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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '50000000.qt', 'ambient_counter': 436, 'ambient_order': 50000000, 'ambient_tex': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1562500, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '50000000.qt.32._.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.H', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 1562500, 'subgroup_tex': 'C_5^8.C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '50000000.qt', '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': [647475510142422447101370, 911748349975248729504920554488349056096, 1046417245634867895428989419790178479557799004, 647475894284776292736090, 33, 187768627290, 41869336903510576997941184846361065697608088960, 2481793606932957757440033, 1596967378493501284365531301632142561804107719, 27439951015054247445135360816480], 'label': '50000000.qt.32._.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '32.H', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32._.H', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[104675255707856353095398173061862774711268041023, 753661818864064240840458566364127230728619599423, 648477314053239749799304948624796545574797622903, 231331230603830409575140005577592265287128246213], [106272223068185567815857471755772038051818378233, 794980233677183349634133967409543246839288067833, 648477315234170945957721512015270984148877622999, 231331231784761605733556026075715187182774575883], [104675255707856353095398173061605968388182094046, 732726778149799333940625364686957961323267233215, 690304988615898172469089824603080731288306368086, 231331231480590571918917336386886399789325573124], [523376278241375436136654474267716371370208848696, 334451549024488932558841419248265757324242123633, 648477314661598244790006329272660006222910160535, 231331231784761605733555378600205045109041455850], [167437969803848486506600331379232821371495519935, 734323744885727279013891227406319752731898115896, 271603966967542744674405515657304180421215869370, 210396934752979235696648308999095855923230467083], [104675256315417232736642356295151439225827647935, 774596114749919985219921315279844145160967161599, 711240028149231901525584231120473794930572806519, 250160045709388229027318245989999214979100379364], [104675255707856353095398173061734350626935103999, 795489491638230587710580861400782342593583423909, 669370692426652537738029169020366512330087942519, 231331231784761622817788902320752301574138553003], [146544592611366876444284806058616481469085177535, 814318306474589081166080371898305488687331507135, 690304988312508326642484978432564116569769189815, 250160044832628031315685814304880875956295640324], [167437969803848486506599684005802125474119553215, 814318305867028227733941664360736533406503687583, 629648499824442109775944688557193871252542160503, 210396934145401945745143201986628041617996652133], [167437969803848477349465062514291120025165939135, 795489491638230552343534073386486251249744585119, 711240029330163079368923026382687603442108664343, 271095085581099973226809938775846144399103551370], [104675255707856334813389114377738005176446746206, 814318306743771953558356267856574414812541703646, 648477314964988127214505340557676945419661827766, 231331231480590581076861673391037088925510218244], [104675256619604676861542718296194977229499143679, 732726778418982153914687726299502207361799962175, 629648501005373315092305690112140217286906380919, 291988463651122889095945516828485362168396652203], [104675255707856334813389114377738005362737651166, 814318306743771953558354973007249434606860058206, 648477314964988099774554325503045357513244982966, 231331231480590581076859835649718748801332995044], [104675255707856362253340672324823547297951923109, 774596115322492721754685868990166841559796095909, 690304988008337292827845641369894504753036806429, 231331230907220264559688645860650393491199551370], [104675255707856334813389657270191959834091823486, 814318306743771953558355620380706116490004479966, 648477314964988099774554325503045357674189520566, 231331231480590581076859191597301732045760815844], [104675255707856362253340672324823547552740041029, 774596115322492721754687703308263632443819599429, 648477314357427220133308847420918293194637622909, 231331230907220264559688645860394633307608246250], [146544592342184057701066692276417094121792787775, 814318306743771918191307645422256454913057990303, 690304988615898181627034805660006593659627526429, 271095085277710118242261298493043776378623551333], [167437970411409375305785179557385467749658394239, 753661817987320515016046549245284681567896783429, 690304988312508352851591641073051270878294328989, 271095085581099956141768645188046323383532718603], [125610297064686745505302456294949653850157235199, 814318306743771918191307645422154016933767142943, 711240028453419388911558984120829144803873676855, 210396934448791800729690550741375914964782403850], [146544592611366894726292674374520347627553887935, 314025767148014945678531121266566295850439071446, 250669670509114289969283145835246678740157260833, 291988463346951873597192473140832502322686296389], [753152559427116156684930671036679492994718152975, 166928710670290247568707283825568393392116458319, 709643062004838507115186082550999130538404146064, 270558299219488594541524598894675570319648324435], [104675256323837401236512705570303205761412681064, 734323745501708371646119051252135992694137475919, 690814246864292517116577092978475901659303215280, 230794444814791722899631125818901371799603109069], [186817341142588671582924337400892368523821223683, 336006476255055242737205572055515323927240538810, 251219847754272614760520594428598041801380860109, 689259311098033402507893647910653951552801054210], [126119183318948434590035484688734788081021892373, 733773194483685834776571458003570840156303100669, 709643061700651027623239037016406467909514236170, 270558300096248756885305601865309872329561816306], [167437969803848460297495503158793480293889120606, 795489491334043100324609237567847676267554791006, 709643061709071214405116610657100720679335106566, 210396934145401945745143744878979558271003971909]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 51200000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 50, 2], [2, 625, 6], [2, 1250, 8], [2, 31250, 2], [2, 390625, 1], [4, 390625, 8], [4, 781250, 12], [5, 8, 4], [5, 16, 28], [5, 32, 160], [5, 64, 896], [5, 128, 2560], [8, 1562500, 16], [10, 200, 12], [10, 400, 60], [10, 800, 256], [10, 1600, 832], [10, 5000, 44], [10, 10000, 