-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6948.b', 'ambient_counter': 2, 'ambient_order': 6948, 'ambient_tex': 'C_{2316}:C_3', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 579, 'counter': 15, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6948.b.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '579.1', 'subgroup_hash': 1, 'subgroup_order': 579, 'subgroup_tex': 'C_{193}:C_3', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '6948.b', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '579.a1.a1', 'complements': ['579.a1.a1', '579.b1.c1', '579.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.b1'], 'contains': ['36.a1.a1', '2316.b1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1607, 9183, 3196, 1389, 2638, 3530, 3915, 3941], 'generators': [4, 36], 'label': '6948.b.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.a1.a1', '6.b1.b1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '6948.b', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '579.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [192, 193], 'aut_gens': [[1, 3], [1, 114], [445, 3]], 'aut_group': '37056.a', 'aut_hash': 1432757702296672986, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 37056, 'aut_permdeg': 193, 'aut_perms': [39053339670721327572543569039395005031096653245802774324204298263788953285647090763476541643345676324473056783378543774660072842471514711015868302482279618194714261105949788702112347134548908091797187306612050281053946057960581089182560863568602379974419627409015496038525465690691519350455551181816446171767151758025418672254963521648341121096265656543605694, 27537046770698028029509447452483255633857520585283838421883440607221768231104384860166214394878916709368227289860720561987161029954363059081082583776521393368876604263321802053274125013685434525755757109968295753899028688290909515762484435944252483952769187280784953622110633939104871157686235761278347542756654691358393510201744955724775767189520816064076473], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 193, 1, 2], [193, 3, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{193}', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [3, 193, 2], [193, 3, 64]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '579.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '193.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 193, 2, 1], [193, 3, 64, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8, 'exponent': 579, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [3, 193], 'faithful_reps': [[3, 0, 64]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '579.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 579, 'inner_gen_orders': [3, 193], 'inner_gens': [[1, 252], [331, 3]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 579, 'inner_split': True, 'inner_tex': 'C_{193}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 6, 'irrep_stats': [[1, 3], [3, 64]], 'label': '579.1', 'linC_count': 64, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C193:C3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, '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': 3, 'number_conjugacy_classes': 67, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 196, 'old_label': None, 'order': 579, 'order_factorization_type': 11, 'order_stats': [[1, 1], [3, 386], [193, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 64, 'outer_gen_orders': [64], 'outer_gen_pows': [2], 'outer_gens': [[1, 447]], 'outer_group': '64.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [2014594330940748694500315964401030837224914941382363373987443624058107002128920420940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{64}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 193, 'pgroup': 0, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [192, 1]], 'representations': {'PC': {'code': 12312959, 'gens': [1, 2], 'pres': [2, -3, -193, 1009]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 603880789]}, 'Perm': {'d': 193, 'gens': [155072081769025479153068005764655310398056985534484553249510570014180068596765767602220702796160851423904603713380353967374496827693048038873577863314427425322295450355127868085281304176469528282592426059218603719048013636231661630498986145587733965119292349387964516295495591000760117599793495606069314966880735163520645227705730930758607614125986326901066, 68159384284216415434244229769722897785298203470789342442007462716964519312047994015473537393503254737883254692840162175520283792238796194464802516244938515792342454228783658226402112128483243230028631870556954631033853483990335822197126471859553676149202878029250924171717175622127511797106029233701101543903723520000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{193}:C_3', 'transitive_degree': 193, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [96, 48, 192, 192], 'aut_gens': [[1, 12], [4597, 3984], [3331, 2364], [3367, 5700], [6769, 696]], 'aut_group': '20000.be', 'aut_hash': 5408501734751148099, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 444672, 'aut_permdeg': 581, 'aut_perms': [266926607884120690028296427677932858453408509674494685449338187750735688463599815027666572224792630717410577148316508429340543391257191616613133433684322449534236261727466805446162644300430593099623856178459340493031420643584909794128196001414844886351103980665670410755610808363432513370316184020537497354344874010873864398566307736098131053085454032605886634167698112005579220602209109407165154615894146318182958142860475703823616655151812977427901671702197934518506138265046599857076857742682488617692928528951741249823747502636350592136404820206895269058131314336000405528505076567888514497389521422035333814710283721185115402462826934904948137998466855882857018962707064562081414791293002594290839684922164321594047450440515975060552048513388956713956636125295997386696501471538558050042679907373825746193186377938041464505941393224140895038037572211816384852160630186662433828385437437946636948718598481234645072930350101710424317241054005779573858436560709735832531615484266968709876375254839637848495401261387101210739106014971609178058181879770735021221561735769223740981559617521997422422678120974506860346935637051019121037887498070098045671069701985936805919211507731080843691890654742592104865264490827171963357210890942226289796936751564945599802568988150001670296998151447469182150047782420796986183267414615075388747023615628788644977757814, 