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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.85027', 'ambient_counter': 85027, 'ambient_order': 768, 'ambient_tex': '(D_6\\times C_2^4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 96, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.85027.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1346', 'subgroup_hash': 1346, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.D_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '768.85027', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.m1', '8.n1', '8.t1', '8.u1', '8.be1', '12.g1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5048, -1, 4764, -1], 'generators': [194163338880, 264, 19200345361, 3, 288848891520, 1680, 25434259200], 'label': '768.85027.4.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [12, 12, 6], 'aut_gens': [[73075, 325175, 180013, 239003, 186925], [107441, 186637, 180013, 266449, 158987], [245479, 325175, 180013, 245627, 317975], [79699, 21025, 180013, 72935, 152363]], 'aut_group': '147456.rf', 'aut_hash': 3620819369663894841, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 147456, 'aut_permdeg': 64, 'aut_perms': [53811940357575476257219734616773486689361179000904311964817376217683431184662452064853811, 90468497532012719359807188065387798951510950963403744098165321434095686274848371243284547, 120693523136939528202187207374567822230339962411094593970106904248508040160907496802557018], 'aut_phi_ratio': 2304.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 12, 1], [2, 6, 8, 1], [3, 2, 1, 1], [4, 2, 8, 1], [4, 6, 8, 1], [6, 2, 1, 3], [6, 2, 12, 1], [12, 2, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.C_2^6:S_3^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 4923965932110249069, 'autcent_nilpotent': False, 'autcent_order': 24576, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^8.C_2^4.S_3', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 6, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 15], [2, 6, 8], [3, 2, 1], [4, 2, 8], [4, 6, 8], [6, 2, 15], [12, 2, 16]], 'center_label': '16.14', 'center_order': 16, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1346, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['48.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [2, 6, 1, 8], [3, 2, 1, 1], [4, 2, 2, 4], [4, 6, 2, 4], [6, 2, 1, 15], [12, 2, 4, 4]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 2730, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '48.51', 'hash': 1346, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 1, 1, 6, 1], 'inner_gens': [[73075, 325175, 180013, 72647, 186925], [73075, 325175, 180013, 239003, 186925], [73075, 325175, 180013, 239003, 186925], [238471, 325175, 180013, 239003, 186925], [73075, 325175, 180013, 239003, 186925]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': None, 'inner_tex': 'D_6', 'inner_used': [1, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 40]], 'label': '192.1346', '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': 'C2^3.D12', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 72, 'number_divisions': 52, 'number_normal_subgroups': 247, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 674, 'number_subgroups': 1784, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 63], [3, 2], [4, 64], [6, 30], [12, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], 'outer_gen_pows': [13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825, 13825], 'outer_gens': [[73075, 325175, 180013, 239003, 186925], [238951, 325175, 180013, 239003, 186925], [73075, 158987, 180013, 239003, 186925], [73075, 159275, 180013, 239003, 186925], [73075, 325175, 180013, 72839, 186925], [73075, 325175, 180013, 73127, 186925], [73075, 325175, 180013, 239003, 20737], [73075, 325175, 180013, 239003, 21025], [266501, 325175, 180013, 239003, 186925], [73075, 325175, 180013, 79751, 186925], [73075, 152075, 180013, 79751, 186925], [266501, 325175, 180013, 239003, 152075], [73075, 325175, 180013, 72839, 186925], [73075, 325175, 180013, 239003, 186925]], 'outer_group': None, 'outer_hash': 3903023637032976567, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 128, 'outer_perms': [0, 3013798735089467537649741005829458087196647419435005276402317849704056941326128691672977797116484281425453048395659141479110874110404045378996478263111296992286315806298896005549572453215899550855992795142832675383, 1949933638391860075532353424149292520819913009206218206407070566013973800736699654728110248907682763804758999847379196949933136832739456797385292885409207603305472290610297, 72977426323458976725059252305043108648199743244442884248650110320582273536051537553013391207906424366508047457723578594694349206088573349996538681023186222997507433069139759930587862707111356248169765639942, 6191388866180659214006511495791075420318296107213964376443194500229050209549468135331794077379943765774087270395153592516857621849618465245593961291450677005732308803983580979480041916318873484848286553445263871097, 9230013298757453671584779233229881982012164794937699500975120467833039321590939622334439364300519327616688006704920144716522794966260212154932272882325576962690538106577478050991221228639504990122758983022041840262, 1095172081912431692461330286226535303915312914810729307820262028920070648218107980552049683097797141009866526198336856718897244051813032434341435887808737929276527561463277063656845925926561713615754617600, 