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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '100000000.bye', 'ambient_counter': 1305, 'ambient_order': 100000000, 'ambient_tex': 'C_5^4.D_5^4.C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 50000000, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100000000.bye.2._.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.B', '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': '50000000.qt', 'subgroup_hash': None, 'subgroup_order': 50000000, 'subgroup_tex': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '100000000.bye', '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': [2481793991075660317056096, 187768627200, 20935040445082060716664072943519283787235328000, 439636057557205928087643883876129960986295857120, 1596967378493484232394033045339680218868050086, 1046417237469572027598599208493334251938606036, 26584437368957304324849359353518240055, 608358494990699441746608044462633164800, 1596973453038670687890355125755823336026497109, 270558299210542291969837829844155587648670665690, 1451520, 550550132858843693658620362687189614120651709, 64, 35367047974958807818174464816480, 2481793606932957757440033], 'label': '100000000.bye.2._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '2.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2._.B', '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': '32.45', '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': [[104675255707856353095398173061862774711268041023, 753661818864064240840458566364127230728619599423, 648477314053239749799304948624796545574797622903, 231331230603830409575140005577592265287128246213], [106272223068185567815857471755772038051818378233, 794980233677183349634133967409543246839288067833, 648477315234170945957721512015270984148877622999, 231331231784761605733556026075715187182774575883], [104675255707856353095398173061605968388182094046, 732726778149799333940625364686957961323267233215, 690304988615898172469089824603080731288306368086, 231331231480590571918917336386886399789325573124], [523376278241375436136654474267716371370208848696, 334451549024488932558841419248265757324242123633, 648477314661598244790006329272660006222910160535, 231331231784761605733555378600205045109041455850], [167437969803848486506600331379232821371495519935, 734323744885727279013891227406319752731898115896, 271603966967542744674405515657304180421215869370, 210396934752979235696648308999095855923230467083], [104675256315417232736642356295151439225827647935, 774596114749919985219921315279844145160967161599, 711240028149231901525584231120473794930572806519, 250160045709388229027318245989999214979100379364], [104675255707856353095398173061734350626935103999, 795489491638230587710580861400782342593583423909, 669370692426652537738029169020366512330087942519, 231331231784761622817788902320752301574138553003], [146544592611366876444284806058616481469085177535, 814318306474589081166080371898305488687331507135, 690304988312508326642484978432564116569769189815, 250160044832628031315685814304880875956295640324], [167437969803848486506599684005802125474119553215, 814318305867028227733941664360736533406503687583, 629648499824442109775944688557193871252542160503, 210396934145401945745143201986628041617996652133], [167437969803848477349465062514291120025165939135, 795489491638230552343534073386486251249744585119, 711240029330163079368923026382687603442108664343, 271095085581099973226809938775846144399103551370], [104675255707856334813389114377738005176446746206, 814318306743771953558356267856574414812541703646, 648477314964988127214505340557676945419661827766, 231331231480590581076861673391037088925510218244], [104675256619604676861542718296194977229499143679, 732726778418982153914687726299502207361799962175, 629648501005373315092305690112140217286906380919, 291988463651122889095945516828485362168396652203], [104675255707856334813389114377738005362737651166, 814318306743771953558354973007249434606860058206, 648477314964988099774554325503045357513244982966, 