-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '28512.a', 'ambient_counter': 1, 'ambient_order': 28512, 'ambient_tex': 'C_{36}.D_{396}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 9, 'counter': 569, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '28512.a.3168._.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3168.A', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3168.c', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': None, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '28512.a', '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': [12263871587, 2127406644], 'label': '28512.a.3168._.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '3168.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3168._.A', 'subgroup_fusion': None, 'weyl_group': None}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '9.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [6], 'aut_gens': [[1], [2]], 'aut_group': '6.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 6, 'aut_permdeg': 5, 'aut_perms': [27], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [9, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 6, 'autcent_group': '6.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6', '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], [3, 1, 2], [9, 1, 6]], 'center_label': '9.1', 'center_order': 9, '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': ['3.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [9, 1, 6, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 9, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 6]], 'familial': True, 'frattini_label': '3.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, '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': 6, 'irrQ_dim': 6, 'irrR_degree': 2, 'irrep_stats': [[1, 9]], 'label': '9.1', 'linC_count': 6, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1, 'linQ_dim': 6, 'linQ_dim_count': 1, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C9', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 9, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 9, 'order_factorization_type': 2, 'order_stats': [[1, 1], [3, 2], [9, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 9, 'pgroup': 3, 'primary_abelian_invariants': [9], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [6, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -3, -3, 6]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [41907234971425459]}, 'GLFp': {'d': 2, 'p': 17, 'gens': [78572]}, 'Perm': {'d': 9, 'gens': [357120, 80884]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [9], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_9', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '72.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 1980, 'aut_gen_orders': [30, 30, 30, 6, 30, 36, 12, 66], 'aut_gens': [[18833802674, 9948752912, 158006], [17895241255, 9385615995, 58087055], [12138729997, 5568798855, 52961785], [2189977268, 5568798855, 48366907], [19897505971, 11638164032, 28554225], [2189977239, 20022647592, 10232278], [19334368858, 13202433246, 3617861], [11075027204, 14203565478, 10557421], [22650620135, 9761040616, 52170961]], 'aut_group': None, 'aut_hash': 8950228953869246878, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1140480, 'aut_permdeg': 410, 'aut_perms': [4125848702928678632559808817666538095752813066890582223101233576458076345316576414699968512288048858111088462237569572954715562648994938436395534866516015042033326559689302321347554202679993351290907353977387452558856707882673115137837350989747664618516617908347219561866616895870294407523423732924575525441104163584806020491362391750739691161584010035986824403081174634223841892152763656218411697896320515477776056430496940672831592828599043269647362927775337505538629053009168607639560799190455487040948839786950779860690994666005696338412956645756421070003056874144766718272417779971888882741111492858601109758783858501586116351026199208897374836811964272723579647963135736789324591232003210541723967965086593849797906596351347577016212689654578359414038638110493326183280806263296487409656621265620640915225217473220982999128481580293876509930711763846849726908335952619119661088296638228708, 