132], [10, 20000, 224], [10, 40000, 64], [10, 125000, 4], [10, 250000, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '50000000.qt', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 15, 'conjugacy_classes_known': False, 'counter': 436, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 50, 1, 2], [2, 625, 1, 6], [2, 1250, 1, 8], [2, 31250, 1, 2], [2, 390625, 1, 1], [4, 390625, 2, 4], [4, 781250, 1, 4], [4, 781250, 2, 4], [5, 8, 1, 4], [5, 16, 1, 28], [5, 32, 1, 160], [5, 64, 1, 896], [5, 128, 1, 2560], [8, 1562500, 2, 8], [10, 200, 1, 12], [10, 400, 1, 60], [10, 800, 1, 256], [10, 1600, 1, 832], [10, 5000, 1, 44], [10, 10000, 1, 132], [10, 20000, 1, 224], [10, 40000, 1, 64], [10, 125000, 1, 4], [10, 250000, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [8, 7], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '50000000.qt', 'hash': 2194229999738254264, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 50000000, 'inner_split': None, 'inner_tex': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '50000000.qt', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C5^6.(C2*C10^2:OD16)', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 7, 0, 0, 27, 0, 0, 51, 0, 51, 0, 43, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 5336, 'number_divisions': 5320, 'number_normal_subgroups': 247, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 50000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 466975], [4, 12500000], [5, 390624], [8, 25000000], [10, 11642400]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 1024, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2833422269794574208067851962568270972716467221300123037231471766226230393630498093372404745097327627271580054718409653664604569990045568189859837038977055100650690847120823877163713745576718111392586462415126241512624149642154692443085489224866095441049500594906678262258970318746063864558577741067708149198952343503542310914228277425301047147354143681736703862396980411867126789149106898042014169635024109284261489388278733696245070943814277209808855866351262593328025969963335555513032614672323561304879186272272405856626053241185223064002378935597448524993317161539784757207261328742851773508408953626547494968551967252319883263', 'gens': [1, 3, 5, 7, 9, 11, 12, 13, 14, 15], 'pres': [15, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 5, 5, 5, 5, 30, 574244776, 551421902, 1122575867, 122, 2175575523, 478485378, 1206963604, 316732219, 424212934, 410110399, 214, 1418408645, 1367282900, 74162195, 1490, 2354073966, 1638865221, 99636636, 225726951, 136383516, 106838106, 306, 4071552007, 57622, 1314268837, 19252, 202089667, 4539369608, 2949804023, 913302038, 316953053, 411331568, 43409333, 8733248, 11367788, 398, 6571248009, 720024, 360039, 240054, 120069, 12099, 3038640010, 2640025, 1320040, 1320055, 660070, 36300100, 6730, 8766720011, 2439360026, 7200041, 7200056, 491940071, 36131, 7693938732, 4311840027, 1427400042, 39000057, 512460072, 2145102, 1911132, 6834260173, 4300800028, 2150400043, 210000058, 598500073, 43596103, 1585633, 10598400014, 2656800029, 2727000044, 1125000059, 636075074, 47655104, 5625134]}, 'Perm': {'d': 40, 'gens': [104675255707856353095398173061862774711268041023, 231331230603830409575140005577592265287128246213, 753661818864064240840458566364127230728619599423, 648477314053239749799304948624796545574797622903]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 32, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^6.(C_2\\times C_{10}^2:\\OD_{16})', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1827, 1921, 2597, 1681], [1827, 1921, 2597, 2833], [1827, 2951, 2597, 3733], [1795, 1953, 2597, 3765], [1827, 1921, 2597, 659], [3847, 4005, 2597, 3733], [1827, 1953, 2597, 1681], [1827, 1921, 2597, 1713], [1827, 4005, 2597, 1681], [1827, 1921, 2597, 3765]], 'aut_group': '512.51562', 'aut_hash': 980934627281771344, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 16, 'aut_perms': [1328072048060, 6411464649512, 5713556723309, 2967138282223, 13732651507006, 878562691454, 14031551910983, 442666638996, 4402772473723], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 1, 4, 1], [2, 2, 4, 1], [4, 2, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6:D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '256.8935', 'autcent_hash': 8935, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6:C_2^2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [4, 2, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 22, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.3', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [4, 2, 2, 4]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 21, 'exponent': 4, 'exponents_of_order': [5], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '8.5', 'hash': 22, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 1, 2], 'inner_gens': [[1827, 1921, 2597, 1681], [1827, 1921, 2597, 3765], [1827, 1921, 2597, 1681], [1827, 4005, 2597, 1681]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4]], 'label': '32.22', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 80, 'linQ_dim': 5, 'linQ_dim_count': 80, 'linR_count': 80, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3:C4', 'ngens': 3, 'nilpotency_class': 2, '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': 20, 'number_divisions': 16, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 22, 'number_subgroup_classes': 66, 'number_subgroups': 94, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 15], [4, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [513, 513, 513, 513, 513, 513, 513], 'outer_gens': [[1827, 1921, 2597, 2833], [1827, 931, 2597, 3733], [3879, 1921, 2597, 1681], [1827, 1921, 2597, 659], [3847, 1921, 2597, 1681], [1827, 3973, 2597, 1681], [1827, 1921, 2597, 3733]], 'outer_group': '128.753', 'outer_hash': 753, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [40723327, 135727216, 90842402, 1508400, 23, 14933663, 135732240], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8]], 'representations': {'PC': {'code': 2114056, 'gens': [1, 2, 3, 4], 'pres': [5, 2, 2, 2, 2, 2, 128, 58]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705946295602, 706461792404, 141602720900]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 122297461254, 30594431879, 30704310001, 61245322049]}, 'GLZq': {'d': 2, 'q': 8, 'gens': [1921, 2565, 1827, 545, 659]}, 'Perm': {'d': 10, 'gens': [408391, 85969, 1, 806400, 806688]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:C_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