231331231480590581076859835649718748801332995044], [104675255707856362253340672324823547297951923109, 774596115322492721754685868990166841559796095909, 690304988008337292827845641369894504753036806429, 231331230907220264559688645860650393491199551370], [104675255707856334813389657270191959834091823486, 814318306743771953558355620380706116490004479966, 648477314964988099774554325503045357674189520566, 231331231480590581076859191597301732045760815844], [104675255707856362253340672324823547552740041029, 774596115322492721754687703308263632443819599429, 648477314357427220133308847420918293194637622909, 231331230907220264559688645860394633307608246250], [146544592342184057701066692276417094121792787775, 814318306743771918191307645422256454913057990303, 690304988615898181627034805660006593659627526429, 271095085277710118242261298493043776378623551333], [167437970411409375305785179557385467749658394239, 753661817987320515016046549245284681567896783429, 690304988312508352851591641073051270878294328989, 271095085581099956141768645188046323383532718603], [125610297064686745505302456294949653850157235199, 814318306743771918191307645422154016933767142943, 711240028453419388911558984120829144803873676855, 210396934448791800729690550741375914964782403850], [146544592611366894726292674374520347627553887935, 314025767148014945678531121266566295850439071446, 250669670509114289969283145835246678740157260833, 291988463346951873597192473140832502322686296389], [753152559427116156684930671036679492994718152975, 166928710670290247568707283825568393392116458319, 709643062004838507115186082550999130538404146064, 270558299219488594541524598894675570319648324435], [104675256323837401236512705570303205761412681064, 734323745501708371646119051252135992694137475919, 690814246864292517116577092978475901659303215280, 230794444814791722899631125818901371799603109069], [186817341142588671582924337400892368523821223683, 336006476255055242737205572055515323927240538810, 251219847754272614760520594428598041801380860109, 689259311098033402507893647910653951552801054210], [126119183318948434590035484688734788081021892373, 733773194483685834776571458003570840156303100669, 709643061700651027623239037016406467909514236170, 270558300096248756885305601865309872329561816306], [167437969803848460297495503158793480293889120606, 795489491334043100324609237567847676267554791006, 709643061709071214405116610657100720679335106566, 210396934145401945745143744878979558271003971909]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 51200000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, '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, 50, 2], [2, 625, 6], [2, 1250, 8], [2, 31250, 2], [2, 390625, 1], [4, 390625, 8], [4, 781250, 12], [5, 8, 4], [5, 16, 28], [5, 32, 160], [5, 64, 896], [5, 128, 2560], [8, 1562500, 16], [10, 200, 12], [10, 400, 60], [10, 800, 256], [10, 1600, 832], [10, 5000, 44], [10, 10000, 132], [10, 20000, 224], [10, 40000, 64], [10, 125000, 4], [10, 250000, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '50000000.qt', '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', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 15, 'conjugacy_classes_known': False, 'counter': 436, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 50, 1, 2], [2, 625, 1, 6], [2, 1250, 1, 8], [2, 31250, 1, 2], [2, 390625, 1, 1], [4, 390625, 2, 4], [4, 781250, 1, 4], [4, 781250, 2, 4], [5, 8, 1, 4], [5, 16, 1, 28], [5, 32, 1, 160], [5, 64, 1, 896], [5, 128, 1, 2560], [8, 1562500, 2, 8], [10, 200, 1, 12], [10, 400, 1, 60], [10, 800, 1, 256], [10, 1600, 1, 832], [10, 5000, 1, 44], [10, 10000, 1, 132], [10, 20000, 1, 224], [10, 40000, 1, 64], [10, 125000, 1, 4], [10, 250000, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [8, 7], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '50000000.qt', 'hash': 2194229999738254264, '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': 50000000, 'inner_split': None, 'inner_tex': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '50000000.qt', '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': 'C5^6.