4778511242496108446003839602670785732514142992666290402733799899979547734553058403516489166455078634728330551916196950903296123243246269935081758107296798686830749698367086814023668415062412029170499854964475712067342325344560321499930531194442562077954987142342005821880334796025549428840913118517813442541155153415812515641084874908137720081461519453631949016948930839445854665194240096318388685374677693038100029159826190777607879632893364239188451469613288963660179450930671745704875002759288419909943410555586590107959654794157860783538611543492546226425326289353223492964345612853935078802892120830638697597671294610504978352184545261286226965971804380508876155421091172567362609089957350154413449290482976546830694822717958525046076497131571251977409469984755870220269385080253644330362061462987931605616253789740913694667871443049088519203874702245697186191396745804445094752937037205057, 2329220674600292672862615510538396464214533009423161677690302746841641305634329802936512554655061057991478031999329094139540746498839205372790538440566266092359419504557270373858964278389560464377399565097553657192380360724576399080011488296016386313667480934858874397820291810510154217907340601633657604582893796666598703697105586960737470612286288642053028551120597401455431608813488107465521969093162099722725927903017834380517203158509022778106059567706409900393539475958546650339184464386977640989716259745594632858976250095515839007141170752886781825727088953631441607968265245295714922452545137551134032905203590204503570305961617041077937360490831634444690667688773243462357985826480064961338658067522297902967419276847188513285518602592382654122035577714074683179456654499023636048912866412516159050160188131420664809070666831428119730172237297163652092078574286024618170223197230553283, 3308430696602982447231791019764740744993919229265687211996708670035503863308837051328447362280263991468646849994123098155987345072837259938155331582123637630004247557007377975258792734774738074979451871405350476504275792013558356897060075287250922097197303500926599418375777807160774327700199929712054666458694594380828024707720348144102852698647772024075959208623299368538176297757164272084405239065314754157234999633484699603333576315456142638067713766543500452064550736111208812599964663067800695658792337019349514329134881139612182657271659601984109447573387146656741892864339130295138236393783442196669866820015504308491474443627638267874242169591852952319786680298718401926755483733864172652818079729283196901375321343990308636964085809834046525271870604281126651680465852170965219743254179338991560485066379554999501609930203788939279050984377443602636547142868464732422225163806524901765, 1293108917053343986908406855118452199391834117748879187892280780935957873671443331915117624709420786765693213526370591162450426221902834476579514086871010533184100317031016294641164432723139710850837878418412383259664395839743175484245901665098909887854275297762684340575612963285236731846448316951275149838328354468208012174153140224239327694581797244068560789496861634215175012680778117413135707010472954506533667343575511215871794577526096074414389685374194401231907206925831846768236385771934499823951153304456280263891139423607435504079911564331394390774804532120569989414100157312111371185583557863569015944444299104796924453730652685219261153781072389623795366805298214625388061930776252751621973132191977653620834232154455889128511717000792160122664428886491790324677495311343405154166768854828025116914265924840105332918569391435891544312496703172412466763175995876081683674021080669879, 7076008473042980884367145523528563341667312990830249772659819879423816427730032272713289438454997022717932583699852536770071074749160784789481240088825226509230965133698059492644492350003217251455707101053073659567236406314040144652225877652478763016649015579349023308808276339953328462321752883729322072649774716599054655334906073309868233134338402904638021733649331364596830562218396828092327192741314070031575056341978911861347142858822289607480122100799344210285528663060458716232829703628979212008503342743138822868504489742273504938032850431747866850698705901270308095547343927018970640034811580764707641660608219865745082992050291312546894548072507696179708803614545335029391548517803118307064465152520519974946635234347976383205359332621148115700667669768542788048109518332496696533335872423690690479792213273487944381898752498141859262127893544197944659360742945007889694469340127113446, 