-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 7260, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '7260.f', 'subgroup_hash': 7584372576544646636, 'subgroup_order': 7260, 'subgroup_tex': 'C_{11}^2:C_{60}', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1', '484.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2701, 5939, 1554, 6360, 7406, 6178, 7413, 5078], 'generators': [30, 2640, 24, 60, 80, 2760], 'label': '29040.c.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '60.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [10, 20, 4, 22], 'aut_gens': [[1, 60, 660], [7091, 1260, 840], [5171, 6000, 6780], [7111, 4800, 5760], [4331, 600, 1200]], 'aut_group': None, 'aut_hash': 1191727547474175236, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 58080, 'aut_permdeg': 244, 'aut_perms': [9858298667526998819407837162436918828750945451470175545431059520005260294201356656628314278694765650887116960052539351508517689098121085934528078914198539402423201677975340919333038457015708781056481666175511442027690245977924071091467631629359810491413948019065583563238951602301084210664650534174854271566046934881623917583112164333803857768169024914385302098786181608694962098182462286043342545531726026803064390711604493974772340942006700927934888782679987690293743577116387, 4792313490302857112982170853225789870731900237011518533815679272141870075424838452393701060516957567326278552696405104779146479147648088708612138613400754690141531183693760960213615886623838348047522451964243144512443833957013971997510610997989694619814512851211364576508398999874347561344991314148499546371020812223385313191256996586548670540263653243753623540402472281875341487640470831439205659840033187360783720592461814205621970749883261139295524501659028941292578366443973, 5875126402739008568563391935878518542606038380049466085784171261838029357967130971200964439397697717418497584772704023973525990623634666468193683662606018535875380531145430089294549410559683705068395338470968041107153092496962434943829358784354349709179574413266839149729143930183699713370434625547848831094437175222868482648877969332257817723242154928150066350493070594229516972583066192501484822050722449901559144093707848864332087470924308011401769739800078563831370017642901, 4971406207422025974930063006767287866718403482646066356946156886498762023968189728931503678221155972162126069917674953646214240876289554962157263898407915255040455396051445343536234204892978640834555056145995682373044648340988720553719197148744557517824096024827815899708442418781054527318238016591436590445410850434259800367356042201363925690352078507528919400151491647903976583985260531746419819399451613183482952290977148405066566381787550394370169942647622728254088977934452], 'aut_phi_ratio': 33.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [3, 1, 2, 1], [4, 121, 2, 1], [5, 121, 1, 4], [6, 121, 2, 1], [10, 121, 1, 4], [11, 20, 6, 1], [12, 121, 4, 1], [15, 121, 2, 4], [20, 121, 2, 4], [30, 121, 2, 4], [33, 20, 12, 1], [60, 121, 4, 4]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [2, 121, 1], [3, 1, 2], [4, 121, 2], [5, 121, 4], [6, 121, 2], [10, 121, 4], [11, 20, 6], [12, 121, 4], [15, 121, 8], [20, 121, 8], [30, 121, 8], [33, 20, 12], [60, 121, 16]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '2420.b', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2420.b', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [3, 1, 2, 1], [4, 121, 2, 1], [5, 121, 4, 1], [6, 121, 2, 1], [10, 121, 4, 1], [11, 20, 1, 6], [12, 121, 4, 1], [15, 121, 8, 1], [20, 121, 8, 1], [30, 121, 8, 1], [33, 20, 2, 6], [60, 121, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 660, 'exponents_of_order': [2, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[20, 0, 12]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '7260.f', 'hash': 7584372576544646636, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [20, 11, 11], 'inner_gens': [[1, 2460, 2400], [5521, 60, 660], [6181, 60, 660]], 'inner_hash': 4831136090400852969, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': False, 'inner_tex': 'C_{11}^2:C_{20}', 'inner_used': [1, 2], 'irrC_degree': 20, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 40, 'irrep_stats': [[1, 60], [20, 18]], 'label': '7260.f', 'linC_count': 12, 'linC_degree': 20, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 22, 'linQ_degree_count': 12, 'linQ_dim': 22, 'linQ_dim_count': 12, 'linR_count': 120, 'linR_degree': 22, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11^2:C60', '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, 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': 32, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 78, 'number_divisions': 24, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 72, 'number_subgroups': 2040, 'old_label': None, 'order': 7260, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 121], [3, 2], [4, 242], [5, 484], [6, 242], [10, 484], [11, 120], [12, 484], [15, 968], [20, 968], [30, 968], [33, 240], [60, 1936]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 13], 'outer_gens': [[41, 600, 6600], [31, 4260, 4380], [1, 1800, 720]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 120, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 3], [8, 3], [16, 