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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800000000.wi', 'ambient_counter': 581, 'ambient_order': 800000000, 'ambient_tex': 'C_5^8.C_4^3.C_4^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 400000000, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800000000.wi.2._.D', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.D', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '400000000.us', 'subgroup_hash': None, 'subgroup_order': 400000000, 'subgroup_tex': 'C_5^8.C_4^3.C_4^2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '800000000.wi', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [187770078720, 229776299400387392548025827316184984565196496600, 629097946023946762869451644650928558033156738493, 20935041053440564865307308801696726468125881600, 26584438305803288667068442944150226000, 647475510142073734571520, 608358530357747416705672668611469312096, 83188495703283265594053411335641059407031426503, 9157944981057054286481081112993, 1294849324980554396261760, 79855162553888795369520, 936846144052247505937412124743, 17374858686459226447630983586322730720, 524973245619868893832470337082007851918116482655, 610180032439698686179643036893, 18315079710452506734496040505600, 816480, 61207781999219961592092557526668750844343086013], 'label': '800000000.wi.2._.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '2.D', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2._.D', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[396663712397674864801044151861526061378926753389, 710689474071125254573913708510653986646450763575], [336006481103886273448430574916020698743904417389, 650032241622989930031572818924620121431187276869], [375233549121193124223643903246882675948032022429, 668861055825203124171282640036111591661059052189], [314576316959072806030223571618441611144833667349, 670430496270086855628677289808093715214062723760], [336006481103886265521332323585356895087982753363, 629097946336283066593260409607187048592228195724], [334960807280505777904652441830833262714807430509, 628051528526503907182909393922121992691148999069], [334960807871489432197307550818970840690547957709, 670430495966696974434217777851729849758507018256], [356404734909227669965768365380807128599694153789, 650032242508153834123171109370863444551733425943], [314576316968274162484247995150132247350414153789, 670430496270086829418765231189763684880065872593], [314576317263243830686919114568927907638913667349, 710689473766954229917220104461423106433171454749], [375770334901022248364040951906199955041646753389, 629097945442164482692571036119656055272120318749], [354835295063501050203581603028806345950908865970, 689796096878643679878647449574693176943918060189], [375770335508583110920245133079744339143582617613, 629097946049725326966766596918984915787288512023], [396663712093503823059308606851422820851695877650, 629097945746335498224392040718563543287595148919], [354835295332683887261877484939675404438062119730, 710689473462766767510313165569861731944882763575], [396663712970247548883721814338229466089521831789, 710689474071125271658953167677919414028071089943], [375770335205193273020735951964334734951217313389, 710689473766954229917217622667816173567861323575], [336006481103886273448430574916020698743904417389, 710689474643697972826671580747531082948690507575], [375770335205193273020735951964590453289228449363, 710689473766954229917217622667816173755629950839], [585629733186977198809716948362026788308484997176, 629097945746335507349264640169015317724151760535], [314576316968274153043598853738765192802240673349, 710689474061923898119889284978963350789503608353], [314576316959072806030222899517205827153262753349, 710689474061923924329801343596807889055652472353], [396663712701064719785592792144328429399406753389, 648477310680564481961540715012479683480209467533]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 