-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '270284.a', 'ambient_counter': 1, 'ambient_order': 270284, 'ambient_tex': 'C_7\\times F_{197}', 'central': False, 'central_factor': False, 'centralizer_order': 1379, 'characteristic': True, 'core_order': 1379, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '270284.a.196.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '196.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '196.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 196, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{196}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1379.2', 'subgroup_hash': 2, 'subgroup_order': 1379, 'subgroup_tex': 'C_{1379}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '270284.a', 'aut_centralizer_order': None, 'aut_label': '196.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '196.a1.a1', 'complements': ['1379.b1.a1', '1379.b1.c1', '1379.b1.e1', '1379.b1.g1', '1379.b1.b1', '1379.b1.d1', '1379.b1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '98.a1.a1'], 'contains': ['1372.a1.a1', '38612.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5166, 4562, 2048, 7019, 5004, 5106, 5906, 6136], 'generators': [38612, 1372], 'label': '270284.a.196.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '196.a1.a1', 'normal_contained_in': ['28.a1.a1', '98.a1.a1'], 'normal_contains': ['1372.a1.a1', '38612.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '196.a1.a1', 'projective_image': '38612.a', 'quotient_action_image': '196.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '196.a1.a1', 'subgroup_fusion': None, 'weyl_group': '196.2'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1379.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 588, 'aut_gen_orders': [2, 588], 'aut_gens': [[1], [986], [396]], 'aut_group': '1176.39', 'aut_hash': 39, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 1176, 'aut_permdeg': 202, 'aut_perms': [477938497491073517010285393091113130526786829518092305155563396284080492069571876859848200675522861855289953214367384925718585395528891725224103463620789230703725193448941631695621136254851160883284030304557547985369041485789958105508978853762625898972183286806642302301626878724405778936646065995943366369550843853808917367540940800000000000000000000000000000000000000000000000, 637235556830753332130006799065896007525228203717891248557224054480734141107865772809059134722568266213943036225418435532115114530473441038851458493372398212231198384791168833042969705996012556111053562344401164926496378292852887527297991605098200401949116060204200385915911759371904196776380490922513093168277575466433675906822409907994804323593105039052556442336528920420940313], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [7, 1, 6, 1], [197, 1, 196, 1], [1379, 1, 1176, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{588}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 588, 'autcent_group': '1176.39', 'autcent_hash': 39, 'autcent_nilpotent': True, 'autcent_order': 1176, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{588}', '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], [7, 1, 6], [197, 1, 196], [1379, 1, 1176]], 'center_label': '1379.2', 'center_order': 1379, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['7.1', '197.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['197.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [7, 1, 6, 1], [197, 1, 196, 1], [1379, 1, 1176, 1]], 'element_repr_type': 'PC', 'elementary': 1379, 'eulerian_function': 1, 'exponent': 1379, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [7, 197], 'faithful_reps': [[1, 0, 1176]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1379.2', 'hash': 2, 'hyperelementary': 1379, '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': 1176, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 1379]], 'label': '1379.2', 'linC_count': None, 'linC_degree': 1, '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': True, 'monomial': True, 'name': 'C1379', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 1379, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 1379, 'order_factorization_type': 11, 'order_stats': [[1, 1], [7, 6], [197, 196], [1379, 1176]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 588, 'outer_gen_orders': [2, 588], 'outer_gen_pows': [0, 0], 'outer_gens': [[986], [396]], 'outer_group': '1176.39', 'outer_hash': 39, 'outer_nilpotent': True, 'outer_order': 1176, 'outer_permdeg': 202, 'outer_perms': [477938497491073517010285393091113130526786829518092305155563396284080492069571876859848200675522861855289953214367384925718585395528891725224103463620789230703725193448941631695621136254851160883284030304557547985369041485789958105508978853762625898972183286806642302301626878724405778936646065995943366369550843853808917367540940800000000000000000000000000000000000000000000000, 637235556830753332130006799065896007525228203717891248557224054480734141107865772809059134722568266213943036225418435532115114530473441038851458493372398212231198384791168833042969705996012556111053562344401164926496378292852887527297991605098200401949116060204200385915911759371904196776380490922513093168277575466433675906822409907994804323593105039052556442336528920420940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{588}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 