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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10364', 'ambient_counter': 10364, 'ambient_order': 960, 'ambient_tex': 'C_2\\times C_{60}.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10364.240.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '240.165', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 165, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.10364', 'aut_centralizer_order': None, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': ['4.l1'], 'conjugacy_class_count': 4, 'contained_in': ['48.f1', '80.f1', '120.b1', '120.f1'], 'contains': ['480.c1', '480.e1'], 'core': '240.f1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3, 488], 'label': '960.10364.240.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '240.f1', 'normal_contained_in': ['48.f1', '80.f1', '120.b1', '120.f1'], 'normal_contains': ['480.c1'], 'normalizer': '1.a1', 'old_label': '240.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', '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, 2], [3, 2], [2, 3]], '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, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': '80.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 4, 4, 12, 4, 4, 12], 'aut_gens': [[1, 2, 4, 16], [491, 10, 574, 656], [489, 490, 4, 26], [1, 10, 572, 664], [491, 10, 84, 946], [9, 2, 84, 114], [489, 482, 726, 664], [491, 10, 492, 314], [491, 482, 566, 304]], 'aut_group': None, 'aut_hash': 526058571217868515, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 98304, 'aut_permdeg': 60, 'aut_perms': [8061907519963328151205901553250721314368949384202116624833577734870965159111241326, 7192827024824797495945707408572059055548323085806953083153442466049935959280601734, 132636148939086731139605411516641779336973925607258352585792438609839939278806835, 8056081067283654852692496953872646901238193209099187155161245072936163257159303730, 2128904952344570160537146992247576970905357010132153679099525253965236668881131770, 7203879860802815087806749572838296740489798086820701908801255933564270128148386999, 8066333655416413530459768765922329960407171501838370359955462189599736950412450140, 8093759267372091911533256045457148836658822476566996833061460007215273240338700371], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 4, 1], [3, 2, 1, 1], [4, 2, 4, 2], [4, 12, 4, 2], [5, 1, 4, 1], [6, 2, 1, 3], [6, 2, 4, 1], [6, 2, 8, 1], [10, 1, 4, 3], [10, 1, 16, 1], [10, 2, 16, 1], [12, 2, 8, 2], [15, 2, 4, 1], [20, 2, 16, 2], [20, 12, 16, 2], [30, 2, 4, 3], [30, 2, 16, 1], [30, 2, 32, 1], [60, 2, 32, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^9.C_2^6)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 7903657167058653875, 'autcent_nilpotent': True, 'autcent_order': 8192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7.C_2^6', '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, 7], [2, 2, 4], [3, 2, 1], [4, 2, 8], [4, 12, 8], [5, 1, 4], [6, 2, 15], [10, 1, 28], [10, 2, 16], [12, 2, 16], [15, 2, 4], [20, 2, 32], [20, 12, 32], [30, 2, 60], [60, 2, 64]], 'center_label': '40.14', 'center_order': 40, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '12.5', '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': 10364, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1], ['96.131', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 2, 1, 1], [4, 2, 1, 4], [4, 2, 2, 2], [4, 12, 1, 8], [5, 1, 4, 1], [6, 2, 1, 7], [6, 2, 2, 4], [10, 1, 4, 7], [10, 2, 4, 4], [12, 2, 2, 4], [12, 2, 4, 2], [15, 2, 4, 1], [20, 2, 4, 4], [20, 2, 8, 2], [20, 12, 4, 8], [30, 2, 4, 7], [30, 2, 8, 4], [60, 2, 8, 4], [60, 2, 16, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2555280, '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': '4.2', 'frattini_quotient': '240.206', 'hash': 10364, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 1, 2, 6], 'inner_gens': [[1, 2, 492, 16], [1, 2, 4, 16], [489, 2, 4, 176], [1, 2, 804, 16]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': False, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 80], [2, 220]], 'label': '960.10364', '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': 'C2*C60.D4', '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': 36, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 300, 'number_divisions': 88, 'number_normal_subgroups': 286, 'number_subgroup_autclasses': 208, 'number_subgroup_classes': 644, 'number_subgroups': 