6400000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1250, 1, 3], [2, 2500, 1, 2], [2, 10000, 1, 2], [2, 390625, 1, 1], [4, 2500, 1, 1], [4, 5000, 1, 1], [4, 62500, 1, 2], [4, 125000, 1, 4], [4, 125000, 2, 2], [4, 390625, 1, 2], [4, 500000, 8, 1], [4, 781250, 1, 3], [4, 1562500, 1, 3], [4, 3125000, 1, 1], [4, 6250000, 1, 2], [5, 32, 1, 1], [5, 64, 1, 3], [5, 128, 1, 4], [5, 128, 2, 2], [5, 256, 1, 1], [5, 256, 2, 4], [5, 256, 4, 1], [5, 256, 8, 1], [5, 512, 1, 2], [5, 512, 2, 2], [5, 512, 4, 7], [5, 1024, 2, 9], [5, 1024, 4, 25], [5, 1024, 8, 18], [5, 1024, 16, 6], [8, 1250000, 2, 4], [8, 6250000, 2, 2], [8, 12500000, 2, 2], [10, 20000, 1, 3], [10, 20000, 2, 2], [10, 40000, 1, 5], [10, 40000, 2, 2], [10, 80000, 1, 12], [10, 80000, 2, 6], [10, 160000, 1, 1], [10, 160000, 2, 8], [10, 160000, 4, 1], [10, 160000, 8, 1], [10, 320000, 1, 2], [10, 320000, 2, 2], [10, 320000, 4, 7], [16, 12500000, 8, 1], [20, 20000, 2, 3], [20, 40000, 2, 2], [20, 40000, 4, 1], [20, 80000, 1, 3], [20, 80000, 2, 1], [20, 160000, 1, 2], [20, 160000, 2, 1], [20, 160000, 4, 5], [20, 500000, 1, 4], [20, 500000, 2, 7], [20, 1000000, 1, 2], [20, 1000000, 2, 1], [20, 1000000, 4, 1], [20, 2000000, 1, 3], [20, 2000000, 2, 1], [20, 2000000, 8, 2], [20, 4000000, 16, 1], [40, 5000000, 2, 4]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1250, 3], [2, 2500, 2], [2, 10000, 2], [2, 390625, 1], [4, 2500, 1], [4, 5000, 1], [4, 62500, 2], [4, 125000, 8], [4, 390625, 2], [4, 500000, 8], [4, 781250, 3], [4, 1562500, 3], [4, 3125000, 1], [4, 6250000, 2], [5, 32, 1], [5, 64, 3], [5, 128, 8], [5, 256, 21], [5, 512, 34], [5, 1024, 358], [8, 1250000, 8], [8, 6250000, 4], [8, 12500000, 4], [10, 20000, 7], [10, 40000, 9], [10, 80000, 24], [10, 160000, 29], [10, 320000, 34], [16, 12500000, 8], [20, 20000, 6], [20, 40000, 8], [20, 80000, 5], [20, 160000, 24], [20, 500000, 18], [20, 1000000, 8], [20, 2000000, 21], [20, 4000000, 16], [40, 5000000, 8]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '400000000.us', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 18, 'conjugacy_classes_known': False, 'counter': 539, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1250, 1, 3], [2, 2500, 1, 2], [2, 10000, 1, 2], [2, 390625, 1, 1], [4, 2500, 1, 1], [4, 5000, 1, 1], [4, 62500, 2, 1], [4, 125000, 1, 4], [4, 125000, 2, 2], [4, 390625, 2, 1], [4, 500000, 2, 4], [4, 781250, 1, 3], [4, 1562500, 1, 3], [4, 3125000, 1, 1], [4, 6250000, 1, 2], [5, 32, 1, 1], [5, 64, 1, 3], [5, 128, 1, 8], [5, 256, 1, 21], [5, 512, 1, 34], [5, 1024, 1, 358], [8, 1250000, 4, 2], [8, 6250000, 2, 2], [8, 12500000, 2, 2], [10, 20000, 1, 7], [10, 40000, 1, 9], [10, 80000, 1, 24], [10, 160000, 1, 29], [10, 320000, 1, 34], [16, 12500000, 4, 2], [20, 20000, 2, 3], [20, 40000, 2, 4], [20, 80000, 1, 1], [20, 80000, 2, 2], [20, 160000, 1, 2], [20, 160000, 2, 11], [20, 500000, 2, 9], [20, 1000000, 2, 4], [20, 2000000, 1, 1], [20, 2000000, 2, 10], [20, 4000000, 2, 8], [40, 5000000, 4, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 80, 'exponents_of_order': [10, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '400000000.us', 'hash': 384373152757797379, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_5^8.C_4^3.C_4^2', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '400000000.us', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C5^8.C4^3.C4^2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 11, 0, 0, 11, 0, 0, 11, 0, 7, 0, 7, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 222, 'number_characteristic_subgroups': 68, 'number_conjugacy_classes': 706, 'number_divisions': 625, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 400000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 419375], [4, 28570000], [5, 390624], [8, 85000000], [10, 17940000], [16, 100000000], [20, 127680000], [40, 