500192555789675713878769687059106875637215578264386476897924524674302753365452137159951279303225522980798556910062812395405235356403296483893151726839143376799167444156343389599033631779915859817800907604433937189213966402461105530264938975287058882031024094994981935124071881027189009062430373213318021344538633392549301471536222671808622568534784508562988285456785541819491009576744619231803695649826359679784624042758922078028446749491913226177366251689464596679955716629238145341169392956686727165736722536943696626693469829036901699238839354713151236275725038918995637884161476120146941235030834587885496928753609936165556585900612971287333797153824096485258824978592838338627741676021204596250241180907016240237665338897864871118885728577708885961705262474782636499253088983797252456895765986167022403626717531497219138061543364422944713534013268911931476587120338610198964880749427938131, 7414133735726062645045352142507706753909123244306267936676895295373007078823754993354251854379539690279300477371700657172649296511769097921926235826437321887841606748607268775251718803335820927206413759942284558406068085153627854993799454570457493391297272107212061628331146983831086481375317850303698023713277098063981491311770461578496616844651196261311126516903199124062351946490572807548290058137917958683337890340634637873710173127236543523405094129574507038810372713502440389914513540452285221441248878335430818521081184297254375437523160992806482137722653872855294161912394767411786354457467004054598387644994971199078632504696846844985925879398617593440921741913947753533729489780776215609926126590608137746200526413367068148193708235656690451988120453507488999835223085197048347214494804708807971095396964286985831961939134653843619972825606033013927109741314724408509471973649664562478], 'aut_phi_ratio': 132.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 396, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 4, 1], [4, 396, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 396, 2, 1], [8, 396, 2, 1], [9, 1, 6, 1], [9, 2, 3, 1], [9, 2, 6, 2], [9, 2, 18, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 2, 8, 2], [12, 2, 16, 1], [12, 396, 2, 1], [18, 1, 6, 1], [18, 2, 3, 1], [18, 2, 6, 4], [18, 2, 12, 2], [18, 2, 18, 1], [18, 2, 36, 1], [18, 396, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 396, 4, 1], [33, 2, 10, 2], [33, 2, 20, 1], [36, 1, 12, 1], [36, 2, 6, 3], [36, 2, 12, 4], [36, 2, 24, 2], [36, 2, 36, 2], [36, 2, 48, 2], [36, 2, 144, 1], [36, 396, 6, 1], [44, 2, 10, 2], [44, 2, 40, 1], [66, 2, 10, 2], [66, 2, 20, 3], [66, 2, 40, 1], [72, 396, 12, 1], [99, 2, 30, 2], [99, 2, 60, 2], [99, 2, 180, 1], [132, 2, 20, 4], [132, 2, 40, 2], [132, 2, 80, 2], [132, 2, 160, 1], [198, 2, 30, 2], [198, 2, 60, 4], [198, 2, 120, 2], [198, 2, 180, 1], [198, 2, 360, 1], [396, 2, 60, 4], [396, 2, 120, 4], [396, 2, 240, 2], [396, 2, 360, 2], [396, 2, 480, 2], [396, 2, 1440, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{99}.C_{30}.C_6.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 990, 'autcentquo_group': None, 'autcentquo_hash': 1708500793111330354, 'autcentquo_nilpotent': False, 'autcentquo_order': 23760, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times C_{99}.C_{30}.C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 396, 1], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 5], [4, 396, 1], [6, 1, 2], [6, 2, 11], [6, 396, 2], [8, 396, 2], [9, 1, 6], [9, 2, 33], [11, 2, 5], [12, 1, 4], [12, 2, 46], [12, 396, 2], [18, 1, 6], [18, 2, 105], [18, 396, 6], [22, 2, 15], [24, 396, 4], [33, 2, 40], [36, 1, 12], [36, 2, 426], [36, 396, 6], [44, 2, 60], [66, 2, 120], [72, 396, 12], [99, 2, 360], [132, 2, 480], [198, 2, 1080], [396, 2, 4320]], 'center_label': '36.2', 'center_order': 36, 'central_product': None, 'central_quotient': '792.25', 'commutator_count': None, 'commutator_label': '396.4', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '11.