1328, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 112], [5, 4], [6, 30], [10, 60], [12, 32], [15, 8], [20, 448], [30, 120], [60, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 4, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 640, 320], 'outer_gens': [[491, 490, 4, 754], [9, 10, 324, 760], [489, 482, 732, 122], [3, 490, 414, 664], [483, 490, 724, 466], [1, 10, 564, 114], [11, 2, 644, 592]], 'outer_group': '1024.dis', 'outer_hash': 3264063356326401077, 'outer_nilpotent': True, 'outer_order': 4096, 'outer_permdeg': 512, 'outer_perms': 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': '(C_2^2\\wr C_2)^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 26], [8, 18], [16, 10], [32, 2]], 'representations': {'PC': {'code': 13556309140114619774992784073275211783, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 11810, 66, 1780, 116, 4245, 141, 9878, 222]}, 'GLZN': {'d': 2, 'p': 44, 'gens': [2486917, 1959255, 1832467, 766665, 1487589, 1788885, 86153, 1190539]}, 'Perm': {'d': 22, 'gens': [2432925914192122320, 6402373705728000, 45968909052240, 68436399316320, 33, 41040, 68436399225600, 53523844179886080000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{60}.D_4', 'transitive_degree': 480, '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': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 6, 4, 4, 2], 'aut_gens': [[1, 2, 4], [1, 2, 29], [1, 2, 164], [1, 22, 124], [1, 182, 197], [121, 123, 4], [1, 2, 124]], 'aut_group': '1536.194556563', 'aut_hash': 1637901404035917049, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 15, 'aut_perms': [193157758089, 193158121080, 561960324000, 561959959680, 348872832000, 124104960], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 6, 4, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 1, 4, 1], [10, 1, 8, 1], [12, 2, 4, 1], [15, 2, 4, 1], [20, 2, 8, 1], [20, 6, 16, 1], [30, 2, 4, 1], [30, 2, 8, 1], [60, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': '(D_6\\times C_4^2):D_4', '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': 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, 3], [3, 2, 1], [4, 2, 2], [4, 6, 4], [5, 1, 4], [6, 2, 3], [10, 1, 12], [12, 2, 4], [15, 2, 4], [20, 2, 8], [20, 6, 16], [30, 2, 12], [60, 2, 16]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, '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', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 165, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.4', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 1, 4], [5, 1, 4, 1], [6, 2, 1, 3], [10, 1, 4, 3], [12, 2, 2, 2], [15, 2, 4, 1], [20, 2, 4, 2], [20, 6, 4, 4], [30, 2, 4, 3], [60, 2, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2604, 'exponent': 60, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '120.45', 'hash': 165, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 6], 'inner_gens': [[1, 2, 4], [1, 2, 44], [1, 202, 4]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 50]], 'label': '240.165', 'linC_count': 384, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 56, 'linQ_dim': 10, 'linQ_dim_count': 52, 'linR_count': 32, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C30:Q8', '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': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 90, 'number_divisions': 32, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 76, 'number_subgroups': 120, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [5, 4], [6, 6], [10, 12], [12, 8], [15, 8], [20, 112], [30, 24], [60, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [0, 12, 0, 0, 0], 'outer_gens': [[121, 2, 124], [1, 62, 196], [1, 123, 4], [1, 2, 148], [121, 2, 5]], 'outer_group': '128.1031', 'outer_hash': 1031, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [367927, 806400, 262897920, 40284862, 127019640], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, '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], [4, 10], [8, 6], [16, 2]], 'representations': {'PC': {'code': 6604223689737096648581127, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -5, 727, 404, 50, 1065, 69, 2650, 118]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1547864562, 106922612, 296010408, 632568400, 297800445, 2143735230]}, 'Perm': {'d': 18, 'gens': [379574279925120, 774405718732801, 1156178136960000, 870, 774405718732800, 403200]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{30}:Q_8', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
