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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1434890700.g', 'ambient_counter': 7, 'ambient_order': 1434890700, 'ambient_tex': 'C_3^{12}.C_{15}^2.D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1434890700, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '1434890700.g.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.A', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1434890700.g', 'subgroup_hash': None, 'subgroup_order': 1434890700, 'subgroup_tex': 'C_3^{12}.C_{15}^2.D_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1434890700.g', 'aut_centralizer_order': None, 'aut_label': '1.a1', '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': [97924026452809295187749374614540365392668536365711253638, 13477399933638919937892418820951354672422602371621516164, 35360028966967316450724827507836661922706227773650253254], 'label': '1434890700.g.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', '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': [[35360028966967316450724827507836661922706227773650253254, 13477399933638919937892418820951354672422602371621516164, 97924026452809295187749374614540365392668536365711253638], [108802849995686647750025059846688879505071945694083676114, 13477708529973966154674704502795795024464408933139425877, 27200439244069133280738946007709331732820507068844627253], [119561052066005546461241084495481217710700948481796814674, 95080669587471357927254013225555270901382146638057012480, 97924575067305163409958675199083985603267481112851246884], [37957917915840487002776087337552002366818864278076067154, 8160824147450671819328506925787000610591089952457147764, 97924026452809295187749374614540365392668536365711253638], [57123265989158597981768961695234904975041022162480502323, 76162195308487067612785290015907309974580679169643213680, 97924575067305152781832817771614430696346314939603738884], [35360028966967316450724827507836661922706227773650253254, 13477399933638919937892418820951354672422602371621516164, 97924026452809295187749374614540365392668536365711253638], [81602961065554724672271047314886943885026004963920916724, 59840615576253235873842202195531908429020496326300101078, 97923784760481420025987577509671226014148304724482428320], [84322023403183332884929260438422415550940652288701529747, 111401050879715940538579992327041256993498707883762405268, 51681332741088918805761125738780631441812061315525093810], [37957917915840487002776096484621170363110825525144163010, 8160856784062001735237898434180574603246159432707963520, 103240636507439419051450833430043390429100083054585311410], [35360061603578625700083352024456589745896241510703757253, 10879543622450621337857463722526671137882268840819233923, 97924060721251201637369393013628099400539116458637308133], [37957885278692391383131080502452141707272745177891597493, 13477333028585672943710916032142934079824271583277004308, 103240636507439419051450842576693728780515898018754040774], [32641342129115483808602409006665099377254844409001212610, 13477367298073614590348960771336246836875591872089979664, 103240569602386192723836626236569597168442009579671045814], [37957851010787281341457803770136557487477265344457955154, 13477399934175685642409239186883516650456409579815355668, 100642780195714333490663797325348218019462503307392462530], [35360028966967316450198565833162667214413491513922893253, 13477333029122479980836047620350975554063593440897074704, 103240636507439419051450833430043390429100082880228728914], [35360028966967316450724818970575232545945781225067817974, 13477333029122479980836029937633519292879417854799880323, 103240603870828089135541468752242893231846649368800760774], [35360028966967316450469910972295665234563145677023843154, 13477399934175706308705171959561156234841647900915698704, 103240569602386202761751784436460047636058587568641567170], [35360028966967316450198565833162640233530220741536435893, 13477399934175706308450255424408016224966236957519880564, 97924026452809295187749383151414014520656630582179836133], [35360028966967316450469919509169341336257114883670774914, 13477399934175706308450263960893833400392125688664117824, 97924093357862521515363581808014158645906258715563388034], [35360028966967316450198565833969250134355780641997581253, 13477399934684965172825630191121707472038565999177804163, 97924026452809295187749383151414014518345373500091733637], [35360028966967316450724827507448881671622241655788749398, 13477399933638919937892418820951354672422978888434153028, 97924026452809295187749374614540365392668536459116565494], [35359994699062185743281879676679751054495092950934298293, 13477333029631738845211413850190992940266390007810018163, 100642780195714344119044580434233495762053084992775566774], [86920670020629934973994419228375798688241602140631472054, 10879202390578902014509364721381874637770524101376520464, 54278642091097932027556475911608261378963557513851184643], [106084130521223495230434687395630953565188640204626604853, 13477675894408691511613682565688434620237373513872417734, 27200506149122370236988827234569572934473989323991507158], [119561052065468750052768072008222310983792795213245051893, 89764059532304458321901736369757193177326308508681674387, 103241083948976950904627566622725387575454070571178779123]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 45916502400, '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': None, 'center_label': '3.1', 'center_order': None, 'central_product': None, 'central_quotient': None, 'commutator_count': None, 'commutator_label': '358722675.