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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9909', 'ambient_counter': 9909, 'ambient_order': 1600, 'ambient_tex': 'D_{10}^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 1, 'counter': 224, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1600.9909.1600.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1600.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1600.9909', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9909, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1600, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}^2.C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '1600.9909', 'aut_centralizer_order': None, 'aut_label': '1600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['320.a1', '320.b1', '800.a1', '800.b1', '800.c1', '800.d1', '800.e1', '800.f1'], 'contains': [], 'core': '1600.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2179, 7259, 2415, 7187], 'generators': [], 'label': '1600.9909.1600.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1600.a1', 'normal_contained_in': ['320.a1', '800.a1', '800.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1600.a1', 'projective_image': '1600.9909', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1600.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [8, 4, 20, 8, 8, 20, 10], 'aut_gens': [[1, 2, 8, 80], [813, 1274, 664, 1424], [1153, 538, 872, 1424], [1329, 1146, 808, 784], [69, 946, 664, 1384], [813, 482, 392, 904], [1505, 970, 808, 880], [69, 1482, 664, 632]], 'aut_group': None, 'aut_hash': 7405880406020351339, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 204800, 'aut_permdeg': 240, 'aut_perms': [181050241282081463770931636730823750944789107244276608495821262068428612520440948729431337787824747906184959604125167054161363703640370067555658657209647844526017211423094803624881196582175008997261998204872508161964889285652025182487473740112318592956381683768398987461897769049434412187164373049595018064161605033673956952775255857505766141822206458786864835191195495514455792606237064213112176603365554984395321552845969807730388213388786053142700934132512593272846, 3992900077264557827634418537221665617012212622353754113784700160745824601780998409304804302891800752304745551712415187502696714023134175910877775163877412917624839405077113558296955155587740953448310007114004925224396700654919178602920616628717807792016081493588480492338922976648328668227279369713613681815848689004259619482229133269767149702407762373488140350429491492068137488670729867778955358695315383327867920948490511810670757966837705897913141861882000273100266, 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1375187177829944490625938088865485264894941421868343333940427318853921169010337628830794992357394624476374108436723749547643125036761846051866211645949060484808140844620886977351928976705831678155529756871468048398569194821483429116035568249931844745320385652855053974445094136153561106129755654915566191632664328537977328760302470558536217386624454492224862874628891274702637094566606072832466768518974255500317185468605995685453839636599473479324070687181829173432293, 2701013942886789379294434508853922472310306051834401763808826641287846762687829896959963701327171402830422312772023031921936448178017647397251017529344645069613640659626756645311058934498305315476625035207412507423816277846881898935386664945932917073859923160917967553267808941022692892098258383788406973370434878182626635748126696209511750482084965646858832535158694659826746037280043529868438582383179543354694159566046009453829532151260182662797460142119168472551647, 3394758068248549335890625692823445440678386221641448625354828761293184027285596321373809680049856808197095924408925957570464151785963906270308950198872327396056921372108897886831472980153855659692192283266654265659248464675448147224801564683637058064915650932478287582872043916769757961659458726691101671764253451263814638019365684541816983783996425781633367427614143736911567852263119001350241036573219207405043291535112786157433402000057302920885068234221559555355729], 'aut_phi_ratio': 320.