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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': False, 'central_factor': False, 'centralizer_order': 400, 'characteristic': False, 'core_order': 5, 'counter': 201, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.9909.320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '320.1591', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1591, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}.C_2^4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1600.9909', 'aut_centralizer_order': 25600, 'aut_label': '320.a1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 51200, 'centralizer': '4.a1', 'complements': ['5.a1'], 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '160.a1', '160.b1', '160.c1', '160.f1', '160.g1', '160.i1', '160.k1'], 'contains': ['1600.a1'], 'core': '320.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1470, 6526, 2289, 6825], 'generators': [16], 'label': '1600.9909.320.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '320.a1', 'normal_contained_in': ['64.a1', '160.a1', '160.b1', '160.c1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '320.a1', 'projective_image': '1600.9909', 'quotient_action_image': '4.1', 'quotient_action_kernel': '80.45', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '320.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [2]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4]], 'center_label': '5.1', 'center_order': 5, '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': ['5.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 1, 'exponent': 5, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5.1', 'hash': 1, 'hyperelementary': 5, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 5]], 'label': '5.1', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5', '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': 5, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 5, 'order_factorization_type': 1, 'order_stats': [[1, 1], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 5, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -5]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26329372]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131]}, 'Perm': {'d': 5, 'gens': [96]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [5], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5', 'transitive_degree': 5, '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, 3107791922344380965921921842041424982906071198746420348501724800386502779901744185649312400063929713042133830473601709252372132127660838763338349642645681129690612849064718960074928348424547969764494929241440508845313932326677210926016032104432006940582953445004412120761760218348183508979439846996032890228572675871243892722490777543757317234313744643547562731666940309633958832299105101719212979141555034284412753895473965420264306435189560670273083183180498254908948, 755353224243175506011801560872044636126461298101101807186340515720210848228460863875415602659250689000530350069559844215557925816285747118861049211366951076720414271871284273522693387094448127222555574676769600642718439884754698052679349874653407953972682173096067744038569893330183516186350083400169165430742524686645900358302691922152429800981812708558239265105523226735585765462468371684194885770815438859170740251381498211318539853770212592158494231811684547425014, 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': 4, 'aut_exponent': 120, 'aut_gen_orders': [2, 4, 2, 5, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8, 16], [169, 10, 8, 144], [1, 2, 8, 272], [161, 170, 8, 144], [1, 130, 8, 16], [1, 251, 8, 144], [161, 171, 168, 304], [1, 2, 8, 153], [1, 162, 8, 144], [1, 162, 8, 304], [8, 162, 1, 144], [1, 11, 8, 144]], 'aut_group': '61440.em', 'aut_hash': 5907412864111550192, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 61440, 'aut_permdeg': 80, 'aut_perms': [5594800199753698094584207757572722539964085204190530852146612122702993900178460505002435004828549318359225558596089842, 68851923750974802716263448293933692482687165113097724521852473440832781786562662607499268713163381834348783286854346240, 16184585276369329221734354900823932319009179047434760936316596063352870419590493377055970504387433429858417645929561709, 7248716704173495525314976137649241214375934829555037409689330589946464425793483170907107476565415864401443898517346560, 57072023638460676751995659883046236043340967401980937427582340289689476813037694038493097496811142305636239422206519039, 6457170821260400442273872841380054963878165564677821450180403488789815231254640259303354268493948146972463521618669539, 7247834141831606432759521472568323921526638270522544616928246172250319522724345875139126121127181799469640669128293984, 18120909197443868393909271234554392357764915068178928901208705677137537843013037787396944592051082728239856414218852784, 18120909197443868393909271234554392357764914661757175663780033243188217570986443300482379334642907049625111905747913264, 17226292869860394149717470855359069007437667227009993108073820756755492136473795238953235334628878451447029793167818008, 6331006711149799453743905293012873782238369273040049414709876767695017073289031784481156777171792160092036880328294399], 'aut_phi_ratio': 480.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 5, 1, 2], [2, 5, 6, 1], [4, 2, 4, 1], [4, 10, 4, 1], [4, 10, 8, 2], [5, 4, 1, 1], [10, 4, 1, 1], [10, 4, 6, 1], [20, 4, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5\\times C_2^6:(C_2\\times S_4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '1536.408640869', 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '40.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 40, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 5, 8], [4, 2, 4], [4, 10, 20], [5, 4, 1], [10, 4, 7], [20, 4, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '40.12', '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', '2.1', '2.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1591, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['80.31', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 5, 1, 8], [4, 2, 1, 4], [4, 10, 1, 4], [4, 10, 2, 8], [5, 4, 1, 1], [10, 4, 1, 7], [20, 4, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 52080, 'exponent': 20, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '160.236', 'hash': 1591, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [1, 4, 1, 10], 'inner_gens': [[1, 2, 8, 16], [1, 2, 8, 48], [1, 2, 8, 16], [1, 290, 8, 16]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 40, 'inner_split': False, 'inner_tex': 'C_2\\times F_5', 'inner_used': [2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 16]], 'label': '320.1591', '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.C2^4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 56, 'number_divisions': 44, 'number_normal_subgroups': 196, 'number_subgroup_autclasses': 78, 'number_subgroup_classes': 418, 'number_subgroups': 1386, 'old_label': None, 'order': 320, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 47], [4, 208], [5, 4], [10, 28], [20, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 80, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[9, 10, 8, 176], [8, 11, 9, 17], [1, 90, 8, 16], [1, 163, 168, 176], [161, 10, 8, 16], [161, 11, 168, 25], [161, 10, 8, 184], [1, 2, 8, 176], [1, 3, 8, 16], [1, 10, 8, 16]], 'outer_group': '1536.408632661', 'outer_hash': 6321312703651895429, 'outer_nilpotent': False, 'outer_order': 1536, 'outer_permdeg': 16, 'outer_perms': [4296764107855, 262017867456, 4302991486080, 7, 126, 2877842004342, 5413204742273, 5167, 2878807236480, 1321086775680], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^6:S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, '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, 8], [8, 4]], 'representations': {'PC': {'code': 728382543465111153222064060268547, 'gens': [1, 2, 4, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -5, 36, 851, 1278, 102, 2028, 3043, 124, 4717, 3156]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [8009, 8201, 28219, 72009, 24069, 8081, 152019]}, 'Perm': {'d': 13, 'gens': [482671449, 1037927520, 1037968560, 1437136560, 16, 1037836800, 34]}}, '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}.C_2^4', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}