204, 'pgroup': 0, 'primary_abelian_invariants': [7, 197], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 1], [6, 1], [196, 1], [1176, 1]], 'representations': {'PC': {'code': 193255, 'gens': [1], 'pres': [2, -7, -197, 14]}, 'GLFp': {'d': 2, 'p': 197, 'gens': [7645571, 1253841336]}, 'Perm': {'d': 204, 'gens': [39001683638047682862733856376306835881356061156654513562605040055771153547870376880626736949055702434304517057728057684107495149709567630018984251998475787451217821457845374227483861319933187469014815814266043408334413761524981138456718779855502960424384771858294874125732361769100464420051957377571450112138909259839380030991808593920000000000000000000000000000000000000000000000000, 99570393372994116545053621392809991743215031488961728865427440048454375266082666326285866899454578360975475219524434206830245409279616608778483002673441726977088385078413145934338802813359727508617103740958928960810158648814977950333626518167340628844823362087763843223581053406560943668904006630292962961731996627658342400000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [1379], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{1379}', 'transitive_degree': 1379, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1372.11', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 115836, 'aut_gen_orders': [294, 294, 84], 'aut_gens': [[1, 196], [24501, 137788], [192277, 166992], [148373, 140924]], 'aut_group': None, 'aut_hash': 8651566897496060826, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1621704, 'aut_permdeg': 1379, 'aut_perms': [2916328079551979974307814191660777998003492089069579880468355287479179702734746234584221071268929328823699406394594784536274953602498679777260098358483595167134087879022630822277521409017318534912600134137160575625641837097361062095219494184596688256538525044474936898849289194807296234997952542917380677374667475819472262503319183351041294031745775880762044814567438645177789828776852344507077366266916871901605343011966499159800930716853352189336926776719543802483346284830722049390012218582391020103777944986286337891595876550680563639213549506776696304882459081461513429314661743755517595076760839151569565658144038164549686482555114750679369847095842564379751977083104687580337565785108510902956017651499753161850562017998917320957618881162255250515362405671660580728285458964732368499684413878066529670655782286884107636148679325929953168206502878721682524534909976639583217738776054913362947424332825826003126316797081149787573734346082823867022348559918357819939912816422862143175719971010782677639736906203914395188897053171370192218419704876377873590500465389485591806873420587774195107332814883033315149163640707665585130169575089284613463215066296163034538756168417550059770039143668234590215028986156687125946086261731558219800280423077063126310320806833396045315886884686497765682377814600050338405053428042667642857848444121495757783705629636764219655045603169276587365918924287274016461267631424185203641866636034133584341311731499788838612827412744847392944275945972876432244012633913227714067366554416727357135754343394953820848516133831065320695229986342862867202416046130366895517865776962511403040093782870591395102701190869546895838821829602766097568008115526750768348660982480923335166614307821288210804458926716974524959938450602503051490977369397243799697044278786859819655482971309605072245317038383146431194135844813397530094871120233541993308062106827152466050640616011004037057455510046113190194078351648302459326271614213551142750339533929198981934385166481129940339472369362793336094150909760235037092371572505973355846461130949504343960198490561221650272463925877262224098363742633574111823071553944965391234428646364087007667740174095861554619692033509931234632712740981924469045908309909354350210522707538677836736220552300777540692255747572901813820508606441076022769282144113299505469658029159252505522109823751058341594664629549798228877095570072415009969581542720003872985020167585544924827519011902419136082680184024932428977709334922185006959082597367291084746545528715538782870731714538892713878572799747561630172469749846551622456976139825948840815520059348987038819691655257612324572635429421886279155859884188280907346670186833990965013163111665459977274858363156266126155050204431357677862358624235619647716334839067852130237664173798845262771883932246778247420115505351348536312607465270277144093102036490472201035131608474689163812304849394020949499494575562838737249464558349071766293661544409599894599747883224767616800268389422493109909444213495437493980515990842198589396743682820153947484882631927687309427932263399083388050833825840377351736951174361789183768532409080239816998715934667650590280052062866630053479850922089493369694761866506092868871953320363693853910297724507826191093549664708058112029818240535529113015519951505713821975490384412535253388165017808325479430713143430508680453240551024495267105785178793472098396807906887745516939292609400801790411033924201763552877875391979582799493521356104837314451950369525466028935106030678232528189364661643201796586352138741374387494648381750359884140852320637468966094594629374336478627683010603160321083694667483290866744659055513928150878501226403870348917462928853358781647386907168787759981218358689429606554770820046, 