184192970012729329403245904327087602036678525432328398771733073971296581629347520293944774129802056241174492189591541551445453672065621433225391414086927547609907281159399640356380142151028237597910018182473393040580004525165913213125431651268393974894440338811226642321269506117374673252141010644704171408883791987654575686852875002786097892383565494497879248045167702356504246633056728767839527376753166134308645527640186931802089891988263591917771436221339725892723046598746331975156725319155545137067843779782555507086341165271421349982913670653623005921709797598981428642773528462056426391885233907271205937970687872164189804128876231589022951812219413227118473673607867056382865075918652081924938468574640749792737671791092158620315714275685709657372716327509243182886793462072255436363756048277693814582997785143777464711267804053980463371302558855198787823622493511788599133058277193742838352078823707310707700183346469733602625782130252572221794758433028571553945503021677397729956354260246909910931265976575802096727121629347447670590721051207936808592795633458112236401479443985510162912924870726419446596987980697592430764281370466383656430495644223007122756100542085556413119229480076489479749538056663266527308750437874232895324838480371763164861636839439144272976117976412780514705785506271575265901402970673519976904573399125178456875596313, 132841509854794019006969119234015125124256076575264754050555079910537471306606132320614711152166219522206689870448381029039875912617728363121858691786238246034540994117785266118756472231698146101210378054872714487433665055238390589120676001394768618691138718189952957826389339766285920042108315898619055381535357430527420154273715522527116320842762627398521636197268901039870700460872308274734995553728064778661318175359469265477199537501791151379396450808923077584368493990256980069512075995761718192001378801181075776637568475835417482837324246244496901350224196732977519814788449708205613717145770795544646806077665276599269259840109003430419835350185683324617817148838969153521847646250175205653306647724085498723998844852456162356916050738179634402743343454654695604960984963776605696986307226249650780547199068914811009602087754413293347016974379191191189072744668173704097159681462576433647539974591559869060027397186207640716436294702461949598372356784697030267640857690486087767651087517717376200902013934535382904078719899724385430215503565280855858325934447893342699580349519159568960634470179444498542232293540889636151031933135557058253011022128843144465655783373995827686635246405614739965797358781594976243704684039052869082296432910956688187855404594313732747446654741617792636223240862995907520211526349706507937996792066786498716507831309, 73914086065122941008100977509673438972093139298897113907342997401387333974041135004969143317771626084581502680066210223187069318186889659374962024828178426933959174008004345083971622831525975846860361852593493342526330377044128397809651029026859276266465529163309678941735768342145287197514010312381232921568172657082005440167515084494392429151675817576080148240510309528965494134850266746851078304539366096891418649206854094929195677416340022348441948108310688734808253760842841467143268430689005659445452841493977258670230878012131762752268246539671161363164120661077540951662026906432258386553391996633183764199213025036849096272950787246724791696658523337018046496986973604358615220408792427188886451932645931343273056937131149287262265362162335356500914558722297018827714348743005799324912894530748116664338433170609791995460964624260494973198937434683968332527168535404175307667653909740925881476397368754556081103438258817423254549527185765067055592769114622764421765918982121328967616173624722498225385143795829506218438047403540399866575168569871921018522224740279877054949297353305644428352021029032485261250060105300163713503430638957693945611982235756549103663587145910050994204256187259700691449566570678389425170055485846598219730917348707521033766541489018992152003889361524490418708552582845241041325657789635554575141125341814574410269220], 'aut_phi_ratio': 193.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 193, 3, 2], [4, 1, 2, 1], [6, 1, 2, 1], [6, 193, 3, 2], [12, 1, 4, 1], [12, 193, 6, 2], [193, 3, 64, 1], [386, 3, 64, 1], [579, 3, 128, 1], [772, 3, 128, 1], [1158, 3, 128, 1], [2316, 3, 256, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_5^4:(C_2\\times \\OD_{16})', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.4', 'autcent_hash': 4, 'autcent_nilpotent': False, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 193, 6], [4, 1, 2], [6, 1, 2], [6, 193, 6], [12, 1, 4], [12, 193, 12], [193, 3, 64], [386, 3, 64], [579, 3, 128], [772, 3, 128], [1158, 3, 128], [2316, 3, 256]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '579.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4.1', 1], ['579.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 193, 2, 3], [4, 1, 2, 1], [6, 1, 2, 1], [6, 193, 2, 3], [12, 1, 4, 1], [12, 193, 4, 3], [193, 3, 64, 1], [386, 3, 64, 1], [579, 3, 128, 1], [772, 3, 128, 1], [1158, 3, 128, 1], [2316, 3, 256, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 2316, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[3, 0, 256]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '3474.b', 'hash': 5992398371646297422, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 579, 'inner_gen_orders': [3, 193], 'inner_gens': [[1, 3324], [3637, 12]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 579, 'inner_split': True, 'inner_tex': 'C_{193}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 768, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 36], [3, 768]], 'label': '6948.b', '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': 'C2316:C3', 'ngens': 5, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 804, 'number_divisions': 21, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 36, 'number_subgroups': 2340, 'old_label': None, 'order': 6948, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 1160], [4, 2], [6, 1160], [12, 2320], [193, 192], [386, 192], [579, 384], [772, 384], [1158, 384], [2316, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 192, 'outer_gen_orders': [32, 16, 192, 