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 5, 8, 1], [2, 25, 1, 2], [2, 25, 2, 1], [4, 2, 2, 1], [4, 10, 4, 1], [4, 50, 2, 1], [4, 50, 4, 2], [4, 50, 8, 1], [5, 4, 2, 1], [5, 8, 2, 1], [10, 4, 2, 1], [10, 4, 4, 1], [10, 8, 2, 1], [10, 8, 4, 1], [10, 20, 8, 1], [20, 4, 8, 1], [20, 8, 8, 1], [20, 20, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5:F_5.C_2^5.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '1600.10254', 'autcentquo_hash': 10254, 'autcentquo_nilpotent': False, 'autcentquo_order': 1600, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 5, 8], [2, 25, 4], [4, 2, 2], [4, 10, 4], [4, 50, 18], [5, 4, 2], [5, 8, 2], [10, 4, 6], [10, 8, 6], [10, 20, 8], [20, 4, 8], [20, 8, 8], [20, 20, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '400.210', 'commutator_count': 1, 'commutator_label': '50.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9909, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['800.1023', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 5, 1, 8], [2, 25, 1, 4], [4, 2, 1, 2], [4, 10, 1, 4], [4, 50, 1, 2], [4, 50, 2, 8], [5, 4, 1, 2], [5, 8, 1, 2], [10, 4, 1, 6], [10, 8, 1, 6], [10, 20, 1, 8], [20, 4, 2, 4], [20, 8, 2, 4], [20, 20, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9686880, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '800.1199', 'hash': 9909, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 5, 10], 'inner_gens': [[1, 2, 8, 784], [1, 2, 24, 240], [1, 66, 8, 80], [977, 1442, 8, 80]], 'inner_hash': 210, 'inner_nilpotent': False, 'inner_order': 400, 'inner_split': False, 'inner_tex': 'D_{10}:F_5', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 32], [8, 16]], 'label': '1600.9909', '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': 'D10^2.C2^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 88, 'number_divisions': 68, 'number_normal_subgroups': 231, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 928, 'number_subgroups': 8748, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 143], [4, 944], [5, 24], [10, 232], [20, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 2, 4, 4, 2, 2], 'outer_gen_pows': [1348, 129, 448, 1284, 1316, 1072, 672], 'outer_gens': [[813, 1274, 664, 1424], [1153, 538, 872, 1424], [1329, 1146, 808, 784], [69, 946, 664, 1384], [813, 482, 392, 904], [1505, 970, 808, 880], [69, 1482, 664, 632]], 'outer_group': '512.7591302', 'outer_hash': 2193488006507047561, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 64, 'outer_perms': [2145142888039248032652750242123192759223888478821552861715944206907251213256897656168618, 189444195744251635044516751007043220197162766853127087797183900230125012455686038758828, 222445366969445410089283620125196071426220114750556787975817963127880839925023626595404, 4222695194103752093111381656955697500621483671267401583056021538600957618222450135011025, 6237189257676642130175069227076591732514183206310020986940085348299895834187534426451183, 8251756535995420001268851387552465427064924589424788187631687658740812491699252307009747, 10167432320601524036686795498769679399465632925833691747374151574362618006035627305273567], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 16], [8, 16], [16, 4]], 'representations': {'PC': {'code': 12471900360284128175491651195045922708142406588418093458875069628611, 'gens': [1, 2, 4, 6], 'pres': [8, 2, 2, 2, 2, 5, 2, 2, 5, 41, 395, 595, 91, 972, 660, 37637, 5773, 8661, 141, 83334, 13454, 20182, 166, 82951, 30735, 20503]}, 'Perm': {'d': 16, 'gens': [93887982729, 7983376, 7984080, 10887120, 186810624016, 7983360, 34, 1407306700800]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}^2.C_2^2', 'transitive_degree': 80, '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [8, 4, 20, 8, 8, 20, 10], 'aut_gens': [[1, 2, 8, 80], [813, 1274, 664, 1424], [1153, 538, 872, 1424], [1329, 1146, 808, 784], [69, 946, 664, 1384], [813, 482, 392, 904], [1505, 970, 808, 880], [69, 1482, 664, 632]], 'aut_group': None, 'aut_hash': 7405880406020351339, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 204800, 'aut_permdeg': 240, 'aut_perms': 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3394758068248549335890625692823445440678386221641448625354828761293184027285596321373809680049856808197095924408925957570464151785963906270308950198872327396056921372108897886831472980153855659692192283266654265659248464675448147224801564683637058064915650932478287582872043916769757961659458726691101671764253451263814638019365684541816983783996425781633367427614143736911567852263119001350241036573219207405043291535112786157433402000057302920885068234221559555355729], 'aut_phi_ratio': 320.