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 19, 'conjugacy_classes_known': False, 'counter': 7, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': None, 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 90, 'exponents_of_order': [15, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': None, 'hash': 7392868699652681735, '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': None, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '1434890700.g', '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': 'C3^12.C15^2.D6', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 1, 0, 0, 0, 1, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 4, 0, 0, 4, 0, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': None, 'number_divisions': None, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1434890700, 'order_factorization_type': 321, 'order_stats': None, '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': 96, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 45, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': None, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2796805579265791428079097110960424057991814118824168746425301393857221419018309917659154701394641027676678600590160746631992777204989181560630643997801469749519358261434597585620130917659269816406600831274100012229189024671480040936472304762575058922252760031369494247907662720570969450535324603592065046704563224242853128748128664269882870608904224418183836998180696114349872858371836552805161078140755224730738012343324481763659546551710568086553970312168208256763494572368962663689840202302282088804411827500745462044944728265604989024563166617521318124756004598475152382692534195496941391594292894541873820566991973359173560107320655478781557928472288514799474003161013930610984429744840316906871856525302416327502814973602271998947984630185432692276050819490217831668334155974909130364910306541718009708995221649884690234979722657191987011032139317426331649694542794684857032784846233977901392085639152555784018658564680211679048142563932625893737924606532077192078111328855750113493954214645267665182288773537558545303744067007781077865813', 'gens': [1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'pres': [19, 2, 2, 3, 3, 5, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8543197620, 36434055189, 96, 56268075086, 5863513090, 45660925251, 29124523486, 16554721625, 288, 96329922484, 32819592263, 6442782432, 146915115125, 32396337852, 35289971827, 10663322372, 174300951, 442, 13269535026, 12174643933, 46643878493, 15465305898, 80290852, 37961589607, 81351950426, 2107404045, 878324464, 453343883, 1011880062, 396582561, 160262995508, 128814327, 30818521, 982882415, 2026434, 65525593, 135212, 143127009, 91599741028, 20263547, 11927316, 568147585, 161569454, 265173, 239543657110, 100679020229, 2864951148, 1774253317, 502101686, 1381704330, 519263759, 253802030411, 5326479030, 39053664049, 730614668, 161680587, 1177492426, 304683365, 231679059312, 119071993981, 6586137725, 1448062269, 731793163, 1258232927, 339551026, 226763749813, 197505032, 7125621351, 890987020, 1034966189, 390321858, 323994777, 162831586514, 13759429533, 90451647052, 1243191446, 541215090, 630135109, 706469528, 157956393615, 196091582434, 92565720053, 3951604872, 670456891, 809272430, 724027809, 404495677816, 156237151085, 4323871854, 1308295423, 957590117, 2231902656, 770724965, 128429242217, 69408284436, 53975038555, 7007067074, 2257943943, 35694652, 671096471, 329502208518, 100232787187, 37994537081, 19025169375, 4814232919, 1287221423, 34322207]}, 'Perm': {'d': 45, 'gens': [97924026452809295187749374614540365392668536365711253638, 13477399933638919937892418820951354672422602371621516164, 35360028966967316450724827507836661922706227773650253254]}}, 'schur_multiplier': [2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 81, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^{12}.C_{15}^2.D_6', 'transitive_degree': 45, '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': '4.2', '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': [[35360028966967316450724827507836661922706227773650253254, 13477399933638919937892418820951354672422602371621516164, 97924026452809295187749374614540365392668536365711253638], [108802849995686647750025059846688879505071945694083676114, 13477708529973966154674704502795795024464408933139425877, 27200439244069133280738946007709331732820507068844627253], [119561052066005546461241084495481217710700948481796814674, 95080669587471357927254013225555270901382146638057012480, 97924575067305163409958675199083985603267481112851246884], [37957917915840487002776087337552002366818864278076067154, 8160824147450671819328506925787000610591089952457147764, 97924026452809295187749374614540365392668536365711253638], [57123265989158597981768961695234904975041022162480502323, 76162195308487067612785290015907309974580679169643213680, 97924575067305152781832817771614430696346314939603738884], [35360028966967316450724827507836661922706227773650253254, 13477399933638919937892418820951354672422602371621516164, 97924026452809295187749374614540365392668536365711253638], [81602961065554724672271047314886943885026004963920916724, 59840615576253235873842202195531908429020496326300101078, 97923784760481420025987577509671226014148304724482428320], [84322023403183332884929260438422415550940652288701529747, 111401050879715940538579992327041256993498707883762405268, 51681332741088918805761125738780631441812061315525093810], [37957917915840487002776096484621170363110825525144163010, 8160856784062001735237898434180574603246159432707963520, 103240636507439419051450833430043390429100083054585311410], [35360061603578625700083352024456589745896241510703757253, 10879543622450621337857463722526671137882268840819233923, 97924060721251201637369393013628099400539116458637308133], [37957885278692391383131080502452141707272745177891597493, 13477333028585672943710916032142934079824271583277004308, 103240636507439419051450842576693728780515898018754040774], [32641342129115483808602409006665099377254844409001212610, 13477367298073614590348960771336246836875591872089979664, 103240569602386192723836626236569597168442009579671045814], [37957851010787281341457803770136557487477265344457955154, 13477399934175685642409239186883516650456409579815355668, 100642780195714333490663797325348218019462503307392462530], [35360028966967316450198565833162667214413491513922893253, 13477333029122479980836047620350975554063593440897074704, 