64], 'outer_gen_pows': [584, 1556, 0, 5980], 'outer_gens': [[4597, 3984], [3331, 2364], [3367, 5700], [6769, 696]], 'outer_group': '768.90601', 'outer_hash': 90601, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 384, 'outer_perms': [531692467869881067325107420522563068894649431388434068646284219459798219496715060950937520422561358331896781499501215427106593035090647798696804163814633351541497995687399316252607699940004626415959201375077796499390703560619090187459875640347643741259229637747200818194382091240912677416576413661571439357998277986912255060558552493006410430618888899965708749146597123050479536711727550796303907062952857071837827158445934470409346421141822641069280935501079919896861513004325154262523266165979816128376856444059236261507935975000663522588909743493078702889376706393441180064921373087335268669325413085473283633403578215741606503783788721436322720550620332009667611556880810602604162562961661682720355531336590648301707814542591881982212636220584900864616026692867827235557445733906736503810433310090053290610406517070201047, 1059241821279843948342768450610633046168362440084135024373613802093179341650128260770767101583553813560393975671857688161728598707761107153453987839702711108284790970470955411894650325203573698554533215270966053734936930354817367461022735729614282336620527351549261129648551732332159439749219594382963813528419870094997842335491821759624625503968730064467847434093655557694922020791609151331010767584539398715271620266980930298016204216729508245593400951866927837263412422200534706182673357754021645559704816935092998590178604717550089968973218056564383300800217942562596353421921205223125190807272621482554339116536789515923490421606597275664379447924447166365717350168449324158249792655088749094584379745714721998554988262820685322348176698447451609986155378145434823204260078162876232412255885769697575016310649171642116699, 1586791174689806829360403307056732254067233393051884423967277133530846401395647963284319105784785094095888535202369897851670536198846846238952462645281986484889413865068432645000345702346699569147241459527531316287474422362346334844377930254677337559054774248173643116203676180423599776137229707784637433356623358244973869016042632312587098794552322188836419468596086580255803397268248660444604853697301065785377749953714644769901243520896818817770338512741257353713045156713107707923792042008970765279014653146611624313765360390159332611685494520030301248664887995119771907407178246012180754736573724067151421549388218190630322457396368965634907100859734612134728504502374676854806343221878364650818476517305471120496649008028044034019248686587738960143048175472270932580258680352552553047402891147884469865043223761969128737, 2114340528050089095453662353402180708637032212885008112986148157185845072604201568334924313307678162535116621512365957119100818068161145872283918413184658954242850659857769271057578597461190641993015783257888289595941580756259177322549576755657550234416787961781841003079942951438740787943180824543231449203502408722366310232340478149915213153325040716282243443691033312202004437475101368358945154000171865193924632623544728731421253751949242431784486168181312121092152736428994727236361014872202658563684383222199153607299299310861351411007016475187178622855622913851101495510980703958582708870003150215809403836287126615569299126519443460712335137626061045726333765675606758535023559122226473394101934023181374730314332683304055728563356330438071051585771337455279677326617031206239770089156089574331635540188825712200709088], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3:(C_2^2\\times C_{64})', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 200, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 9], [4, 4], [192, 2], [384, 3], [768, 1]], 'representations': {'PC': {'code': '1927311637039041982917565101925670997572626452863', 'gens': [1, 4], 'pres': [5, -2, -2, -3, -3, -193, 10, 26, 66483, 36128, 16633, 78, 75604, 48609, 18914]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 352263842, 783607298]}, 'Perm': {'d': 200, 'gens': [3982923446508433727399271292639814002694554544055963950190683128170866233837794050861292577643721980023786961410793227937087957091406058529345249237581364375966712351963016540986910895090225309277344851400435089518399341432028350721745540121368058072509097652375387621804570768611541110401946487482218121646908679735358388285984454366347253847123051593322240946177551174400, 867, 59850450400663429717256695228343615920505790074175839106287069203651965716114062416067220129620738905768619137002664071285881220871628574336521326500823087837471865562026253683394872735209176359131232531982900551081140139279187600415697223737466657994846201838952684289240272875845328657743646297319017425529511987421359308321262132806607665618033140797776187147944070160]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{2316}:C_3', 'transitive_degree': 2316, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '12.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2], 'aut_gens': [[1], [5], [7]], 'aut_group': '4.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [1, 6], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [12, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2', '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': 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], [3, 1, 2], [4, 1, 2], [6, 1, 2], [12, 1, 4]], 'center_label': '12.2', 'center_order': 12, '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', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [12, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 12, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 12]], 'label': '12.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 3, 'linQ_dim': 4, 'linQ_dim_count': 3, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C12', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 12, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5], [7]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 1]], 'representations': {'PC': {'code': 3865, 'gens': [1], 'pres': [3, -2, -2, -3, 6, 16]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [20970031]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [619]}, 'Perm': {'d': 7, 'gens': [2400, 4, 744]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