2804941902648393102137707573167893283064304511389573384533805394844795258855872596655388501777480073498568504012044880860824616403545353041826573464159990394620663193797619163746085841807128411463565932319784699906493818290357390015212760710946246005643234559483238268134356507274212939160812226107096840355749527922257072152091339200629830745781430289728424852239148456076988287860876785226629475654713890579825901184406495332100968270122841405946838801865561229041201470273599984339630173487146388287337285363236785511175540217321452840439738550176144310844131551436471569421649135321568575686847585920613462119575153686756698851170087340284645093076372125795100748163764584921328228507645110252810199714142400499168274153199210116381155808538106676808117860937456476150403150847776840840648018551710890061046196486599022513937008637439623336467003876154366273092560006375717126315381029839996082636675105595270757546415417580256418045930778106297822444332036829618553607567412696028042018942769096617959028394625689609294057574709616878352059037098153349889636993670902041266554211070345429455748153428988879508831763504069817989284784625484139237925607379256391033969307286144619340193631225228667306797822115632343666283901552757651653698691437895242322545648199857779695085616544987065150247438422049149945076229669927943857862149418021270379911689186562037332423492898731014286386914834208131941739986965533608504357542758090679840605339407858671642437619982787286755340179909230189636639159338346583315385002155929555377389473897044514578166135048087797344770624873188199112304582130313716496616103461901262406758444351728933143085502614682566789507952309605424932792811713512929475898426352512254277398476327688132219303502643915736254112832645647103646649213997808346610508367232870501487227547713863513247186058436761114083507225099237020746602584904249714702079369684127245037605582627302254697148246268734234008194036388700067685052890944957799700623871553407967835656485476326211532938641536325944087257056597964659134226539464199358475423749164141696600903613331358528392077546485417082596418769610981873981999910135670523464528801069777303174332961643474954114695913380403480808388187021279103515732247066019282549475614284574649508980042393499620509960868280923122771771467088520593268445916570211111424154043505885066524929344336845902751297799168424642537141126654695990478875359611139183906479487523623082729691448988611744128808088466135363334087834326899648722668510443331711893261432522049422461553556648946013906713839827249227303710065227398851000615046894643744756223981347009801778334292802042831510898140679695739361586414828699807465204631028409205892212987719071026918691060354434128295085029670284707905341533054246152164027621150168843673859333657866577154174295333933818278817806130862315482481974973198919518172059552584803529757538180285617693181246279399973297832162460684521983051058123771974992866326260234868906086013902423978737968528814345092542408910623472418041921040847119803094596339676264795348625881193096498552615659741120661274509619663874809964259492403698786479982329137643561289139192776019115261307384157398987561157979291940618956874209406302619389969854036879454987307906699054238626842364948558145400413520788210906516405587029473423950563196775548371476138187941784120521898857489197905726599655288017421947000662942768262443117620629308883632438988338937587465381856529571936381400515908798445348071449816099167637503286903471573149419669742335765098100842821401759434447513757907068052646412833086856295605723987754628519131663252044870931452195650076392065677515325611214884149919516726649981918655557899701255119424405966555459320468709805705931084047205829873236065894147, 2927529853147140413290955015641798173772463690480894481253690816594396883128302873289719108408451727152375684829650603606659205906506839687520597851109235983974212702801765253691565382051350622258230000876271589832390762650562898295168141382475195000536085538975758127141869876452109738891488561120556965095932434957412693433089957395014105123777451487355995769158503717325704404967878167454081529295462278908505172209318697480753317575159803600010473909998372827993588890443957445554638516550410628937203569700816434722190593420649927057517435495620493162430396315938732011792005787721590413473769644857269269008392126146093009919447236480003124815081067995590167004501251622457691393273593217174852142627940323540686848236433434731791863366384350026829191972473122151853598930631935912089955448416002511449040542956924228884566978586529226181351446597737795855971354432828488839014670330362015056861099335293698544915877394223286972424496214851231322716117846980762512595054795027722544785252848779069431387971254162836577938009487419691152009556806128716528092468117738967381982069380682085340761971588750022852593620524245260142960236282240857469957130198979928814542938462466254418993655952919629386312641149216036642348314643333450910697658348919336095018780897792255265999089045849932049757583445978317673435440613410715748595742918289877011160943902322431411805922265017470169969834994815108513320067160779441132585598386812486268921276867977333255985995283757022915956649440705438226116266295