1], [20, 6], [40, 6]], 'representations': {'PC': {'code': '854385113673286876184905823656331269862044423001399', 'gens': [1, 5, 6], 'pres': [6, -2, -2, -3, -5, -11, 11, 12, 31, 68, 73804, 7210, 4066, 472, 86405, 95051, 53477, 5963]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [16280793, 207272754, 140740226, 1830210, 207916856, 58532609]}, 'Perm': {'d': 25, 'gens': [79102345851399529250184, 3, 732043497760373920319400, 1370644348715594434681923, 156754629610948768432443, 2051866659042956398467003]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [60], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:C_{60}', 'transitive_degree': 66, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '240.84', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [20, 10, 4, 10, 60], 'aut_gens': [[1, 120, 1320], [15811, 21360, 12240], [24811, 8040, 28680], [24811, 10920, 25920], [27251, 19200, 7080], [19921, 19200, 23280]], 'aut_group': None, 'aut_hash': 8062377920923750923, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 116160, 'aut_permdeg': 486, 'aut_perms': [13738413653091597271419506300259758901437022017107733345360470825934127988583553445230669428683709002160883266716348779060744744426715694400260225369790022810379831551312670555927641605475656996990161866255805730370523960132600293055306551555821756063461127302427743501690749374868734172674761706704243558886238179473802326734924120549196108391127792292467065787735389887736369114496307181636798111138659036007500682456251323236429686214531944905352844738322302161820765633278946326145784125870855606982274767265785168532873977064238192744455855219396226475029529672682531970496206861222525620197535419258719172045903669666780620200771575168189771187719624796143330739667068329722784433102205839615952774534017375450335575378026497421763309767815983454041822253963744715310891194221614176796400283470523694375992393975127520991848061331382713069520016266424255624974956365773844160098706971751692009581644947055382195116084204780926706518112076887477465099679673747350400741075802702601047850640634949312056158390192361563500772068437728962951500388026380595993707991444526510466566619093395536770, 9500558387198882119679056399891573184717129690048048378838284149131416049817567525184850659362081134577298440549402411097217554484048442402793342293658006324997262539162857441292658499493308853714772813138037893401293551643248610288895502081385791743341265963377149072740430711393413015798909337803092370242986615059752885361698446457429805079565786206554889847131756939865428608436422075822561402675150133238443054645815531637029377870463549294345428578767243354559951201995046983679079687048946213956100254703376395292149457832571031298958428557706482310099884891812967073316250874455308130184020358177592562910201137047103109715374719197965346514767727717572411280598883490919769160326045775378478872731735474184575119732646300122181960792732344825701601315467756747929808362523995258012421832816139463690257287687486472248613198729583320958504486150726550588027253638295584676689713556073843771553123922944334405252246892334348348904643882294895661763458009600333113582332749180677100951562406308217021537926380458498693821396120488163012004958010847070861213567008889245660876546075104551386, 17815706726420534930198163444347251981458624860391234077409996436196196717916713008405376333613216996782395651359031910801868533526030634565300764281534626703982583416749443785799250312930684952695087433365678250601399537130342046576784726702262195524627090845660762807795207866944087241778894804853971526265594032908064591108020902273901659128393870125905884564588363860703340451614447865572495042115825838589035301404863935778085627388607862186895288686247567160208172788514399830010755664302946239456279600658861204116504397963396846505290729044885673565766727773975576117488902497803697754034173070972941303434743179958213220294874675086330345615662818708605808919852818450350937842459899246121526084463660872302122856480643736338920419068384626928230176666076980922271695728144984835218802699086964746735214456602539361050516478469428174195552481852269614407652344276156016469654850177055770204216212482292030259252212201942000915833924464748125998491973628693982434703202148939230901399179906010222950182428448606514072090865175247575257205554272489417464053930260320420336468248451261922742, 6824853068639334040166932895093283966298076711849167090271270760046840425974547121415828885868086275640013700549406751655419754278388015037679343982775959862285373665337773741726185234382963939645547368181280527612605311191263817329374409343876997638938508852807511185979298370624490289463911593831333609153143870410933914185068763810828690811078556155365713792238839282034177882763361029031202222461513061445342515499523597968613047756550032758366959831260897598805422149656722414862410494218361079232486877673201352131341691820963530217552401127062190252316799445464070212436399004684515502108483216710113088103045918535836171226410881608264022785761410775307371718903232635065959086154156219455826474519537343746696168096429239357305357929460245803930087418640839992186612430469142215988071261962473517132048063400654176751816611128052792875209908301021800738863929056847710438321776994065821075988510981873936017027353838427517045610945074507055010786120338821092561876122427639055343630842620337137034118406715929290792216303615128972702395011255018068567493443868950295743295885454064501652, 