(C2*C10^2:OD16)', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 7, 0, 0, 27, 0, 0, 51, 0, 51, 0, 43, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 5336, 'number_divisions': 5320, 'number_normal_subgroups': 247, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 50000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 466975], [4, 12500000], [5, 390624], [8, 25000000], [10, 11642400]], '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': 1024, '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, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2833422269794574208067851962568270972716467221300123037231471766226230393630498093372404745097327627271580054718409653664604569990045568189859837038977055100650690847120823877163713745576718111392586462415126241512624149642154692443085489224866095441049500594906678262258970318746063864558577741067708149198952343503542310914228277425301047147354143681736703862396980411867126789149106898042014169635024109284261489388278733696245070943814277209808855866351262593328025969963335555513032614672323561304879186272272405856626053241185223064002378935597448524993317161539784757207261328742851773508408953626547494968551967252319883263', 'gens': [1, 3, 5, 7, 9, 11, 12, 13, 14, 15], 'pres': [15, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 5, 5, 5, 5, 30, 574244776, 551421902, 1122575867, 122, 2175575523, 478485378, 1206963604, 316732219, 424212934, 410110399, 214, 1418408645, 1367282900, 74162195, 1490, 2354073966, 1638865221, 99636636, 225726951, 136383516, 106838106, 306, 4071552007, 57622, 1314268837, 19252, 202089667, 4539369608, 2949804023, 913302038, 316953053, 411331568, 43409333, 8733248, 11367788, 398, 6571248009, 720024, 360039, 240054, 120069, 12099, 3038640010, 2640025, 1320040, 1320055, 660070, 36300100, 6730, 8766720011, 2439360026, 7200041, 7200056, 491940071, 36131, 7693938732, 4311840027, 1427400042, 39000057, 512460072, 2145102, 1911132, 6834260173, 4300800028, 2150400043, 210000058, 598500073, 43596103, 1585633, 10598400014, 2656800029, 2727000044, 1125000059, 636075074, 47655104, 5625134]}, 'Perm': {'d': 40, 'gens': [104675255707856353095398173061862774711268041023, 231331230603830409575140005577592265287128246213, 753661818864064240840458566364127230728619599423, 648477314053239749799304948624796545574797622903]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 32, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'transitive_degree': None, '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': '32.21', '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': [[584584052062548184892557000313860641014951842066, 166928714875723933298395447826679586583767308133, 814318314992660498079686689593297648903063984513], [564185797961965784801553652260862536988489930283, 146544596555783012446631295837592367826923358636, 794980241891067323653684870214947227109024284806], [544820197962022336710389470672711456198706995116, 166928714875723968665442235840949733948362007050, 376279225690691815415905349104900063730656358335], [166928710321073021328979274228918010035990993955, 186266783101909915837908907875659390115304113239, 732726786667870750854229204011307931873847523776], [585120838407047845518215890885568675597807707429, 104675259044695127182108426116413452549272091596, 794980242802815646188983232038846156281532119015], [125610299793964529727337042798014129956707717176, 524422687882316842949193929062193286883944971486, 794980242802815655313855831489425267005117161575], [146544596555782874750989901269369805437352547064, 564185798266153081462281188943045842796353920799, 355895101636213226517220263594831317615483059080], [605518348520976665806784950313612652279001785555, 125101040347272545639095019521469061139718952133, 814318315600221396002938201672976070412974001984], [584584051758360696276543398781683687879017591635, 106272226118474905615735403506052583007675176170, 