-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '19600.h', 'ambient_counter': 8, 'ambient_order': 19600, 'ambient_tex': 'C_{140}.C_{140}', 'central': False, 'central_factor': False, 'centralizer_order': 9800, 'characteristic': True, 'core_order': 20, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '19600.h.980.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '980.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '980.15', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 980, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{35}:C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '19600.h', 'aut_centralizer_order': None, 'aut_label': '980.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['140.a1', '140.b1', '140.m1', '196.a1', '490.a1'], 'contains': ['1960.a1', '1960.d1', '4900.a1'], 'core': '980.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3719, 3362, 7158, 6630], 'generators': [14770, 9884, 9800], 'label': '19600.h.980.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '980.a1', 'normal_contained_in': ['140.a1', '140.b1', '196.a1', '490.a1'], 'normal_contains': ['1960.a1', '4900.a1'], 'normalizer': '1.a1', 'old_label': '980.a1', 'projective_image': '1960.102', 'quotient_action_image': '2.1', 'quotient_action_kernel': '490.10', 'quotient_action_kernel_order': 490, 'quotient_fusion': None, 'short_label': '980.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12], 'aut_gens': [[1, 2], [10, 13], [10, 15]], 'aut_group': '24.5', 'aut_hash': 5, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [127, 857], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [10, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.5', 'autcent_hash': 5, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3], [5, 1, 4], [10, 1, 12]], 'center_label': '20.5', 'center_order': 20, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [10, 1, 4, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 20]], 'label': '20.5', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 6, 'linQ_dim': 5, 'linQ_dim_count': 6, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C10', '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [5, 4], [10, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[10, 13], [10, 15]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [127, 857], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4]], 'representations': {'PC': {'code': 2179, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 16]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706303489327]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [13320, 4001]}, 'Perm': {'d': 9, 'gens': [40320, 720, 96]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{10}', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '280.29', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 12, 70, 12, 12, 12, 60, 12], 'aut_gens': [[1, 140], [2287, 6580], [14471, 4620], [10121, 9940], [10019, 12180], [303, 16380], [69, 16380], [2717, 18340], [19227, 6580]], 'aut_group': None, 'aut_hash': 8774458014669774073, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 322560, 'aut_permdeg': 290, 'aut_perms': [19043426971732706117298682838113643746439479699367529386031406185546868891603764160650410061118073610399663299982926255812801072340330619087816850180603398987160319709971421443720576132762881870216880576430956507017592730579869664191818785317666149975668637825232958166570295706899454814388019690891886782738692356663964512276017788604007421424501558244768639046201094811379952829446882098603970045834939355846519068253678972119559505491510090869356278105710360787758123095207119239164850600934279421893347101755509105212061004336993934117799276884111425094541787680440661426341550503028299, 51239384484150775494681326673602025990217682213176615130336374070516452772297381049475088919001070729547370097035582848297728390050147028464017062560150735000784342302270657501744633657160734550857428128769375863056334017494330220718544044962695323176069506127352601022532496102344206362056125170538193260128071443461041557945696747627272335201025369382311857435587036498345779997040417060400248768968422135225156546251272824856034387523448180925700592718432897075591461913541972705869387924195922922417888855380117071008448593127115883118027752830145383511091191115690279891900936957959038, 16381838475838268976459942579249344897007875861983259973651912387108715805459014431076810880237795161845744770560198094578749144311128255600668038771724376775398900661712967429577173307458495516916099014833735203064469163330576138114553974758189384431339377668146785180116663482138242844647290460137219054525731188267795992044375370372596803248997041052632672557309528057679345700218742560413736075311033123560594681741225679799072756402595833069767183931522679541194403062582185060122446872042552486211624179868258893299273616061654430756959438200634538667619500483885374916774787330292531, 24477763789187531825657387895024484612146734176254434374479812165731704587153300112754773390552216338147787266171561626985361670445348814909139916993704393259937041973320262714248447961826397620124319639175245284346999666149563627053029859073400872055537218859014960878441779006765987746489209772802397730826231256168458700431797879039413227657547229294949993577778574123137362806638459819800274495044149875475142885633049857159783083832239583102978545405331986894961651736575168817439174262551469043212741880953529886688233876941226278929168023050859376771866995574477114027746513885226944, 