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 396, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 2, 2], [4, 396, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 396, 2, 1], [8, 396, 2, 1], [9, 1, 6, 1], [9, 2, 3, 1], [9, 2, 6, 5], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 10], [12, 396, 2, 1], [18, 1, 6, 1], [18, 2, 3, 1], [18, 2, 6, 17], [18, 396, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 396, 4, 1], [33, 2, 10, 2], [33, 2, 20, 1], [36, 1, 12, 1], [36, 2, 6, 3], [36, 2, 12, 34], [36, 396, 6, 1], [44, 2, 10, 2], [44, 2, 20, 2], [66, 2, 10, 2], [66, 2, 20, 5], [72, 396, 12, 1], [99, 2, 30, 2], [99, 2, 60, 5], [132, 2, 20, 4], [132, 2, 40, 10], [198, 2, 30, 2], [198, 2, 60, 17], [396, 2, 60, 4], [396, 2, 120, 34]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 792, 'exponents_of_order': [5, 4, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': None, 'familial': False, 'frattini_label': '72.36', 'frattini_quotient': '396.27', 'hash': 8620365606197845628, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 396, 'inner_gen_orders': [36, 198, 2], 'inner_gens': [[18833802674, 9948752912, 24233674], [18833802674, 9948752912, 4047415], [62571074, 312854024, 158006]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 792, 'inner_split': True, 'inner_tex': 'D_{396}', 'inner_used': [1, 2, 3], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '28512.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': False, 'monomial': True, 'name': 'C36.D396', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 2, 3, 2, 1, 3, 1, 6, 1, 3, 1, 2, 2, 0, 2, 9, 3, 2, 2, 2, 3, 1, 1, 0, 3, 6, 6, 3, 1, 1, 3, 2, 2, 0, 2, 3, 0, 9, 2, 2, 2, 1, 5, 0, 1, 0, 6, 1, 5, 1, 4, 0, 1, 3, 4, 3, 1, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 117, 'number_characteristic_subgroups': 141, 'number_conjugacy_classes': 7182, 'number_divisions': 199, 'number_normal_subgroups': 141, 'number_subgroup_autclasses': None, 'number_subgroup_classes': 606, 'number_subgroups': 9582, 'old_label': None, 'order': 28512, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 399], [3, 8], [4, 408], [6, 816], [8, 792], [9, 72], [11, 10], [12, 888], [18, 2592], [22, 30], [24, 1584], [33, 80], [36, 3240], [44, 120], [66, 240], [72, 4752], [99, 720], [132, 960], [198, 2160], [396, 8640]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 6, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 62570774, 62570774], 'outer_gens': [[18833802674, 9886182232, 158006], [20898638486, 24527743254, 158006], [6006794604, 9886182232, 158006], [15016985832, 24402601640, 158006], [5506228058, 14516419656, 158006]], 'outer_group': '1440.5958', 'outer_hash': 5958, 'outer_nilpotent': True, 'outer_order': 1440, 'outer_permdeg': 21, 'outer_perms': [20923268889600, 87178291200, 2432902008176640000, 482999040, 6402373705733793], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 37, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '590887531235878144316880845930159970931417298078010213551699122093740001190011', 'gens': [1, 2, 7], 'pres': [10, -2, -2, -2, -3, -3, -11, -2, -2, -3, -3, 63321, 51, 166202, 82, 411523, 153, 38404, 194, 43205, 206, 237, 358]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [18833802674, 9948752912, 158006]}, 'Perm': {'d': 37, 'gens': [393571650649489694616425854315367444083200, 894398426278376992365553965074350126233, 775020847460377189845581200419234277824000]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 36], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{36}.D_{396}', 'transitive_degree': 792, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '72.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [2, 10, 30, 20, 30, 10, 10], 'aut_gens': [[13702999292, 15767835078, 158006], [9886182226, 17644958238, 43033609], [8634766984, 500566333, 28893263], [9010191600, 125141745, 40463034], [20272930639, 24340030945, 1320025], [3816817200, 11450451587, 61979640], [5068232659, 8009059127, 57551899], [9635899419, 20961208987, 31363397]], 'aut_group': None, 'aut_hash': 663454934575270710, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 58, 'aut_perms': [1732732255107955792136087714523083155611527696282609392845413795515060656585530, 1715500695344529927630688436017572204067639240528097053880490743038690386126869, 410949957957637167701383941578475739672622923628152146625556499012530057811211, 23440870890990985064437392413157911354402545286639407489330654141706757358531, 1439559129500943182807148742255642695193111227337758557736047596152297216861084, 1752221241673055078784697114190557739888993379513555775212589631060461638953067, 1766464214964711651262414835527118663334041021630008231056518429352221596925084], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 4, 1], [4, 44, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 