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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3960.o', 'ambient_counter': 15, 'ambient_order': 3960, 'ambient_tex': 'S_3\\times \\PSL(2,11)', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 660, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3960.o.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['PC', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '660.13', 'subgroup_hash': 13, 'subgroup_order': 660, 'subgroup_tex': '\\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3960.o', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1320.133', 'aut_weyl_index': 6, 'centralizer': '660.a1.a1', 'complements': ['660.a1.a1', '660.h1.a1', '660.j1.a1', '660.j1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['66.b1.a1', '66.b1.a2', '72.a1.a1', '330.k1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4615, 3083, 6116, 8081, 3500, 6321, 3304, 6321], 'generators': [21755830320, 3369392664], 'label': '3960.o.6.a1.a1', 'mobius_quo': -1, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['3960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '3960.o', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '660.13'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 660, 'aut_gen_orders': [10, 3], 'aut_gens': [[7988, 1231], [9292, 5462], [13133, 13983]], 'aut_group': '1320.133', 'aut_hash': 133, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1320, 'aut_permdeg': 55, 'aut_perms': [10299310315736846349545050806255504276824179669471403681048038491519960685, 9190322706449422501021556741162746997157193402922283564318926257519329496], 'aut_phi_ratio': 8.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 55, 1, 1], [3, 110, 1, 1], [5, 132, 1, 2], [6, 110, 1, 1], [11, 60, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,11)', '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': 660, 'autcentquo_group': '1320.133', 'autcentquo_hash': 133, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 55, 1], [3, 110, 1], [5, 132, 2], [6, 110, 1], [11, 60, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '660.13', 'commutator_count': 1, 'commutator_label': '660.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['660.13'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 55, 1, 1], [3, 110, 1, 1], [5, 132, 2, 1], [6, 110, 1, 1], [11, 60, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 254, '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': [[5, 0, 2], [10, 1, 2], [11, 1, 1], [12, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '660.13', 'hash': 13, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [5, 3], 'inner_gens': [[7988, 890], [3152, 1231]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 660, 'inner_split': True, 'inner_tex': '\\PSL(2,11)', 'inner_used': [1, 2], 'irrC_degree': 5, 'irrQ_degree': 10, 'irrQ_dim': 10, 'irrR_degree': 10, 'irrep_stats': [[1, 1], [5, 2], [10, 2], [11, 1], [12, 2]], 'label': '660.13', 'linC_count': 2, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 3, 'linQ_dim': 10, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,11)', 'ngens': 2, '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': 7, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 8, 'number_divisions': 6, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 16, 'number_subgroups': 620, 'old_label': None, 'order': 660, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 55], [3, 110], [5, 264], [6, 110], [11, 120]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [10942], 'outer_gens': [[14254, 10466]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [10, 3], [11, 1], [24, 1]], 'representations': {'Lie': [{'d': 2, 'q': 11, 'gens': [7988, 1231], 'family': 'PSL'}, {'d': 2, 'q': 11, 'gens': [10629368, 1126278], 'family': 'PSU'}, {'d': 3, 'q': 11, 'gens': [857450168, 17876563], 'family': 'Omega'}, {'d': 3, 'q': 11, 'gens': [857450168, 17876563], 'family': 'POmega'}, {'d': 2, 'q': 11, 'gens': [7988, 1231], 'family': 'PSigmaL'}], 'GLFp': {'d': 3, 'p': 11, 'gens': [2029823638, 1448050408]}, 'Perm': {'d': 11, 'gens': [16460074, 6020472]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,11)', 'transitive_degree': 11, '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': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 2], 'aut_gens': [[6785983586, 1089851041], [45274781045, 19160161225], [59730175585, 59422694642]], 'aut_group': '7920.q', 'aut_hash': 1157788818429169362, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7920, 'aut_permdeg': 58, 'aut_perms': [587897353636398588644797072549007850204173044572507477404105747126651443728771, 23427148710332319059999225189100172835085593432025207827219142312268916422626], 'aut_phi_ratio': 8.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 55, 1, 1], [2, 165, 1, 1], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [5, 132, 1, 2], [6, 110, 1, 2], [6, 220, 1, 1], [6, 330, 1, 2], [10, 396, 1, 2], [11, 60, 2, 1], [15, 264, 1, 2], [22, 180, 2, 1], [33, 120, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times \\PGL(2,11)', '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': 660, 'autcentquo_group': '7920.q', 'autcentquo_hash': 1157788818429169362, 'autcentquo_nilpotent': False, 'autcentquo_order': 7920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times \\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 55, 1], [2, 165, 1], [3, 2, 1], [3, 110, 1], [3, 220, 1], [5, 132, 2], [6, 110, 2], [6, 220, 1], [6, 330, 2], [10, 396, 2], [11, 60, 2], [15, 264, 2], [22, 180, 2], [33, 120, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '3960.o', 'commutator_count': 1, 'commutator_label': '1980.57', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '660.13'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 1], ['660.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 55, 1, 1], [2, 165, 1, 1], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [5, 132, 2, 1], [6, 110, 1, 2], [6, 220, 1, 1], [6, 330, 1, 2], [10, 396, 2, 1], [11, 60, 2, 1], [15, 264, 2, 1], [22, 180, 2, 1], [33, 120, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 762, 'exponent': 330, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 0, 2], [20, 1, 2], [22, 1, 1], [24, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3960.o', 'hash': 6655759197249528573, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [10, 6], 'inner_gens': [[6785983586, 37864835429], [19452708005, 1089851041]], 'inner_hash': 6655759197249528573, 'inner_nilpotent': False, 'inner_order': 3960, 'inner_split': True, 'inner_tex': 'S_3\\times \\PSL(2,11)', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 2], [2, 1], [5, 4], [10, 6], [11, 2], [12, 4], [20, 2], [22, 1], [24, 2]], 'label': '3960.o', 'linC_count': 4, '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': False, 'metacyclic': False, 'monomial': False, 'name': 'S3*PSL(2,11)', 'ngens': 2, '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, 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': 6, 'number_conjugacy_classes': 24, 'number_divisions': 18, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 75, 'number_subgroup_classes': 88, 'number_subgroups': 7504, 'old_label': None, 'order': 3960, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 223], [3, 332], [5, 264], [6, 1100], [10, 792], [11, 120], [15, 528], [22, 360], [33, 240]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [53460381024], 'outer_gens': [[58530145082, 56723690425]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [10, 6], [11, 2], [20, 3], [22, 1], [24, 2], [48, 1]], 'representations': {'Perm': {'d': 14, 'gens': [6785983586, 1089851041]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times \\PSL(2,11)', 'transitive_degree': 33, '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}
