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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.11067', 'ambient_counter': 11067, 'ambient_order': 960, 'ambient_tex': 'A_4:Q_8\\times C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.11067.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.11067', 'aut_centralizer_order': 128, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.5', 'aut_weyl_index': 256, 'centralizer': '6.a1', 'complements': ['40.e1'], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.a1'], 'contains': ['48.c1', '48.h1', '48.j1', '120.c1'], 'core': '24.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9465, 6938, 2334, 1469], 'generators': [1959255, 2001847, 2129625, 128745], 'label': '960.11067.24.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.b1', '12.a1'], 'normal_contains': ['48.c1', '96.b1', '120.c1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '96.185', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 84, 'aut_gen_orders': [4, 6], 'aut_gens': [[1, 2, 4], [23, 21, 35], [20, 1, 18]], 'aut_group': '672.1046', 'aut_hash': 1046, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 672, 'aut_permdeg': 11, 'aut_perms': [16062618, 404056], 'aut_phi_ratio': 42.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1], [5, 1, 4, 1], [10, 1, 28, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times \\GL(3,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '672.1046', 'autcent_hash': 1046, 'autcent_nilpotent': False, 'autcent_order': 672, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_4\\times \\GL(3,2)', '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, 7], [5, 1, 4], [10, 1, 28]], 'center_label': '40.14', 'center_order': 40, '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', '2.1', '2.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [5, 1, 4, 1], [10, 1, 4, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 31, 'exponent': 10, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '40.14', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 40]], 'label': '40.14', 'linC_count': 3472, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 84, 'linQ_dim': 6, 'linQ_dim_count': 84, 'linR_count': 168, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C10', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 40, 'number_divisions': 16, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 32, 'number_subgroups': 32, 'old_label': None, 'order': 40, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [5, 4], [10, 28]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [4, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[23, 21, 35], [20, 1, 18]], 'outer_group': '672.1046', 'outer_hash': 1046, 'outer_nilpotent': False, 'outer_order': 672, 'outer_permdeg': 11, 'outer_perms': [16062618, 404056], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_4\\times \\GL(3,2)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 8]], 'representations': {'PC': {'code': 132099, 'gens': [1, 2, 3], 'pres': [4, -2, -2, -2, -5, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101729074815868, 24992906222183252, 25038633859490725]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1094544393, 510353318, 857494092, 1714988184]}, 'Perm': {'d': 11, 'gens': [3628800, 40320, 720, 96]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_{10}', 'transitive_degree': 40, '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 12, 6, 12, 4], 'aut_gens': [[1959255, 2879547, 2031892, 2300963, 2001847], [3662955, 3189655, 2030946, 2300963, 2001847], [3662955, 936662, 3252437, 1278743, 128745], [3662955, 2030049, 115274, 3195405, 1960223], [3662955, 254846, 156898, 2342587, 128745], [3662955, 1024572, 3720976, 298147, 128745], [1959255, 936662, 582823, 1278743, 128745]], 'aut_group': None, 'aut_hash': 4508704614955838314, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 52, 'aut_perms': [72229531562281434355516845056731037966014645310323831769608119184776, 76437622261969062800358526628006512760029312498369226685341572225325, 76437626473948181324066753748859427159394977904610787763169338455358, 49583253924496989563214889252837570918120784314061507086137653022345, 7383552325318410975550796736157691495579646378027041301187571933365, 77441101020996640240446189695587781643362990063826783857810738934030], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [4, 12, 4, 2], [5, 1, 4, 1], [6, 8, 1, 1], [6, 8, 2, 1], [10, 1, 4, 1], [10, 1, 8, 1], [10, 3, 4, 2], [10, 3, 8, 1], [12, 8, 4, 1], [15, 8, 4, 1], [20, 2, 8, 1], [20, 6, 8, 1], [20, 12, 16, 2], [30, 8, 4, 1], [30, 8, 8, 1], [60, 8, 16, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^4\\times A_4).C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1031', 'autcent_hash': 1031, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3.C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.48', 'autcentquo_hash': 48, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [3, 8, 1], [4, 2, 2], [4, 6, 2], [4, 12, 8], [5, 1, 4], [6, 8, 3], [10, 1, 12], [10, 3, 16], [12, 8, 4], [15, 8, 4], [20, 2, 8], [20, 6, 8], [20, 12, 32], [30, 8, 12], [60, 8, 16]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '48.48', 'commutator_count': 1, 'commutator_label': '24.