40000000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '16.14', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 16, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [4, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '39748992787973809094942940366581791305499569285845487978384660585898599458546534481757985089190631982324234879196395566902216974657793206804892527279846541432053552134099912038879250742821481475653787598235366552104289025304251676371162406537994931923742541328000779206369460114683366466460552412970840087075870262482376076174729289926274744461978376718832841967960048505814611444410017259562909482468468568368167599931986430379742545925123298004374367645879325282499183870804282079873150389081917232095474250524208602273526732137853362943752650985935239520257595575058783935944026434661943330436913848463810900471846848579878016801691784917503351374064004260051454102586146426376224560331903246807242413816344431609940383369720346908945626377817420206378200988825511816064659420208648191888253201210397885745803627242035888315574988390546794566872006768014100248215224847365663173550011022863125502731095685556049633376386400116648749034781051362746418415252369707374711187153684559050886232541783263950871658305575794624368410140845010838828557660861267262288944653615103', 'gens': [1, 3, 6, 8, 11, 13, 14, 15, 16, 17, 18], 'pres': [18, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 5, 36, 3856075795, 13980825290, 5816771048, 146, 23509900227, 2738712693, 201, 26041865764, 2343168742, 12145528805, 18422854295, 3745714793, 167229419, 2077349, 311, 40737402726, 18320843544, 10789188522, 84358572, 218310, 457027314, 29828085127, 22740874009, 4091465131, 639159613, 467261647, 918635425, 862896787, 421, 24172496936, 26180615258, 15315674444, 521526014, 765700208, 565448786, 587612348, 476, 921609, 6829056027, 17280045, 34623, 23121, 8739, 5877, 7205299210, 12019392028, 5387288590, 309767104, 2249362, 28084420, 10446598, 21894976, 5447134, 586, 16389734411, 25292390429, 787968047, 553025, 103781, 69239, 34697, 1377792012, 29952030, 3067084848, 2246466, 1497684, 374502, 374520, 187338, 9552, 1838592013, 9676831, 32305, 12096067, 8064085, 4032103, 504139, 504157, 50593, 76032014, 25085030450, 267840068, 28080104, 50220122, 32130140, 8370158, 270194, 3583180815, 2200780833, 18907324467, 368640069, 62208087, 108288105, 40896123, 3744141, 12096159, 1440195, 82315468816, 1183186978, 11981256244, 1963296070, 1299888088, 624729706, 117748924, 90759742, 90055960, 3770116, 121596401681, 446404643, 8276318261, 3936729671, 3161203289, 1553126507, 448934525, 419968943, 419288561, 10332557]}, 'Perm': {'d': 40, 'gens': [396663712397674864801044151861526061378926753389, 710689474071125254573913708510653986646450763575]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 256, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^8.C_4^3.C_4^2', 'transitive_degree': 40, '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': '16.10', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[524973245619868893832470337082007851918116482655, 21980714867619686891797953885462014409929169479, 629097946023946762869451644650948497451919628813], [524973244716540730639100448017955508998608564370, 21980714867619686891797953885820212572811729479, 628602078919335798620168639940446999922948329533], [543802059240308038865131155403002482193471617215, 41319158790563163246489538220206871833819417004, 669920864830602401658184450163592646721149398993], [565755245134256345513908873392882264482011037490, 82637946456377938519986334397849454930602044113, 650032242786546268440378162286990886128306051693], [543802059240308055950170614570523628167972482719, 82637946760565399696854859745615157496150255376, 689796097477800801014503183557377480958322685366], [544311318122313179706399779620000322585397916236, 21980714867619686891797306512491954750050180679, 