721958523165204425932258301088234850358861765219583178043854567669574098547576759041332884735401211084681864691892274192124010957898392877935581926369677534213373585208606665271783007625547347424447570813275644461953010409070508281916561568054348207825799135774433224985440092069526386412838949334523091088057016120988674114815889094287601865547581245911000370552316049086572899522028431813638274742644727824604552346138617199256111783835769543592062966245533542204276754103330016010520006536943647701029441231766697485710012838466619501859665302366866440197878213940522591040762963249118061741831960536170967717258576063108650943735960934210241639204401509643592806515609343230674165810797523353646349711499847592484656160808345190599340130576559668479511282655096543861680698579881982683857106712591444657938386793072365649406957483518201332980060274158741451267086505277779414187522859995579962076346768833787214754348539579093537326825370682230451369910928546284511840623035150414048102946061652465337696740467378201915463925637747988482014405258834063807527580269367308002114993401090372868836160336786591016761237930229674026521429179840110931058678316306386580739527811212006116170654063118638646982244418498697800897559969663300262504679268379362929097430468274436076071842191654009390948786694018345448073894999203761295636449476940715423437208696200837205508336679187016091949357533243699657530480583842945532161020792372973848973380421453349390869349330965193556770373971683016540533034474256572084210234933872107294237615113805805410316384073704506564625136197490462862251829525975008559046462883522490664192650739856854349229007105235367851773346504293342477757240570522870881218480751571622547415746992111015297410201258722062040198708442607963255792683723821539753836080129708994368788917726893368334260132501103282689024509210341539534234747501189214952109813671352344843128730209632331875052515662696078845505231638024190629984211592955497031748394663829134979379794885883549632274428932201570303268748582896559800312487639455592861178935983638345854678871870195207877519470355462833995953040705859801694067599913946769614332347275462921331645255299370531761266516926818985874461975721462503696591348161999110503199], 'aut_phi_ratio': 14.071428571428571, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 197, 1, 1], [4, 197, 1, 2], [7, 1, 6, 1], [7, 197, 1, 6], [7, 197, 6, 6], [14, 197, 1, 6], [14, 197, 6, 7], [28, 197, 1, 12], [28, 197, 6, 14], [49, 197, 7, 42], [98, 197, 7, 42], [196, 197, 7, 84], [197, 196, 1, 1], [1379, 196, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{1379}.C_7.C_{84}.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 42, 'autcent_group': '42.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 42, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'F_7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 38612, 'autcentquo_group': '38612.a', 'autcentquo_hash': 3526511167592259168, 'autcentquo_nilpotent': False, 'autcentquo_order': 38612, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{197}', 'cc_stats': [[1, 1, 1], [2, 197, 1], [4, 197, 2], [7, 1, 6], [7, 197, 42], [14, 197, 48], [28, 197, 96], [49, 197, 294], [98, 197, 294], [196, 197, 588], [197, 196, 1], [1379, 196, 6]], 'center_label': '7.1', 'center_order': 7, 'central_product': True, 'central_quotient': '38612.a', 'commutator_count': 1, 'commutator_label': '197.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '7.1', '7.1', '7.1', '197.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['38612.a', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 197, 1, 1], [4, 197, 2, 1], [7, 1, 6, 1], [7, 197, 6, 7], [14, 197, 6, 8], [28, 197, 12, 8], [49, 197, 42, 7], [98, 197, 42, 7], [196, 197, 84, 7], [197, 196, 1, 1], [1379, 196, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 28224, 'exponent': 38612, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 7, 197], 'factors_of_order': [2, 7, 197], 'faithful_reps': [[196, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '270284.a', 'hash': 4067671817825709084, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 38612, 'inner_gen_orders': [196, 197], 'inner_gens': [[1, 167580], [102901, 196]], 'inner_hash': 3526511167592259168, 'inner_nilpotent': False, 'inner_order': 38612, 'inner_split': True, 'inner_tex': 'F_{197}', 'inner_used': [1, 2], 'irrC_degree': 196, 'irrQ_degree': 1176, 'irrQ_dim': 1176, 'irrR_degree': None, 'irrep_stats': [[1, 1372], [196, 7]], 'label': '270284.a', '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': True, 'monomial': True, 'name': 'C7*F197', 'ngens': 6, '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, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 226, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 1379, 'number_divisions': 50, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 42, 'number_subgroup_classes': 108, 'number_subgroups': 10300, 'old_label': None, 'order': 270284, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 197], [4, 394], [7, 8280], [14, 9456], [28, 18912], [49, 57918], [98, 57918], [196, 115836], [197, 196], [1379, 1176]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 42, 'outer_gen_orders': [6, 7], 'outer_gen_pows': [0, 0], 'outer_gens': [[38613, 231476], [193061, 196]], 'outer_group': '42.