44, 2, 1], [8, 44, 2, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 8, 1], [12, 44, 2, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 44, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 44, 4, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 24, 1], [36, 44, 6, 1], [44, 2, 10, 2], [44, 2, 40, 1], [66, 2, 10, 1], [66, 2, 20, 1], [72, 44, 12, 1], [99, 2, 30, 1], [132, 2, 20, 2], [132, 2, 80, 1], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2], [396, 2, 240, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.C_{30}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '440.42', 'autcentquo_hash': 42, 'autcentquo_nilpotent': False, 'autcentquo_order': 440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 44, 1], [3, 1, 2], [4, 1, 2], [4, 2, 5], [4, 44, 1], [6, 1, 2], [6, 2, 2], [6, 44, 2], [8, 44, 2], [9, 1, 6], [11, 2, 5], [12, 1, 4], [12, 2, 10], [12, 44, 2], [18, 1, 6], [18, 2, 6], [18, 44, 6], [22, 2, 15], [24, 44, 4], [33, 2, 10], [36, 1, 12], [36, 2, 30], [36, 44, 6], [44, 2, 60], [66, 2, 30], [72, 44, 12], [99, 2, 30], [132, 2, 120], [198, 2, 90], [396, 2, 360]], 'center_label': '36.2', 'center_order': 36, 'central_product': True, 'central_quotient': '88.5', 'commutator_count': 1, 'commutator_label': '44.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['352.11', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 2, 2], [4, 44, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 44, 2, 1], [8, 44, 2, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 2], [12, 44, 2, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 44, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 44, 4, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 44, 6, 1], [44, 2, 10, 2], [44, 2, 20, 2], [66, 2, 10, 1], [66, 2, 20, 1], [72, 44, 12, 1], [99, 2, 30, 1], [132, 2, 20, 2], [132, 2, 40, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2], [396, 2, 120, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 144, 'exponent': 792, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 240]], 'familial': False, 'frattini_label': '24.9', 'frattini_quotient': '132.7', 'hash': 8813592882577988912, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 44, 'inner_gen_orders': [44, 22, 2], 'inner_gens': [[13702999292, 15767835078, 39829422], [13702999292, 15767835078, 19694773], [312854084, 17644958238, 158006]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 88, 'inner_split': True, 'inner_tex': 'D_{44}', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': None, 'irrep_stats': [[1, 72], [2, 774]], 'label': '3168.c', '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': False, 'monomial': True, 'name': 'D44:C36', 'ngens': 3, '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': 45, 'number_characteristic_subgroups': 57, 'number_conjugacy_classes': 846, 'number_divisions': 51, 'number_normal_subgroups': 57, 'number_subgroup_autclasses': 126, 'number_subgroup_classes': 132, 'number_subgroups': 774, 'old_label': None, 'order': 3168, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 56], [6, 94], [8, 88], [9, 6], [11, 10], [12, 112], [18, 282], [22, 30], [24, 176], [33, 20], [36, 336], [44, 120], [66, 60], [72, 528], [99, 60], [132, 240], [198, 180], [396, 720]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 62570774], 'outer_gens': [[19709793593, 7195639040, 158006], [5130803685, 7195639040, 158006], [19084086004, 15767835078, 158006], [10574460798, 500566333, 158006]], 'outer_group': '240.208', 'outer_hash': 208, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [40279680, 1307674368000, 362880, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 6], [6, 4], [8, 2], [10, 2], [12, 4], [20, 5], [24, 2], [40, 5], [60, 2], [80, 2], [120, 3], [240, 2]], 'representations': {'PC': {'code': '3976166881536833915045964957510993751887459000011900', 'gens': [1, 2, 7], 'pres': [8, -2, -2, -2, -3, -3, -11, -2, -2, 47841, 41, 48482, 66, 2563, 123, 9604, 156, 34565, 166]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [13702999292, 15767835078, 158006]}, 'Perm': {'d': 28, 'gens': [837608818963245301260293356, 12129846060497475056316969246, 22632721498791788066242577348]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 36], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{44}:C_{36}', 'transitive_degree': 792, 'wreath_data': None, 'wreath_product': False}