629648496173374415525485396058161918276535443255], [564185805861900086456731416771901706846333560309, 21980714598436840708627638206659395062815703879, 629097945754763881319235188331434809223575641683], [544311317809713735988523371896579353755157453970, 21980714867619686891798601361330354554097540679, 628602078928282247075915437310011537824865769556], [606564773032910317291783382012209029210916482655, 61744569272316541448651971217039012748024791879, 710689474079553663878668914741369791036348505683], [524973244716540730639099234097162416443241372290, 21980714867619686891798601360972156483662289479, 628602078928282237918779520969688118490533910389], [544311317505526265654519473100457606135317453970, 21980713990875961067385936766619465436974980679, 629097945147186591367730624210960355185548089709], [564695435860216929477721690763975897670436482655, 40809528219673601090746196834580338083057540679, 668861055834412676938272046264249769526786873709], [543802059848666524698694680808775628825597876479, 82637946733980962327896420282443447761500028999, 629097945450576446352281102235310796098258412173], [524973244708120570067134313670570360194693491166, 21980714867619705174613052599104335954276817415, 629097946328117778369012461628691328919305606483], [585629732318645418319046496084618177937338105535, 21980714867619669807563786214679667564631539789, 650032242213192371358338115093653823934801795693], [564695437041148151846050312772423256935709427103, 21980714867619705174613052599232760038609361415, 629097946023946727502403669692498835594758412813], [606564772763727461951478984310437441455721824575, 21980714867619696049740453148422787251402227879, 650032242482375208416632806636506855233546877389], [564695436129399783587987132029600297243064244446, 21980714867619678964700993980901641370825576909, 668861056711172874649905125322338168559659237869], [585629733499576606550367391098586738146008188255, 21980714867619686891797953885462014409929169479, 629097946023946762869451644650948497357995398483], [564695436736960655302134355358328588879465023935, 21980714867619686891797953885462014409929818919, 710689474348736536304012771610560086947617099570], [356404734293246585880497688915506189888262738055, 82637946464798142386902127484608775214653025319, 629097945754763881319235188331563233307907385043], [564695436137819953002118551577679577200079821935, 40809529096417326915158861428574830874414980679, 668861056720119332262787839032252111552237068836], [524422695192032395296345877036181958689383409970, 61744568968926686464103330934134206842097540679, 649495455243222523608753332653295710967814934429], [564695436736960655302134355358328588624676482655, 40809528523844625747441739784939298477879172679, 709643056842865253618705850342478343480022208615]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 12800000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 100, 1, 1], [2, 1250, 1, 3], [2, 2500, 1, 2], [2, 5000, 1, 1], [2, 10000, 2, 1], [2, 20000, 1, 1], [2, 62500, 1, 1], [2, 390625, 1, 1], [4, 2500, 1, 2], [4, 5000, 1, 1], [4, 25000, 2, 2], [4, 62500, 1, 4], [4, 125000, 1, 6], [4, 125000, 2, 2], [4, 390625, 1, 2], [4, 625000, 2, 2], [4, 781250, 1, 3], [4, 1000000, 8, 1], [4, 1562500, 1, 6], [4, 3125000, 1, 2], [4, 6250000, 2, 1], [4, 12500000, 1, 1], [5, 32, 1, 1], [5, 64, 1, 3], [5, 128, 1, 2], [5, 128, 2, 3], [5, 256, 1, 1], [5, 256, 2, 2], [5, 256, 4, 1], [5, 512, 1, 4], [5, 512, 2, 1], [5, 512, 8, 3], [5, 1024, 1, 1], [5, 1024, 2, 3], [5, 1024, 4, 13], [5, 2048, 2, 2], [5, 2048, 4, 17], [5, 2048, 8, 6], [5, 2048, 16, 2], [8, 2500000, 2, 4], [8, 6250000, 4, 1], [8, 12500000, 2, 5], [10, 800, 1, 3], [10, 1600, 1, 3], [10, 1600, 2, 1], [10, 3200, 1, 1], [10, 3200, 2, 2], [10, 3200, 4, 1], [10, 6400, 2, 7], [10, 6400, 4, 1], [10, 12800, 1, 4], [10, 12800, 2, 1], [10, 12800, 8, 2], [10, 20000, 1, 3], [10, 20000, 2, 4], [10, 