35922328232313350374452886457034050097060795768476326262962389140627282160308662927980638570715071229358019379636242329760467386347241204732859289123339903958576587689238511644207280753594134879289533238447417971725938263920586735415063299943424665408459399188743482111841254399716425127474733555610559086705558013393569591934352954463744069217850924502668499540520055710125242575931423815889182315501730688725791401229132205538504722499138357833028678989417930858588112165839495279309191449691305523238876768949075082452021615307582814264693769234435330762494829517623507305816976178550356, 32499531533415786931530788609381104052499954005235351311593940700675238262327855136254365543631633261028652205706892557587353788885936058062354761427705468724058967939437424406354515860352251367652058683113902692594972103469300824893412892777403045092484751512967772286634262574574503481786819452611959076879263382879553654558628430239937775170936777117840376646552303634367705474710567089363995863163981835749260975793624424518775835441841774059948004855469418224197806657517284237714643252462533311709394499858254466826242428417676683905899206176371040627537315665112722705503339961511074, 34705317573382447285653924933763266585648539816029910687373680541455528659282630127619596721413007735241792749628145203311377062862147055755002265222916588395151808849599563680183595767370905850745700227299694162941713660064401379249450672274088574596563674444452550694707718608916632161669118309365770644396471565352212521076736291672203518232903693313645273683685414672880316593443149886276057989091780494771673023122692868138622096227059442432399592552164247137653727423168359014112009392237049684453726780052509640351955186795712895788242591697492834777956469178790337936689253651787409, 40279726473624495097946775241056773522680703936952066670163367824642211560907108886996150629345757832108709870812773780529760220201270831840491386383995210771854095954294559578422212799791927485931565395667378486812789115001419113874716636325973349097016131143352691125741907485289117539821014010299804229171703496389073634338582541241064738369025075932757671769152197132152313792085805087687662366064329728461004960572668162853022127834717824591296825130977760274700291249325298797467315629580928820136690393108358395998986934614450382230380943742179277836582320513454397018310018284095903], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 18, 1], [8, 70, 4, 1], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 2], [10, 2, 8, 1], [10, 2, 16, 1], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 6, 2], [14, 2, 18, 1], [14, 2, 36, 1], [20, 1, 8, 1], [20, 2, 4, 3], [20, 2, 16, 2], [28, 1, 12, 1], [28, 2, 6, 3], [28, 2, 36, 2], [35, 1, 24, 1], [35, 2, 12, 3], [35, 2, 48, 2], [35, 2, 72, 2], [35, 2, 288, 1], [40, 70, 16, 1], [56, 70, 24, 1], [70, 1, 24, 1], [70, 2, 12, 3], [70, 2, 24, 4], [70, 2, 48, 2], [70, 2, 72, 2], [70, 2, 96, 2], [70, 2, 144, 2], [70, 2, 288, 1], [70, 2, 576, 1], [140, 1, 48, 1], [140, 2, 24, 7], [140, 2, 96, 4], [140, 2, 144, 4], [140, 2, 576, 2], [280, 70, 96, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{70}.C_6^2.C_2^6.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 1530, 'autcent_nilpotent': True, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{12}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': None, 'autcentquo_hash': 934, 'autcentquo_nilpotent': False, 'autcentquo_order': 1680, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_7:(C_2\\times C_6\\times F_5)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 2, 1], [5, 1, 4], [5, 2, 10], [7, 1, 6], [7, 2, 21], [8, 70, 4], [10, 1, 4], [10, 2, 34], [14, 1, 6], [14, 2, 69], [20, 1, 8], [20, 2, 44], [28, 1, 12], [28, 2, 90], [35, 1, 24], [35, 2, 564], [40, 70, 16], [56, 70, 24], [70, 1, 24], [70, 2, 1716], [140, 1, 48], [140, 2, 2280], [280, 70, 96]], 'center_label': '140.4', 'center_order': 140, 'central_product': True, 'central_quotient': '140.10', 'commutator_count': None, 'commutator_label': '70.4', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '7.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['560.70', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 6, 3], [8, 70, 2, 2], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 8], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 6, 11], [20, 1, 8, 1], [20, 2, 4, 3], [20, 2, 8, 4], [28, 1, 12, 1], [28, 2, 6, 3], [28, 2, 12, 6], [35, 1, 24, 1], [35, 2, 12, 3], [35, 2, 24, 22], [40, 70, 8, 2], [56, 70, 12, 2], [70, 1, 24, 1], [70, 2, 12, 3], [70, 2, 24, 70], [140, 1, 48, 1], [140, 2, 24, 7], [140, 2, 48, 44], [280, 70, 48, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 288, 'exponent': 280, 'exponents_of_order': [4, 2, 2], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '4900.c', 'hash': 3718123535203291041, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 70], 'inner_gens': [[1, 19460], [281, 140]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 140, 'inner_split': True, 'inner_tex': 'D_{70}', 'inner_used': [1, 2], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '19600.h', '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': 'C140.C140', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 84, 'number_characteristic_subgroups': 100, 'number_conjugacy_classes': 5110, 'number_divisions': 215, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 207, 'number_subgroup_classes': 416, 'number_subgroups': 1216, 'old_label': None, 'order': 19600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3], [4, 4], [5, 24], [7, 48], [8, 280], [10, 72], [14, 