21939587551569205065924284798304894994960104357175708838554275094163046262660365174506602561119192591233931338785740509556139059548806506614879921347863981401303272362078306347261203694453013341375166264835382405734088474542581371684729153744572586104480805569245247956186078347960926638282418715314431408572347653655562032005067778497019036805688984516532483397370356202416363737398459859113621678532936927633371115044968490233993913030080733857489327732726896874281230579017526826902935835359461442849977259791940132507535467784309700688368803003431610668434988847757610019791342177098419079570390125867831130840144037170555250137233369758943906594217261175559110348840885429853128323348893034853769873434850708565263645382754426274632639935577876793645870178826261787693207020946367292740060553780432874569852775307186587901412023725332428404496341349803154554896299029185574963184790293884610319590185438734723361694763848315844961854809072606020500925065356929103663224274121326944162541527181357008609824779828079604796226876149795738744896878922494655378237432980490105942707553138778759928], 'aut_phi_ratio': 16.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 1, 4], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 1, 12], [11, 40, 3, 1], [12, 121, 4, 2], [15, 121, 2, 4], [20, 121, 2, 8], [22, 40, 3, 1], [24, 121, 8, 2], [30, 121, 2, 12], [33, 40, 6, 1], [40, 121, 4, 8], [60, 121, 4, 8], [66, 40, 6, 1], [120, 121, 8, 8]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [3, 1, 2], [4, 121, 4], [5, 121, 4], [6, 1, 2], [6, 121, 4], [8, 121, 8], [10, 121, 12], [11, 40, 3], [12, 121, 8], [15, 121, 8], [20, 121, 16], [22, 40, 3], [24, 121, 16], [30, 121, 24], [33, 40, 6], [40, 121, 32], [60, 121, 32], [66, 40, 6], [120, 121, 64]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '4840.c', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4840.c', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 4, 1], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 4, 3], [11, 40, 1, 3], [12, 121, 4, 2], [15, 121, 8, 1], [20, 121, 8, 2], [22, 40, 1, 3], [24, 121, 8, 2], [30, 121, 8, 3], [33, 40, 2, 3], [40, 121, 16, 2], [60, 121, 16, 2], [66, 40, 2, 3], [120, 121, 32, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2304, 'exponent': 1320, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[40, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '29040.c', 'hash': 1832492014362143934, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 440, 'inner_gen_orders': [40, 11, 11], 'inner_gens': [[1, 22200, 12840], [8281, 120, 1320], [18841, 120, 1320]], 'inner_hash': 1340125317553616686, 'inner_nilpotent': False, 'inner_order': 4840, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_{40}', 'inner_used': [1, 2], 'irrC_degree': 40, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 80, 'irrep_stats': [[1, 240], [40, 18]], 'label': '29040.c', 'linC_count': 6, 'linC_degree': 40, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 18, 'linQ_dim': 42, 'linQ_dim_count': 18, 'linR_count': 360, 'linR_degree': 42, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C11^2:C120', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 84, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 258, 'number_divisions': 44, 'number_normal_subgroups': 48, 'number_subgroup_autclasses': 100, 'number_subgroup_classes': 148, 'number_subgroups': 7048, 'old_label': None, 'order': 29040, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [3, 2], [4, 484], [5, 484], [6, 486], [8, 968], [10, 1452], [11, 120], [12, 968], [15, 968], [20, 1936], [22, 120], [24, 1936], [30, 2904], [33, 240], [40, 3872], [60, 3872], [66, 240], [120, 7744]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 102], 'outer_gens': [[41, 1200, 27720], [91, 27000, 22560], [14521, 21480, 4920]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 49, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 8], [8, 8], [16, 4], [32, 2], [40, 6], [80, 6]], 'representations': {'PC': {'code': '172219749243564175609130683064643333843943974933224474218801318983668488034901316703038770080775900013909', 'gens': [1, 6, 7], 'pres': [8, 2, 2, 2, 3, 5, 11, 2, 11, 16, 41, 66, 123, 1065605, 63373, 2901, 2909, 2197, 719046, 409934, 240262, 138630, 27758, 166, 1559047, 7695, 84503, 84511, 63399]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [16280793, 207272754, 140740226, 80979421, 1830210, 207916856, 58532609, 26573430]}, 'Perm': {'d': 49, 'gens': [14000005658767194322138849151509273456093287375561934835649870, 26667169170766690187178353532046274075554480316325393817632000, 30, 39334312563777554177172541404234401431449219459601552468275840, 52045486600559582527271472987696799888995126791267305791810481, 64672597377446824496185695107136948366849105137185555170832590, 77330186214435394099468424732940748724002691259426604052585550, 31]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 120], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{11}^2:C_{120}', 'transitive_degree': 264, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