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 5, 8, 1], [2, 25, 1, 2], [2, 25, 2, 1], [4, 2, 2, 1], [4, 10, 4, 1], [4, 50, 2, 1], [4, 50, 4, 2], [4, 50, 8, 1], [5, 4, 2, 1], [5, 8, 2, 1], [10, 4, 2, 1], [10, 4, 4, 1], [10, 8, 2, 1], [10, 8, 4, 1], [10, 20, 8, 1], [20, 4, 8, 1], [20, 8, 8, 1], [20, 20, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5:F_5.C_2^5.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '1600.10254', 'autcentquo_hash': 10254, 'autcentquo_nilpotent': False, 'autcentquo_order': 1600, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 5, 8], [2, 25, 4], [4, 2, 2], [4, 10, 4], [4, 50, 18], [5, 4, 2], [5, 8, 2], [10, 4, 6], [10, 8, 6], [10, 20, 8], [20, 4, 8], [20, 8, 8], [20, 20, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '400.210', 'commutator_count': 1, 'commutator_label': '50.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9909, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['800.1023', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 5, 1, 8], [2, 25, 1, 4], [4, 2, 1, 2], [4, 10, 1, 4], [4, 50, 1, 2], [4, 50, 2, 8], [5, 4, 1, 2], [5, 8, 1, 2], [10, 4, 1, 6], [10, 8, 1, 6], [10, 20, 1, 8], [20, 4, 2, 4], [20, 8, 2, 4], [20, 20, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9686880, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '800.1199', 'hash': 9909, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 5, 10], 'inner_gens': [[1, 2, 8, 784], [1, 2, 24, 240], [1, 66, 8, 80], [977, 1442, 8, 80]], 'inner_hash': 210, 'inner_nilpotent': False, 'inner_order': 400, 'inner_split': False, 'inner_tex': 'D_{10}:F_5', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 32], [8, 16]], 'label': '1600.9909', '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': 'D10^2.C2^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 88, 'number_divisions': 68, 'number_normal_subgroups': 231, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 928, 'number_subgroups': 8748, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 143], [4, 944], [5, 24], [10, 232], [20, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 2, 4, 4, 2, 2], 'outer_gen_pows': [1348, 129, 448, 1284, 1316, 1072, 672], 'outer_gens': [[813, 1274, 664, 1424], [1153, 538, 872, 1424], [1329, 1146, 808, 784], [69, 946, 664, 1384], [813, 482, 392, 904], [1505, 970, 808, 880], [69, 1482, 664, 632]], 'outer_group': '512.7591302', 'outer_hash': 2193488006507047561, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 64, 'outer_perms': [2145142888039248032652750242123192759223888478821552861715944206907251213256897656168618, 189444195744251635044516751007043220197162766853127087797183900230125012455686038758828, 222445366969445410089283620125196071426220114750556787975817963127880839925023626595404, 4222695194103752093111381656955697500621483671267401583056021538600957618222450135011025, 6237189257676642130175069227076591732514183206310020986940085348299895834187534426451183, 8251756535995420001268851387552465427064924589424788187631687658740812491699252307009747, 10167432320601524036686795498769679399465632925833691747374151574362618006035627305273567], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 16], [8, 16], [16, 4]], 'representations': {'PC': {'code': 12471900360284128175491651195045922708142406588418093458875069628611, 'gens': [1, 2, 4, 6], 'pres': [8, 2, 2, 2, 2, 5, 2, 2, 5, 41, 395, 595, 91, 972, 660, 37637, 5773, 8661, 141, 83334, 13454, 20182, 166, 82951, 30735, 20503]}, 'Perm': {'d': 16, 'gens': [93887982729, 7983376, 7984080, 10887120, 186810624016, 7983360, 34, 1407306700800]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}^2.C_2^2', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}