103240636507439419051450833430043390429100082880228728914], [35360028966967316450724818970575232545945781225067817974, 13477333029122479980836029937633519292879417854799880323, 103240603870828089135541468752242893231846649368800760774], [35360028966967316450469910972295665234563145677023843154, 13477399934175706308705171959561156234841647900915698704, 103240569602386202761751784436460047636058587568641567170], [35360028966967316450198565833162640233530220741536435893, 13477399934175706308450255424408016224966236957519880564, 97924026452809295187749383151414014520656630582179836133], [35360028966967316450469919509169341336257114883670774914, 13477399934175706308450263960893833400392125688664117824, 97924093357862521515363581808014158645906258715563388034], [35360028966967316450198565833969250134355780641997581253, 13477399934684965172825630191121707472038565999177804163, 97924026452809295187749383151414014518345373500091733637], [35360028966967316450724827507448881671622241655788749398, 13477399933638919937892418820951354672422978888434153028, 97924026452809295187749374614540365392668536459116565494], [35359994699062185743281879676679751054495092950934298293, 13477333029631738845211413850190992940266390007810018163, 100642780195714344119044580434233495762053084992775566774], [86920670020629934973994419228375798688241602140631472054, 10879202390578902014509364721381874637770524101376520464, 54278642091097932027556475911608261378963557513851184643], [106084130521223495230434687395630953565188640204626604853, 13477675894408691511613682565688434620237373513872417734, 27200506149122370236988827234569572934473989323991507158], [119561052065468750052768072008222310983792795213245051893, 89764059532304458321901736369757193177326308508681674387, 103241083948976950904627566622725387575454070571178779123]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 45916502400, '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': None, 'center_label': '3.1', 'center_order': None, 'central_product': None, 'central_quotient': None, 'commutator_count': None, 'commutator_label': '358722675.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 19, 'conjugacy_classes_known': False, 'counter': 7, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': None, 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 90, 'exponents_of_order': [15, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': None, 'hash': 7392868699652681735, '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': None, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '1434890700.g', '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': 'C3^12.C15^2.D6', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 1, 0, 0, 0, 1, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 4, 0, 0, 4, 0, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': None, 'number_divisions': None, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1434890700, 'order_factorization_type': 321, 'order_stats': None, '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': 96, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 45, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': None, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2796805579265791428079097110960424057991814118824168746425301393857221419018309917659154701394641027676678600590160746631992777204989181560630643997801469749519358261434597585620130917659269816406600831274100012229189024671480040936472304762575058922252760031369494247907662720570969450535324603592065046704563224242853128748128664269882870608904224418183836998180696114349872858371836552805161078140755224730738012343324481763659546551710568086553970312168208256763494572368962663689840202302282088804411827500745462044944728265604989024563166617521318124756004598475152382692534195496941391594292894541873820566991973359173560107320655478781557928472288514799474003161013930610984429744840316906871856525302416327502814973602271998947984630185432692276050819490217831668334155974909130364910306541718009708995221649884690234979722657191987011032139317426331649694542794684857032784846233977901392085639152555784018658564680211679048142563932625893737924606532077192078111328855750113493954214645267665182288773537558545303744067007781077865813', 'gens': [1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'pres': [19, 2, 2, 3, 3, 5, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8543197620, 36434055189, 96, 56268075086, 5863513090, 45660925251, 29124523486, 16554721625, 288, 96329922484, 32819592263, 6442782432, 146915115125, 32396337852, 35289971827, 10663322372, 174300951, 442, 13269535026, 12174643933, 46643878493, 15465305898, 80290852, 37961589607, 81351950426, 2107404045, 878324464, 453343883, 1011880062, 396582561, 160262995508, 128814327, 30818521, 982882415, 2026434, 65525593, 135212, 143127009, 91599741028, 20263547, 11927316, 568147585, 161569454, 265173, 239543657110, 100679020229, 2864951148, 1774253317, 502101686, 1381704330, 519263759, 253802030411, 5326479030, 39053664049, 730614668, 161680587, 1177492426, 304683365, 231679059312, 119071993981, 6586137725, 1448062269, 731793163, 1258232927, 339551026, 226763749813, 197505032, 7125621351, 890987020, 1034966189, 390321858, 323994777, 162831586514, 13759429533, 90451647052, 1243191446, 541215090, 630135109, 706469528, 157956393615, 196091582434, 92565720053, 3951604872, 670456891, 809272430, 724027809, 404495677816, 156237151085, 4323871854, 1308295423, 957590117, 2231902656, 770724965, 128429242217, 69408284436, 53975038555, 7007067074, 2257943943, 35694652, 671096471, 329502208518, 100232787187, 37994537081, 19025169375, 4814232919, 1287221423, 34322207]}, 'Perm': {'d': 45, 'gens': [97924026452809295187749374614540365392668536365711253638, 13477399933638919937892418820951354672422602371621516164, 35360028966967316450724827507836661922706227773650253254]}}, 'schur_multiplier': [2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 81, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^{12}.C_{15}^2.D_6', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
