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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1120.833', 'ambient_counter': 833, 'ambient_order': 1120, 'ambient_tex': 'D_{70}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 560, 'characteristic': True, 'core_order': 14, 'counter': 108, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1120.833.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1120.833', 'aut_centralizer_order': 17920, 'aut_label': '80.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17920, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.c1.a1', '40.c1.b1'], 'contains': ['160.a1.a1', '560.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [96, 8113, 2251, 4825, 2984, 3730, 2566, 2728], 'generators': [700, 40], 'label': '1120.833.80.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1'], 'normal_contains': ['160.a1.a1', '560.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '560.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.11', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '14.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [6], 'aut_gens': [[1], [3]], 'aut_group': '6.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 6, 'aut_permdeg': 5, 'aut_perms': [27], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [7, 1, 6, 1], [14, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 6, 'autcent_group': '6.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6', '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], [7, 1, 6], [14, 1, 6]], 'center_label': '14.2', 'center_order': 14, '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', '7.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [7, 1, 6, 1], [14, 1, 6, 1]], 'element_repr_type': 'PC', 'elementary': 14, 'eulerian_function': 1, 'exponent': 14, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 7], 'faithful_reps': [[1, 0, 6]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '14.2', 'hash': 2, 'hyperelementary': 14, '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': 6, 'irrQ_dim': 6, 'irrR_degree': 2, 'irrep_stats': [[1, 14]], 'label': '14.2', 'linC_count': 6, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1, 'linQ_dim': 6, 'linQ_dim_count': 1, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C14', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 14, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 14, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [7, 6], [14, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2]], 'representations': {'PC': {'code': 185, 'gens': [1], 'pres': [2, -2, -7, 4]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [75621406240170985]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [351, 2064]}, 'Perm': {'d': 9, 'gens': [40320, 4320]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [14], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{14}', 'transitive_degree': 14, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 6, 70, 12, 4, 70, 12, 12], 'aut_gens': [[1, 2, 280], [649, 934, 840], [77, 778, 280], [129, 842, 840], [237, 1058, 980], [713, 1034, 280], [629, 702, 420], [657, 666, 840], [601, 934, 980]], 'aut_group': None, 'aut_hash': 8888889471875883849, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 107520, 'aut_permdeg': 148, 'aut_perms': [1418089327225558418349404754068400429515415316834461102918627228209717353793167720047967042393559922726306801586690398543539707052988096573681250608120931830507045426984930960138130909117843388279679817020119893225318630352246821736982190758361312266343111466, 1691960250254592207233851207219764348847269418770374816288255910853766121540774680511404670350686471547820551269471022767236660704084848490798259632048984718078877679732575937772385667745380798904797492877611494589250072112122906659972046489554512511558111271, 1469619792013869778822374215171553465539459939951508999048927986662534289191246600851426412483691043728624231378484312668775339370105729580095959197122814111310094191041238470086797541194378073149528218831733635349222209661847811232145786191463504160958876271, 54863505189857120029285471346930284036131290456961363268342369217925646535796413933282743528516868928464252741037335868425849068457642551749157145262759568635925088698037426866543612856837597260308579421294744275974706500444261791481928433177824027131844063, 1272953079307668288716246311066626663915098473573104002234994916407301519573862436211339081781069198630186692930264587128811714442580208130117208598506777843418166444780147119484243779549879340552602976374023150193823925517177362050170018281409568390995948641, 1121275643745191657294015810399874146063675471176712887715780058616417985626193264285646683207851714362275914689797193529267895339481366652094087542736960958853488883329442250630457706280849608279997376358122134699330678347423097474741410637648162177970833786, 858408285720550663202298846586368853250995651138743199772801017336482747318302877542422624507626310829536913937532908081148294218436339295993468410805096865855959919627049715868120137142701654539471683842294854968067616879011024183986045057969913484766420915, 461481132510138719665932322164925400645346094430452989425473223806008046546494149364891993464584904109472789728263271542309615621424899377436472200660562102258415971482953467151125267719411737048608789961973308153796238149887530331676056774373729739160172413], 'aut_phi_ratio': 280.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 70, 2, 1], [4, 2, 2, 1], [4, 4, 2, 1], [4, 70, 2, 1], [4, 140, 2, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 3], [14, 2, 3, 3], [20, 4, 4, 1], [20, 4, 8, 1], [28, 4, 6, 1], [28, 4, 12, 1], [35, 2, 12, 1], [70, 2, 12, 3], [140, 4, 24, 1], [140, 4, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{70}.