753661827720513655845089485229179637823001094490], [565755238102933381927491978104325865864940359116, 106272226691845231290848344025174533498673206283, 795489501640606574722794113063607295768057777920], [523926820769540754087217730008322401696650957490, 125101041224813868530953779464295381264779941124, 795489500763862884265429423428062423082125539680], [584584052062548184892556356261443624445752260466, 166928714875723933298394904934328069999258519013, 814318314688473027745682790797175901283224377633], [544820197388668475027659423800613278368159642316, 166928714302370097825576916680561011210553603083, 795489500763862884265429423428062423082125539680], [584584052062548184892557000314244783717511458066, 166928714302370062458531423515001927550748940133, 814318314992660498079686689593527422981614000576], [584584052062548175767683756810864513722168653516, 166928714875723968665440940991880471800473475083, 795489500763862858056323947731959659223353776544], [584584051454970832134054741029783198473778705229, 187863755016634995567469453515432283110655875083, 814318314992660516361694662492232804892658480544], [584584052062548166610548484522573968721063842035, 166928714875723959507500923522526631916759308164, 774596123571381266276018772520855164576663984570], [584584051454970867501102068512825156424266425549, 145994418113124435654566540892079590255008600389, 795489500459675413931427463532940373497522796800], [524422687578927106758017138990895325481569337003, 167437972871504432725218579775772293506729304275, 774596123571381284558026745419917656385301305633], [524973237988591167213677463501627484713785910360, 105721676290584895148719244010285346087998670079, 732726787275431604286369745866974724270639513056], [565755237226173227477742455920859959926288878866, 187863755016634977285459750778890497192926040293, 733277337382248516814658911760716334216469722930], [565755238407104406584189459956451721154610995090, 166928714302370079510499795925500214539201815044, 793934563477454331043146786587049159940709219243], [104675255081291148778034808075375807058551244886, 125101035489231734194017401097822489726955960956, 774596123875552290932712481153372006379901855456]], '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, 50, 1, 2], [2, 625, 1, 2], [2, 1250, 2, 1], [2, 2500, 1, 4], [2, 31250, 1, 2], [2, 390625, 1, 1], [4, 25000, 4, 1], [4, 390625, 1, 4], [4, 625000, 4, 1], [4, 781250, 1, 4], [4, 781250, 2, 1], [4, 1562500, 1, 4], [5, 16, 1, 2], [5, 16, 2, 2], [5, 32, 1, 4], [5, 32, 4, 1], [5, 32, 8, 1], [5, 64, 2, 3], [5, 64, 4, 2], [5, 64, 8, 7], [5, 64, 16, 2], [5, 128, 4, 1], [5, 128, 8, 14], [5, 128, 16, 4], [5, 128, 32, 6], [5, 128, 64, 1], [5, 256, 8, 6], [5, 256, 16, 11], [5, 256, 32, 15], [5, 256, 64, 9], [8, 3125000, 4, 2], [8, 3125000, 8, 1], [10, 400, 1, 2], [10, 400, 2, 3], [10, 400, 4, 1], [10, 800, 1, 1], [10, 800, 2, 5], [10, 800, 4, 2], [10, 800, 8, 2], [10, 1600, 2, 2], [10, 1600, 4, 2], [10, 1600, 8, 11], [10, 1600, 16, 3], [10, 3200, 4, 1], [10, 3200, 8, 10], [10, 3200, 16, 4], [10, 3200, 32, 6], [10, 3200, 64, 1], [10, 10000, 1, 2], [10, 10000, 2, 12], [10, 20000, 1, 4], [10, 20000, 2, 10], [10, 20000, 4, 1], [10, 20000, 8, 5], [10, 40000, 2, 3], [10, 40000, 4, 2], [10, 40000, 8, 10], [10, 40000, 16, 1], [10, 80000, 8, 4], [10, 250000, 1, 2], [10, 250000, 2, 1], [10, 500000, 1, 1], [20, 100000, 4, 1], [20, 100000, 8, 1], [20, 100000, 16, 1], [20, 200000, 16, 1], [20, 200000, 32, 1], [20, 2500000, 4, 1]], '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, 50, 2], [2, 625, 2], [2, 1250, 2], [2, 2500, 4], [2, 31250, 2], [2, 390625, 1], [4, 25000, 4], [4, 390625, 4], [4, 625000, 4], [4, 781250, 6], [4, 1562500, 4], [5, 16, 6], [5, 32, 16], [5, 64, 102], [5, 128, 436], [5, 256, 1280], [8, 3125000, 16], [10, 400, 12], [10, 800, 35], [10, 1600, 148], [10, 3200, 404], [10, 10000, 26], [10, 20000, 68], [10, 40000, 110], [10, 80000, 32], [10, 250000, 4], [10, 500000, 1], [20, 100000, 28], [20, 200000, 48], [20, 2500000, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '100000000.bye', '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', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 