144], [20, 96], [28, 192], [35, 1152], [40, 1120], [56, 1680], [70, 3456], [140, 4608], [280, 6720]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 12, 6, 12, 12, 6, 4], 'outer_gen_pows': [0, 0, 14700, 0, 0, 14700, 0], 'outer_gens': [[9831, 14140], [4909, 4620], [5031, 8540], [9917, 14140], [9893, 420], [4941, 14140], [4943, 6020]], 'outer_group': None, 'outer_hash': 3046548263569564644, 'outer_nilpotent': True, 'outer_order': 2304, 'outer_permdeg': 22, 'outer_perms': [51091299180224316867, 122002102257235444, 51212944280633148964, 1321087582323, 357013784695923, 122002108923708723, 51212588598474513840], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{12}^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 32, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2414961508229043150805851989755667569179571037408602365318023', 'gens': [1, 5], 'pres': [8, -2, -2, -5, -7, -2, -2, -5, -7, 16, 41, 138, 15707, 778404, 116, 927365, 141, 1066246, 334, 1075207]}, 'GLFp': {'d': 2, 'p': 281, 'gens': [81490, 1797231322, 2773505134]}, 'Perm': {'d': 32, 'gens': [8781100940903568444306543960823680, 17260687812918522442383547336322793, 8789964883927716565885006255641424]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 140], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{140}.C_{140}', 'transitive_degree': 280, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '28.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 12, 42, 12, 12], 'aut_gens': [[1, 28], [515, 56], [31, 84], [745, 812], [473, 476], [213, 756]], 'aut_group': None, 'aut_hash': 7158233851684636341, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10080, 'aut_permdeg': 76, 'aut_perms': [397031386815353566376800844011240434036831351464707079498917502153044455194606752372627183232046537730760621570, 34430860685813628627146478705857808177371118435438957367411817995774096076872362616719174466790506032942593413, 799927473040085959689556771106733269196824865805807761087690951033268623761946600497705034062994864351290039493, 895769037317025467323707399008269538734887387456753640510472929903640533444777094310526704492921257123405330150, 568315651210613430941798428121301790968034572595849907393585871749604604339148018663497843715536615169067102453], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 35, 2, 1], [5, 2, 2, 1], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 18, 1], [10, 2, 2, 1], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 18, 1], [28, 35, 12, 1], [35, 2, 12, 2], [35, 2, 72, 1], [70, 2, 12, 2], [70, 2, 72, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6\\times F_5\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '840.139', 'autcentquo_hash': 139, 'autcentquo_nilpotent': False, 'autcentquo_order': 840, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 35, 2], [5, 2, 2], [7, 1, 6], [7, 2, 21], [10, 2, 2], [14, 1, 6], [14, 2, 21], [28, 35, 12], [35, 2, 96], [70, 2, 96]], 'center_label': '14.2', 'center_order': 14, 'central_product': True, 'central_quotient': '70.3', 'commutator_count': 1, 'commutator_label': '35.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '7.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['140.3', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 35, 2, 1], [5, 2, 2, 1], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 6, 3], [10, 2, 2, 1], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 6, 3], [28, 35, 12, 1], [35, 2, 12, 2], [35, 2, 24, 3], [70, 2, 12, 2], [70, 2, 24, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 140, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7], 'faithful_reps': [[2, 0, 72]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '490.8', 'hash': 15, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 35], 'inner_gens': [[1, 952], [57, 28]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 70, 'inner_split': True, 'inner_tex': 'D_{35}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 4, 'irrep_stats': [[1, 28], [2, 238]], 'label': '980.15', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 15, 'linQ_dim': 16, 'linQ_dim_count': 3, 'linR_count': 108, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C35:C28', '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': 18, 'number_conjugacy_classes': 266, 'number_divisions': 26, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 36, 'number_subgroups': 136, 'old_label': None, 'order': 980, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [4, 70], [5, 4], [7, 48], [10, 4], [14, 48], [28, 420], [35, 192], [70, 192]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 6, 12], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[15, 28], [5, 28], [1, 476]], 'outer_group': '144.178', 'outer_hash': 178, 'outer_nilpotent': True, 'outer_order': 144, 'outer_permdeg': 14, 'outer_perms': [6227020800, 39917040, 408243], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6\\times C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [4, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 2], [6, 4], [12, 7], [24, 4], [48, 6]], 'representations': {'PC': {'code': 590795357229488805611, 'gens': [1, 4], 'pres': [5, -2, -2, -7, -5, -7, 10, 26, 19043, 118, 21004]}, 'GLFp': {'d': 2, 'p': 71, 'gens': [16105996, 8662, 21832578]}, 'Perm': {'d': 23, 'gens': [51212587272118640049, 378011776665600, 16, 1226304257221435392000, 4364760]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [28], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{35}:C_{28}', 'transitive_degree': 140, 'wreath_data': None, 'wreath_product': False}