25600, 2, 2], [10, 25600, 4, 10], [10, 40000, 1, 5], [10, 40000, 2, 3], [10, 80000, 1, 7], [10, 80000, 2, 9], [10, 80000, 4, 2], [10, 160000, 1, 1], [10, 160000, 2, 4], [10, 160000, 4, 6], [10, 320000, 1, 4], [10, 320000, 2, 2], [10, 320000, 8, 5], [10, 500000, 1, 1], [10, 640000, 1, 1], [10, 640000, 2, 1], [10, 640000, 4, 3], [10, 1000000, 1, 1], [16, 25000000, 8, 1], [20, 20000, 2, 4], [20, 40000, 2, 3], [20, 40000, 4, 1], [20, 80000, 1, 5], [20, 80000, 2, 1], [20, 100000, 2, 6], [20, 160000, 2, 4], [20, 160000, 4, 4], [20, 200000, 4, 2], [20, 320000, 2, 2], [20, 400000, 2, 4], [20, 500000, 1, 8], [20, 500000, 2, 8], [20, 800000, 4, 2], [20, 1000000, 1, 4], [20, 1000000, 2, 1], [20, 1000000, 4, 1], [20, 2000000, 1, 5], [20, 2000000, 2, 1], [20, 2500000, 2, 2], [20, 4000000, 8, 2], [20, 8000000, 16, 1], [40, 10000000, 2, 4]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 100, 1], [2, 1250, 3], [2, 2500, 2], [2, 5000, 1], [2, 10000, 2], [2, 20000, 1], [2, 62500, 1], [2, 390625, 1], [4, 2500, 2], [4, 5000, 1], [4, 25000, 4], [4, 62500, 4], [4, 125000, 10], [4, 390625, 2], [4, 625000, 4], [4, 781250, 3], [4, 1000000, 8], [4, 1562500, 6], [4, 3125000, 2], [4, 6250000, 2], [4, 12500000, 1], [5, 32, 1], [5, 64, 3], [5, 128, 8], [5, 256, 9], [5, 512, 30], [5, 1024, 59], [5, 2048, 152], [8, 2500000, 8], [8, 6250000, 4], [8, 12500000, 10], [10, 800, 3], [10, 1600, 5], [10, 3200, 9], [10, 6400, 18], [10, 12800, 22], [10, 20000, 11], [10, 25600, 44], [10, 40000, 11], [10, 80000, 33], [10, 160000, 33], [10, 320000, 48], [10, 500000, 1], [10, 640000, 15], [10, 1000000, 1], [16, 25000000, 8], [20, 20000, 8], [20, 40000, 10], [20, 80000, 7], [20, 100000, 12], [20, 160000, 24], [20, 200000, 8], [20, 320000, 4], [20, 400000, 8], [20, 500000, 24], [20, 800000, 8], [20, 1000000, 10], [20, 2000000, 7], [20, 2500000, 4], [20, 4000000, 16], [20, 8000000, 16], [40, 10000000, 8]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '800000000.wi', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 19, 'conjugacy_classes_known': False, 'counter': 581, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 100, 1, 1], [2, 1250, 1, 3], [2, 2500, 1, 2], [2, 5000, 1, 1], [2, 10000, 1, 2], [2, 20000, 1, 1], [2, 62500, 1, 1], [2, 390625, 1, 1], [4, 2500, 1, 2], [4, 5000, 1, 1], [4, 25000, 2, 2], [4, 62500, 2, 2], [4, 125000, 1, 6], [4, 125000, 2, 2], [4, 390625, 2, 1], [4, 625000, 2, 2], [4, 781250, 1, 3], [4, 1000000, 2, 4], [4, 1562500, 1, 4], [4, 1562500, 2, 1], [4, 3125000, 1, 2], [4, 6250000, 1, 2], [4, 12500000, 1, 1], [5, 32, 1, 1], [5, 64, 1, 3], [5, 128, 1, 8], [5, 256, 1, 9], [5, 512, 1, 30], [5, 1024, 1, 59], [5, 2048, 1, 152], [8, 2500000, 2, 4], [8, 6250000, 2, 2], [8, 12500000, 2, 5], [10, 800, 1, 3], [10, 1600, 1, 5], [10, 3200, 1, 9], [10, 6400, 1, 18], [10, 12800, 1, 22], [10, 20000, 1, 11], [10, 25600, 1, 44], [10, 40000, 1, 11], [10, 80000, 1, 33], [10, 160000, 1, 33], [10, 320000, 1, 48], [10, 500000, 1, 1], [10, 640000, 1, 15], [10, 1000000, 1, 1], [16, 25000000, 4, 2], [20, 20000, 2, 4], [20, 40000, 2, 5], [20, 80000, 1, 3], [20, 80000, 2, 2], [20, 100000, 2, 6], [20, 160000, 1, 4], [20, 160000, 2, 10], [20, 200000, 2, 4], [20, 320000, 2, 2], [20, 400000, 2, 4], [20, 500000, 2, 12], [20, 800000, 2, 4], [20, 1000000, 2, 5], [20, 2000000, 1, 3], [20, 2000000, 2, 2], [20, 2500000, 2, 2], [20, 4000000, 2, 8], [20, 8000000, 2, 8], [40, 10000000, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 80, 'exponents_of_order': [11, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '800000000.wi', 'hash': 5979178778527936304, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_5^8.C_4^3.C_4^2.C_2', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '800000000.wi', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C5^8.C4^3.C4^2.C2', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 21, 0, 0, 15, 0, 11, 0, 11, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 298, 'number_characteristic_subgroups': 105, 'number_conjugacy_classes': 782, 'number_divisions': 669, 'number_normal_subgroups': 129, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 800000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 506975], [4, 55860000], [5, 390624], [8, 170000000], [10, 36602400], [16, 200000000], [20, 256640000], [40, 80000000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 16, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '53466101321923295439885344093821220941113462633235126373397251021897985434611327824228550886832805652604979250891995474395649401619211617510485693735241900692999244835219627203561623175918112294252220394197120800287225926021784287559161317550661995008647806861755635152805244031064055632847653615318351573837463092475808375026384372674877419723475496417011031720561357628743929403464102681362498990941751867095980778712167814288004549675980571682855539203290928205899157126034366909514666383505400558219597094969285789589593917428266749819132484852685368533142713555050236540984687225233803271560736695828722931205122911551332605095988437791045562077086703840803007493274295637104334690312421239147400140749089787794408111190388279072122481175668563291401887804932277427694559814004217069351490947801554378734828157563747833785141175060819246324172243774270690478317194058542586733099095871613441152045017880633330767419361255202946393186862326687752654032755014696590494633002620344594070968679492774993163377230856026469312697147602995933878679053325328819647367337753018095746153973907698263400484635675815296431272213631966471278772646741928606027063498676354223420602399319128626611870016961688402499349273723258200891429440454797804351070446538891687881510566809599', 'gens': [1, 3, 5, 7, 10, 13, 15, 16, 17, 18, 19], 'pres': [19, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 38, 10114498324, 34153127534, 13842739923, 154, 199365027, 25303127814, 692268860, 44684950124, 32655433783, 16155814042, 341696251, 270, 8902612037, 7976782488, 8891434603, 186778118, 114000100, 18876831518, 22842925585, 7451796928, 3294408999, 3099651798, 2351229695, 386, 1167442695, 40001752474, 5187885293, 6503384512, 7172944531, 1056952774, 444, 116487936008, 9797506587, 5844971566, 13680021953, 5130008292, 1763357575, 82725571369, 12473630748, 12260672687, 2411601666, 175119285, 40743704, 1124545523, 974489242, 378291111, 560, 95476851370, 61831683613, 2098065776, 1169664387, 169908726, 50845625, 1880858004, 270985363, 269403252, 618, 6338764811, 24020883486, 40697102641, 2357191748, 142345047, 149604586, 530838845, 33324624, 185580482060, 17462516687, 10248326450, 22505059269, 1879966488, 367338507, 2191680526, 383788745, 337426864, 145221363, 21289132, 3990506, 734, 124753438221, 43547392032, 1269990451, 5107270, 159174489, 174070508, 126190527, 43517746, 6299064, 21483, 18536217614, 16490419233, 4446912052, 1085280071, 378480090, 266760109, 43320128, 6783185, 1083204, 333692, 6381568015, 3151872034, 25078784053, 145920072, 72960091, 48640110, 18240129, 12160148, 608186, 608205, 61043, 20842337296, 23939002915, 22135577654, 237728073, 108528092, 240312111, 86564130, 29070149, 516987, 1841306, 300634, 7144243217, 30555823140, 1794816055, 342000131, 342000150, 1710245, 18390784018, 11767329317, 12014080056, 22110528075, 4031648094, 1917632113, 138190989, 94437808, 9025246]}, 'Perm': {'d': 40, 'gens': [524973245619868893832470337082007851918116482655, 21980714867619686891797953885462014409929169479, 629097946023946762869451644650948497451919628813]}}, 'schur_multiplier': None, 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 50, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^8.C_4^3.C_4^2.C_2', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'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}