16, 'conjugacy_classes_known': False, 'counter': 1305, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 50, 1, 2], [2, 625, 1, 2], [2, 1250, 1, 2], [2, 2500, 1, 4], [2, 31250, 1, 2], [2, 390625, 1, 1], [4, 25000, 2, 2], [4, 390625, 2, 2], [4, 625000, 2, 2], [4, 781250, 1, 2], [4, 781250, 2, 2], [4, 1562500, 1, 4], [5, 16, 1, 6], [5, 32, 1, 16], [5, 64, 1, 102], [5, 128, 1, 436], [5, 256, 1, 1280], [8, 3125000, 2, 8], [10, 400, 1, 12], [10, 800, 1, 35], [10, 1600, 1, 148], [10, 3200, 1, 404], [10, 10000, 1, 26], [10, 20000, 1, 68], [10, 40000, 1, 110], [10, 80000, 1, 32], [10, 250000, 1, 4], [10, 500000, 1, 1], [20, 100000, 2, 14], [20, 200000, 2, 24], [20, 2500000, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [8, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '100000000.bye', 'hash': 4506779824941145017, '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': 100000000, 'inner_split': None, 'inner_tex': 'C_5^4.D_5^4.C_4^2', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '100000000.bye', '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': 'C5^4.D5^4.C4^2', '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, 2, 0, 0, 0, 2, 0, 0, 0, 2, 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, 3, 0, 0, 0, 11, 0, 0, 19, 0, 0, 35, 0, 27, 0, 19, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 242, 'number_characteristic_subgroups': 90, 'number_conjugacy_classes': 2812, 'number_divisions': 2756, 'number_normal_subgroups': 130, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 100000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 466975], [4, 15100000], [5, 390624], [8, 50000000], [10, 11642400], [20, 22400000]], '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': 64, '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, 4, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '187820498444729854423830439779289677659518820207291232795835542139777312169792711112332837578529248494477562963327680061859029646369637206994281066272082914053053463527760840827406047878694236455622681712639298651898404096975162042434094891839424553428621465492597458086903697853160025445444989080779665828618773586215591021015054092844047304546377437642624965127255911233328011432687400498527851569080914321336452135659491722370393884113718456348526268103940318557444346421465711543005231079217540134202954745044814312960305498049877391246118877370815868655770365622492957447958926720185412488960014410248342696046124843399257803440335699162306834215720734326616728095694730181345182346263042941911275353697470784616656853655040946580696756954910719', 'gens': [1, 3, 6, 8, 10, 12, 13, 14, 15, 16], 'pres': [16, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 5, 5, 5, 5, 32, 134676497, 3971506370, 1412253426, 130, 2385984003, 1539569939, 179, 859198724, 3563064980, 6671992325, 3047806485, 1360442917, 356737205, 222529797, 277, 7986585606, 360923158, 959633958, 1248130742, 1862, 1132238855, 4370452503, 3086566439, 244362295, 255203911, 112933207, 12890343, 375, 12667576328, 232012840, 1583447096, 23112, 11608, 5794419209, 3133696025, 3952866601, 1622592057, 80608073, 247056089, 116648105, 2110521, 17744937, 473, 16879104010, 1521490474, 422458, 281674, 22137402, 19029737483, 3548160027, 2790604843, 2304059, 1536075, 768091, 22176123, 7835, 12089958412, 4239246380, 2309632060, 8320076, 562640092, 26041724, 2604316, 19257749517, 4243456029, 870596653, 2563456061, 44800077, 601440093, 18502525, 3039837, 14913546254, 2530560030, 707865646, 834240062, 240000078, 557280094, 37488126, 1200158, 8893415439, 1007616031, 1386582063, 1225728063, 1280000079, 710912095, 70016127, 41119]}, 'Perm': {'d': 40, 'gens': [814318314992660498079686689593297648903063984513, 584584052062548184892557000313860641014951842066, 166928714875723933298395447826679586583767308133]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^4.D_5^4.C_4^2', '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}