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 11067, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1], ['96.185', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [3, 8, 1, 1], [4, 2, 1, 2], [4, 6, 1, 2], [4, 12, 1, 8], [5, 1, 4, 1], [6, 8, 1, 3], [10, 1, 4, 3], [10, 3, 4, 4], [12, 8, 2, 2], [15, 8, 4, 1], [20, 2, 4, 2], [20, 6, 4, 2], [20, 12, 4, 8], [30, 8, 4, 3], [60, 8, 8, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 39060, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '480.1198', 'hash': 11067, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [1, 2, 6, 2, 2], 'inner_gens': [[1959255, 2879547, 2031892, 2300963, 2001847], [1959255, 2879547, 1377443, 469485, 2001847], [1959255, 2029081, 2031892, 469485, 1960223], [1959255, 1005521, 156898, 2300963, 2001847], [1959255, 2879547, 115274, 2300963, 2001847]], 'inner_hash': 48, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': False, 'inner_tex': 'C_2\\times S_4', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 50], [3, 40], [6, 10]], 'label': '960.11067', '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': 'A4:Q8*C10', '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, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 140, 'number_divisions': 52, 'number_normal_subgroups': 70, 'number_subgroup_autclasses': 160, 'number_subgroup_classes': 330, 'number_subgroups': 1068, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 8], [4, 112], [5, 4], [6, 24], [10, 60], [12, 32], [15, 32], [20, 448], [30, 96], [60, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [2486917, 2486917, 85185, 85185, 85185], 'outer_gens': [[3662955, 962929, 3720976, 2300963, 2001847], [1959255, 3189655, 2414279, 810225, 2001847], [1959255, 955713, 2031892, 2300963, 2001847], [1959255, 2879547, 2031892, 256523, 2001847], [3662955, 955713, 114284, 2300963, 2001847]], 'outer_group': '128.1031', 'outer_hash': 1031, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [5167, 16680, 127387560, 127387582, 216074880], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [3, 8], [4, 10], [6, 2], [8, 6], [12, 8], [16, 2], [24, 2]], 'representations': {'PC': {'code': 19869075773353293235867443950001539067476192189116973132, 'gens': [1, 2, 3, 6, 8], 'pres': [8, 2, 2, 2, 2, 3, 2, 5, 2, 201, 538, 66, 651, 91, 652, 12685, 6357, 4637, 1621, 141, 3863, 5791, 999]}, 'GLZN': {'d': 2, 'p': 44, 'gens': [2837945, 2486917, 1959255, 766665, 2445403, 1788885, 86153, 2002815]}, 'Perm': {'d': 19, 'gens': [6446835208720080, 6423383673907200, 6423384760461360, 33, 1614937680, 13581593164339200, 6402460884019200, 6423296495616000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4:Q_8\\times C_{10}', 'transitive_degree': 240, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 12], 'aut_gens': [[1, 2], [1, 10], [1, 14], [15, 2]], 'aut_group': '48.38', 'aut_hash': 38, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 7, 'aut_perms': [745, 1680, 2403], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 6, 2, 1], [6, 2, 1, 1], [12, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3\\times D_4', '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': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 2, 1], [4, 6, 2], [6, 2, 1], [12, 2, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [6, 2, 1, 1], [12, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, -1, 2]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '12.4', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6], 'inner_gens': [[1, 22], [5, 2]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 5]], 'label': '24.4', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 3, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3:Q8', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_conjugacy_classes': 9, 'number_divisions': 8, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 12, 'number_subgroups': 18, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 14], [6, 2], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [6, 0], 'outer_gens': [[7, 2], [1, 14]], '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': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 1]], 'representations': {'PC': {'code': 71237207025, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -3, 48, 177, 21, 242, 34, 259]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [41715828716014388, 58415889162259849]}, 'Lie': [{'d': 2, 'q': 13, 'gens': [910, 13193, 26376, 15381], 'family': 'CSOPlus'}, {'d': 2, 'q': 11, 'gens': [13900, 11058, 10959, 13320], 'family': 'CSOMinus'}], 'GLFp': {'d': 2, 'p': 11, 'gens': [1561, 11822]}, 'Perm': {'d': 11, 'gens': [4531705, 8448744, 12541704, 3]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:Q_8', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