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 42, 'outer_permdeg': 7, 'outer_perms': [183, 4842], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'F_7', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 204, 'pgroup': 0, 'primary_abelian_invariants': [4, 7, 49], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [6, 16], [12, 8], [42, 14], [84, 7], [196, 1], [1176, 1]], 'representations': {'PC': {'code': '6352070546951151222586919201890191535464659741637004502619252456746542207510566951', 'gens': [1, 5], 'pres': [6, -2, -2, -7, -7, -7, -197, 12, 31, 140, 5027404, 455710, 855556, 288352, 238, 3309269, 3827891, 2321441, 336947]}, 'GLFp': {'d': 2, 'p': 197, 'gens': [1353231080, 7645571, 275233532]}, 'Perm': {'d': 204, 'gens': [64841119371544830366035398461941532344919835157502503974143135742979298297369716893706991630785613233141178830663786997898821012682697769324179730465809535073324512352115144832885351506239067158987277131482562222827762647261382858037775892372660596089841830325305157569423154468809128338630564041686946131669667218427081818661956900460382247104052750751898364531871646980254257280, 6564329921378778562564165724118424425034637771713849085670687229211267936556464713594389803490705602078479050616923561959470655487529908436180683479480112180674044851289388766603748035105115899152194487489966314975483906588415267798618383606086046256914615216969231614021774510975997350668167606247127642728148827193497388781247800895047629485242725696398240676931306488063582817920, 97022315716219300429444600472216605317649628714491409410236778153672448013533133356592846678985837377130089015213540110569766056667434640763803522062032413188624822035564697526471940635861383821127978375564978521783531730511174179682157096068207004261791219238498495672503186980268783606874354688992693574239366516582423301552594785189292118934499315213210811803701333223618883433]}}, 'schur_multiplier': [7], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [7, 196], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7\\times F_{197}', 'transitive_degree': 1379, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '196.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 42, 'aut_gen_orders': [2, 42], 'aut_gens': [[1], [99], [101]], 'aut_group': '84.15', 'aut_hash': 15, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 84, 'aut_permdeg': 14, 'aut_perms': [6227020800, 40320873], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [28, 1, 12, 1], [49, 1, 42, 1], [98, 1, 42, 1], [196, 1, 84, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{42}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 42, 'autcent_group': '84.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 84, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{42}', '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], [4, 1, 2], [7, 1, 6], [14, 1, 6], [28, 1, 12], [49, 1, 42], [98, 1, 42], [196, 1, 84]], 'center_label': '196.2', 'center_order': 196, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '7.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['49.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [28, 1, 12, 1], [49, 1, 42, 1], [98, 1, 42, 1], [196, 1, 84, 1]], 'element_repr_type': 'PC', 'elementary': 14, 'eulerian_function': 1, 'exponent': 196, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[1, 0, 84]], 'familial': True, 'frattini_label': '14.2', 'frattini_quotient': '14.2', 'hash': 2, 'hyperelementary': 14, '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': 84, 'irrQ_dim': 84, 'irrR_degree': 2, 'irrep_stats': [[1, 196]], 'label': '196.2', 'linC_count': 84, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 44, 'linQ_degree_count': 2, 'linQ_dim': 44, 'linQ_dim_count': 2, 'linR_count': 42, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C196', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 196, 'number_divisions': 9, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 9, 'number_subgroups': 9, 'old_label': None, 'order': 196, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [4, 2], [7, 6], [14, 6], [28, 12], [49, 42], [98, 42], [196, 84]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 42, 'outer_gen_orders': [2, 42], 'outer_gen_pows': [0, 0], 'outer_gens': [[99], [101]], 'outer_group': '84.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 84, 'outer_permdeg': 14, 'outer_perms': [6227020800, 40320873], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{42}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 53, 'pgroup': 0, 'primary_abelian_invariants': [4, 49], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [6, 2], [12, 1], [42, 2], [84, 1]], 'representations': {'PC': {'code': 26433930131, 'gens': [1], 'pres': [4, -2, -2, -7, -7, 8, 21, 94]}, 'GLFp': {'d': 2, 'p': 97, 'gens': [35435496]}, 'Perm': {'d': 53, 'gens': [245076763019406400275430396602149907347995035762683805696000000000000, 606966373093046456414630002811177732290999513742573568000000000, 80688589264145591949704249464569831744133883082452238336000000000000, 74483493555417151184854488523683573561511365457240384149969120]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [196], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{196}', 'transitive_degree': 196, 'wreath_data': None, 'wreath_product': False}