(C_2^3\\times C_6).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '1680.934', 'autcentquo_hash': 934, 'autcentquo_nilpotent': False, 'autcentquo_order': 1680, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{70}:C_{12}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 70, 2], [4, 2, 2], [4, 4, 2], [4, 70, 2], [4, 140, 2], [5, 2, 2], [7, 2, 3], [10, 2, 6], [14, 2, 9], [20, 4, 12], [28, 4, 18], [35, 2, 12], [70, 2, 36], [140, 4, 72]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '280.39', 'commutator_count': 1, 'commutator_label': '140.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 833, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 70, 1, 2], [4, 2, 1, 2], [4, 4, 1, 2], [4, 70, 2, 1], [4, 140, 1, 2], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 3], [14, 2, 3, 3], [20, 4, 2, 2], [20, 4, 4, 2], [28, 4, 3, 2], [28, 4, 6, 2], [35, 2, 12, 1], [70, 2, 12, 3], [140, 4, 12, 2], [140, 4, 24, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4032, 'exponent': 140, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '280.39', 'hash': 833, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 70, 2], 'inner_gens': [[1, 838, 280], [565, 2, 840], [1, 562, 280]], 'inner_hash': 39, 'inner_nilpotent': False, 'inner_order': 280, 'inner_split': True, 'inner_tex': 'C_2\\times D_{70}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 142], [4, 34]], 'label': '1120.833', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 64, 'linQ_dim': 16, 'linQ_dim_count': 96, 'linR_count': 144, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D70:Q8', 'ngens': 7, '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': 27, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 184, 'number_divisions': 37, 'number_normal_subgroups': 57, 'number_subgroup_autclasses': 104, 'number_subgroup_classes': 148, 'number_subgroups': 1740, 'old_label': None, 'order': 1120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 143], [4, 432], [5, 4], [7, 6], [10, 12], [14, 18], [20, 48], [28, 72], [35, 24], [70, 72], [140, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 4, 12], 'outer_gen_pows': [280, 0, 0, 0, 0], 'outer_gens': [[1, 338, 280], [561, 58, 280], [701, 2, 280], [561, 114, 280], [141, 442, 980]], 'outer_group': '384.19882', 'outer_hash': 19882, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [744, 7985040, 11654160, 187301278080, 868], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4\\times C_{12}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 5], [6, 4], [8, 4], [12, 4], [24, 4], [48, 4]], 'representations': {'PC': {'code': 94697043635958366789446912668668076092, 'gens': [1, 2, 6], 'pres': [7, -2, -2, -2, -5, -7, -2, -2, 11733, 36, 5798, 58, 7619, 164, 8404, 17652, 124]}, 'Perm': {'d': 24, 'gens': [1126440033473391805009, 40292140, 87472603, 40279680, 5329, 23544365644800, 28104890400830251008000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{70}:Q_8', 'transitive_degree': 560, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 12, 2, 10], 'aut_gens': [[1, 2, 4], [1, 42, 4], [21, 2, 44], [61, 2, 73], [1, 2, 44], [41, 18, 4]], 'aut_group': '960.11361', 'aut_hash': 11361, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 11, 'aut_perms': [120, 1, 1088643, 16, 4072327], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 2, 1], [4, 2, 3, 1], [4, 10, 3, 1], [5, 2, 2, 1], [10, 2, 2, 1], [20, 4, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times F_5\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [4, 2, 3], [4, 10, 3], [5, 2, 2], [10, 2, 2], [20, 4, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '40.13', 'commutator_count': 1, 'commutator_label': '10.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 41, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['10.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [4, 2, 1, 3], [4, 10, 1, 3], [5, 2, 2, 1], [10, 2, 2, 1], [20, 4, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 168, 'exponent': 20, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[4, -1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '40.13', 'hash': 41, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 2, 10], 'inner_gens': [[1, 2, 44], [1, 2, 36], [41, 50, 4]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 40, 'inner_split': False, 'inner_tex': 'C_2\\times D_{10}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 2]], 'label': '80.41', 'linC_count': 18, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'Q8*D5', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 20, 'number_divisions': 15, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 20, 'number_subgroup_classes': 38, 'number_subgroups': 90, 'old_label': None, 'order': 80, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 11], [4, 36], [5, 4], [10, 4], [20, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 1, 2], 'outer_gens': [[1, 42, 4], [1, 2, 5], [20, 2, 29]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 120, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 4], [8, 1]], 'representations': {'PC': {'code': 13415476492148454403, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -5, 200, 662, 277, 42, 728, 58, 809]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [116397747727, 111158879322, 73926457827, 3381495366, 67540780101]}, 'Perm': {'d': 13, 'gens': [40285009, 12460, 18523, 5329, 559198080]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8\\times D_5', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}
