-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26484', 'ambient_counter': 26484, 'ambient_order': 256, 'ambient_tex': '(C_2\\times Q_8):C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.26484.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2136', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2136, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '256.26484', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2994, 3852, 3042, 3842], 'generators': [128], 'label': '256.26484.128.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1', '64.c1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], '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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '128.2136', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 6, 8, 4, 4, 12, 4], 'aut_gens': [[1, 2, 4, 64], [131, 130, 253, 66], [225, 162, 188, 33], [3, 2, 110, 99], [161, 162, 143, 67], [66, 130, 103, 163], [67, 162, 181, 33], [99, 162, 84, 192]], 'aut_group': None, 'aut_hash': 4868006769324068202, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 128, 'aut_perms': [204215455495098308913409131187609831070442132251834941910728320993976758117782075338974095957579650180504030710066545650932214861335413375411120974013150847665746251209035978880167995579441109046104264325592882513995, 227648743623278595340649796510851767805905533812336503312808265016539393674934861344153088296623353537260929870847586272537962271727548747786029122819883286896384530502516581159989593233861180800335298917348319667559, 15941570513496648143718706472506859345447392427311805615816934342514722604095201404792474903051213883881946707698544441791215545663570203394900850136461823551330974948237632549377658711161148254696527483575652864127, 364374552068468020431834113254701186857658218852993755475583256070194822385954342270750858837168685860045633643291300124866000963239213441192139783092369403053102475431257238681869286554979285161559092269782632475818, 76098558416279522926091742227453385850029560209061740849782781520404369301141028641892107485830362533256402584370792737891721673637230506353778994406460587068186273347925658431549114246000385453550111477229590233466, 344807348103034556991295201230001447276918602278995544349186196564449493494269806846480228707634555996591769652169860259668797325416750233701830848510537725995059346627300322412135403931800376760399953547057680537363, 296610065268528307141449644646011621372121689161653999534642748285335075857666383807081224502820757168069951716956750089078007518741651613074654277467124397537725815432038977328627281171922805944038157955681789841057], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [4, 1, 2, 2], [4, 2, 2, 1], [4, 2, 12, 2], [8, 1, 8, 1], [8, 2, 4, 1], [8, 2, 24, 1], [16, 2, 64, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.A_4.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 1718285292446712972, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8\\times C_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, 2, 2], [4, 1, 4], [4, 2, 26], [8, 1, 8], [8, 2, 28], [16, 2, 64]], 'center_label': '16.5', 'center_order': 16, 'central_product': True, 'central_quotient': '16.14', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 26484, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 1, 2, 2], [4, 2, 1, 12], [4, 2, 2, 7], [8, 1, 4, 2], [8, 2, 4, 7], [16, 2, 8, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 26880, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '16.14', 'hash': 26484, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[1, 2, 4, 192], [1, 2, 132, 64], [1, 130, 4, 64], [129, 2, 4, 64]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 128], [4, 8]], 'label': '256.26484', '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*Q8):C16', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 136, 'number_divisions': 44, 'number_normal_subgroups': 227, 'number_subgroup_autclasses': 64, 'number_subgroup_classes': 263, 'number_subgroups': 311, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64], [16, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 4, 12, 12, 8], 'outer_gen_pows': [34, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 165, 194], [35, 2, 255, 226], [35, 34, 125, 226], [194, 34, 133, 227], [97, 2, 12, 161], [35, 34, 247, 193]], 'outer_group': None, 'outer_hash': 8991648998182181198, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 34, 'outer_perms': [38773870993069156149599171137268528646, 43696438943022609835371852923774461495, 207321820052937419129062084190496639367, 178597830970990141716434057465604796200, 92105689206060703495470712926586237368, 273317810245617088954408333959354462054], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^3:A_4.C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 16], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 10], [8, 9], [16, 1]], 'representations': {'PC': {'code': 9709335386730759807062109, 'gens': [1, 2, 3, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1024, 1594, 66, 91, 116, 10758, 166]}, 'Perm': {'d': 32, 'gens': [8285353364295028324197332433734823, 17810447957534352342604021558733284, 25535979500253751095462337600973284, 34564280686318150196513398152653284, 43061319207073932108668083888128000, 4397976680734, 5800817303020, 2966658509284]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 16], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times Q_8):C_{16}', 'transitive_degree': 128, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '128.2136', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 168, 'aut_gen_orders': [2, 2, 2, 2, 4, 4, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 8], [70, 2, 67, 79], [1, 2, 4, 15], [1, 2, 4, 72], [1, 67, 69, 8], [1, 2, 4, 24], [1, 2, 4, 104], [65, 2, 68, 72], [1, 2, 4, 77], [1, 71, 4, 77], [1, 2, 4, 73]], 'aut_group': '86016.bk', 'aut_hash': 3270269662069206077, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 86016, 'aut_permdeg': 34, 'aut_perms': [144837903429120095961757595345979273720, 1920833431893351976830076735493046, 18684210223057525662467576180300790966, 118064606089713125444838326400371758080, 8980437409661352453257127716943575047, 52103747306013426605553945216122908080, 144840469689942105726824542131498651774, 18682617177822394450571338564155941046, 100023423486098033691920128413066110934, 18684209003500424626973511562010926080], 'aut_phi_ratio': 1344.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 14, 1], [4, 1, 2, 1], [4, 1, 14, 1], [8, 1, 4, 1], [8, 1, 28, 1], [16, 1, 64, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4.C_2^7:\\GL(3,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 168, 'autcent_group': '86016.bk', 'autcent_hash': 3270269662069206077, 'autcent_nilpotent': False, 'autcent_order': 86016, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_4.C_2^7:\\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, 15], [4, 1, 16], [8, 1, 32], [16, 1, 64]], 'center_label': '128.2136', 'center_order': 128, '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', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 2136, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [4, 1, 2, 8], [8, 1, 4, 8], [16, 1, 8, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 960, 'exponent': 16, 'exponents_of_order': [7], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '16.14', 'hash': 2136, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8]], '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, 128]], 'label': '128.2136', 'linC_count': None, 'linC_degree': 4, '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': 'C2^3*C16', '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 128, 'number_divisions': 40, 'number_normal_subgroups': 220, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 220, 'number_subgroups': 220, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 15], [4, 16], [8, 32], [16, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 168, 'outer_gen_orders': [2, 2, 2, 2, 4, 4, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[70, 2, 67, 79], [1, 2, 4, 15], [1, 2, 4, 72], [1, 67, 69, 8], [1, 2, 4, 24], [1, 2, 4, 104], [65, 2, 68, 72], [1, 2, 4, 77], [1, 71, 4, 77], [1, 2, 4, 73]], 'outer_group': '86016.bk', 'outer_hash': 3270269662069206077, 'outer_nilpotent': False, 'outer_order': 86016, 'outer_permdeg': 34, 'outer_perms': [144837903429120095961757595345979273720, 1920833431893351976830076735493046, 18684210223057525662467576180300790966, 118064606089713125444838326400371758080, 8980437409661352453257127716943575047, 52103747306013426605553945216122908080, 144840469689942105726824542131498651774, 18682617177822394450571338564155941046, 100023423486098033691920128413066110934, 18684209003500424626973511562010926080], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_4.C_2^7:\\GL(3,2)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 16], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 8], [8, 8]], 'representations': {'PC': {'code': 2233919864888, 'gens': [1, 2, 3, 4], 'pres': [7, -2, 2, 2, 2, -2, -2, -2, 80, 102, 124]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [28573, 562037, 285389, 22345, 30431, 111609, 337745]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [102991, 565385, 33041, 1032719, 33281, 557073, 573969]}, 'Perm': {'d': 22, 'gens': [20916435456000, 121645100408832000, 355687428096000, 51090942171709440000, 9703614452976, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 16], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3\\times C_{16}', 'transitive_degree': 128, 'wreath_data': None, 'wreath_product': False}
