 'label': '900.149.6.a1', 'mobius_quo': 5, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '18.a1', '30.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '450.33', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '150.13', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [4, 8, 24, 2, 2], 'aut_gens': [[1, 5], [2, 35], [31, 96], [34, 69], [1, 55], [4, 145]], 'aut_group': '960.5693', 'aut_hash': 5693, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 26, 'aut_perms': [63292485907789234817437446, 288446469221612031823032630, 79614322471884741770744280, 15565162463473822778880415, 1], 'aut_phi_ratio': 24.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [5, 1, 24, 1], [6, 1, 2, 1], [10, 1, 24, 1], [15, 1, 48, 1], [30, 1, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\GL(2,5)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 120, 'autcent_group': '960.5693', 'autcent_hash': 5693, 'autcent_nilpotent': False, 'autcent_order': 960, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times \\GL(2,5)', '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], [5, 1, 24], [6, 1, 2], [10, 1, 24], [15, 1, 48], [30, 1, 48]], 'center_label': '150.13', 'center_order': 150, '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', '5.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['5.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [5, 1, 4, 6], [6, 1, 2, 1], [10, 1, 4, 6], [15, 1, 8, 6], [30, 1, 8, 6]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 12, 'exponent': 30, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '150.13', 'hash': 13, 'hyperelementary': 5, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 5], [1, 5]], '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, 150]], 'label': '150.13', 'linC_count': 5760, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 105, 'linQ_dim': 10, 'linQ_dim_count': 105, 'linR_count': 1440, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5*C30', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 150, 'number_divisions': 28, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 32, 'number_subgroups': 32, 'old_label': None, 'order': 150, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 2], [5, 24], [6, 2], [10, 24], [15, 48], [30, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 120, 'outer_gen_orders': [4, 8, 24, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[2, 35], [31, 96], [34, 69], [1, 55], [4, 145]], 'outer_group': '960.5693', 'outer_hash': 5693, 'outer_nilpotent': False, 'outer_order': 960, 'outer_permdeg': 26, 'outer_perms': [63292485907789234817437446, 288446469221612031823032630, 79614322471884741770744280, 15565162463473822778880415, 1], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(2,5)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [4, 12], [8, 12]], 'representations': {'PC': {'code': 20317895, 'gens': [1, 2], 'pres': [4, -5, -2, -3, -5, 21, 46]}, 'GLFp': {'d': 2, 'p': 31, 'gens': [208546, 804358]}, 'Perm': {'d': 15, 'gens': [87178291200, 958003200, 1451520, 96]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5, 30], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_{30}', 'transitive_degree': 150, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [24, 60, 12, 40], 'aut_gens': [[1, 2, 30], [693, 844, 278], [335, 14, 340], [443, 200, 522], [135, 308, 592]], 'aut_group': None, 'aut_hash': 2443820986999158619, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10368000, 'aut_permdeg': 450, 'aut_perms': 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'aut_phi_ratio': 43200.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 225, 2, 1], [3, 2, 4, 1], [5, 2, 12, 1], [6, 2, 4, 1], [10, 2, 12, 1], [15, 2, 96, 1], [30, 2, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\AGL(2,3)\\times C_5^2:C_4.S_5', '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': 120, 'autcentquo_group': None, 'autcentquo_hash': 1463275603679416697, 'autcentquo_nilpotent': False, 'autcentquo_order': 5184000, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\AGL(2,3)\\times C_5^2:C_4.S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 225, 2], [3, 2, 4], [5, 2, 12], [6, 2, 4], [10, 2, 12], [15, 2, 96], [30, 2, 96]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '450.33', 'commutator_count': 1, 'commutator_label': '225.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 149, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['450.33', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 225, 1, 2], [3, 2, 1, 4], [5, 2, 2, 6], [6, 2, 1, 4], [10, 2, 2, 6], [15, 2, 4, 24], [30, 2, 4, 24]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21, 'exponent': 30, 'exponents_of_order': [2, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '900.149', 'hash': 149, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 15, 15], 'inner_gens': [[1, 28, 870], [5, 2, 30], [61, 2, 30]], 'inner_hash': 33, 'inner_nilpotent': False, 'inner_order': 450, 'inner_split': False, 'inner_tex': 'C_{15}:D_{15}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 224]], 'label': '900.149', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:D30', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 228, 'number_divisions': 72, 'number_normal_subgroups': 99, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 240, 'number_subgroups': 3792, 'old_label': None, 'order': 900, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 451], [3, 8], [5, 24], [6, 8], [10, 24], [15, 192], [30, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 120, 'outer_gen_orders': [12, 4, 24, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 790, 284], [1, 14, 704], [451, 568, 582], [451, 856, 162]], 'outer_group': None, 'outer_hash': 3720365842847593956, 'outer_nilpotent': False, 'outer_order': 23040, 'outer_permdeg': 98, 'outer_perms': [4973859280141071579834316136914400232726979338218654435030447231498829981002722847133683207273216661663043477457079275791362649498654927192855206203377368, 7978966871923097392711942899029950855898152592332138117715866669044276952709162364372043187986337164393154389853981234309982022890058095280956862524849774, 2798650651480867671811714649715489468224952015280963155772800916823762327758539260577237538671794430269119393458321506786113814562380171981110395927763927, 6689277898364230410821541617155252313808334141265648595660094931678695532500240178183117435802762958111014121430523068002023823174359244388837799407444761], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '(C_2\\times (C_2.S_4):C_2).S_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 12], [8, 48]], 'representations': {'PC': {'code': 6183387085619575407315395781063, 'gens': [1, 2, 4], 'pres': [6, -2, -3, -5, -2, -3, -5, 337, 43, 434, 20883, 69, 25204, 118, 25925]}, 'Perm': {'d': 18, 'gens': [44460968792401, 24, 3, 5764, 421071705694080, 754615288627200]}}, 'schur_multiplier': [30], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:D_{30}', 'transitive_degree': 450, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 4], [1, 3], [2, 4]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': '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': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 3, 1], [3, 2, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 2, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 3], [2, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 1]], 'label': '6.1', 'linC_count': 1, 'linC_degree': 2, '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': 'S3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 3, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 6, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 3], [3, 2]], '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': 2, 'perfect': False, 'permutation_degree': 3, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 25, 'gens': [1, 2], 'pres': [2, -2, -3, 17]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [28, 45]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'GL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'SL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGL'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'SO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'SU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PSO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'PSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'GO'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'Omega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PGO'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'POmega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CSO'}, {'d': 2, 'q': 4, 'gens': [20, 194], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'CSOMinus'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'CSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CO'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'COMinus'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGammaL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSigmaL'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGammaU'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGL'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11, 6]}, 'Perm': {'d': 3, 'gens': [1, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