1193922523920801637172292366879640582614891444996968197789605679055931741528972298153134561575582589267304841752655003646959941246677210555482117317780241181280019444512349723385286948896973763032461847223, 12266605739541452333078044622925881736051461314640469560791506184558067310761795270210585808007810195053226008919784816310885142229585156436276559976653583272100541322031715589567595608150618910298997690279714959360, 15303174432811898709582303402930789176940778435673408060487689829620363854703446576012817241767288205827637811566962437205558849556589021779160695502279715482654927826798277401538273845541236653054978068118027504080, 18339744464738466993362813982326223866618034327901946283092403200372686002569978771749082232104702915903873214333697438271032551159973989789625653044181796657189525253359474185803580720870343323044811417989879648767, 21376312929024305329635786067315898364979831969743620082008048060482449873166510421039289744468938272310579908502513626928383788958528913172386535426030060380199091876913559501786321049222106557347324243799656770047, 6191388866180659214006511495791075420318296107213964376443194500229050209549468135331794077379943765774087270395153592516857621849618465245593961291450677005732308803983580979480041916318873484848286553445263871097, 0], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5.C_2^6.S_3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 12]], 'representations': {'PC': {'code': 47196182682620103682, 'gens': [1, 2, 3, 4, 7], 'pres': [7, -2, -2, -2, 2, -2, -3, -2, 1235, 80, 2804, 102, 2693]}, 'GLZN': {'d': 2, 'p': 24, 'gens': [14017, 266257, 73075, 158987, 186925, 14113, 179725]}, 'Perm': {'d': 15, 'gens': [87657655680, 186810624007, 5176, 261534885263, 186810629160, 186810624000, 3991680]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.D_{12}', 'transitive_degree': 96, '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': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 12, 12, 4, 12, 4, 4, 4], 'aut_gens': [[89214089064, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [386713959264, 31661644442, 1560, 205662967440, 1680, 27390224400, 25434259200, 288848891520, 4], [562986951144, 282611710082, 288848891784, 205662965760, 1680, 268248516480, 25434259200, 288848891520, 4], [562986951144, 282611711642, 264, 205662967440, 1680, 268248516480, 25434259200, 288848891520, 3], [562986952824, 295076597765, 288848893080, 636677354880, 1680, 268248516480, 25434259200, 288848891520, 3], [437328503280, 31661642881, 1560, 649138654080, 1680, 287404590480, 25434259200, 288848891520, 4], [437818712544, 617477012882, 288848893080, 649138654080, 1680, 287404590480, 270160934400, 288848891520, 3], [388162576104, 642911271965, 25434259464, 205662967440, 288848893200, 268248516480, 270160934400, 288848891520, 4], [437818714104, 282611710081, 1560, 205662965760, 1680, 287404588800, 25434259200, 288848891520, 4], [388162576224, 199435259525, 25434259464, 636677354880, 288848893200, 268248518160, 270160934400, 288848891520, 4]], 'aut_group': None, 'aut_hash': 8414629624453799526, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 98304, 'aut_permdeg': 160, 'aut_perms': [22735495313422756785566932289311564585603988548295444015275992324990455068905715111633139962040248141103823467443166972017188582715656157681520296307448695689302660087397125939616213505894116431344112253382184908633238396633976496232777762478145896360657557884182101942442020347595394, 216926413695619706460179178162208769429102956976190035758559915334512358743348020725884823859670256305746662818703973226530439670202723344855041742528573074680701102166930533973024474286794869859961295168058563126983236935861087244367505183137699300784508680015227365855347872410675358, 249409221006867414976124348570691429689631777715024225363146986057447596104123633724196041458407987866547924272881727052578244348659222621489447501586758137721702875053442700830665462949355589470699588497878816644707081664563074510721334167042042970289095932097162140270928036255602776, 264077255786887331740496327063308329622434789262041499157754529217334677691668552171414938090492455258984025061698194375847093840718018028196851304150212659099874805233135655707318684343681052382119574278450505863190167086607211174147770024263424279478580780613495986987257841814267015, 74348443118235962086208189865163647524566946086899147933910464744719496467930884040072876283294597506985999230633304697323599657523558803228039010790768688821771629746817079209666359549254174650483306332954325741359334554270199590911495525628602892815667536020170157457966766784127735, 371415646161606021373888788920228544717360842555822872042822739163851463421044737164733146280935061128025158381315613509683678797593682667446465695081282628695141157527426520225592034948452608875803618191729116486915658096958806344471774517337924598272315599104067894277101857251640364, 5700159565474724312621457295525436914872892903677731744596452971944623435846155859439661917123908831451098021870900509690320119848072765471503949705372240394571903532274956559560635661620009877770285855819826404394204392312120884381466362695109583862767864919473912126273328421333581, 404198918248890996260403234510663267933514499504478585583721694036102616293493377651333969867933372882826494965751113249286239857504125805778834241621363957399609457303615759036824902784501555454694064850876035309161312048084354351526569255888525284552538831420814607536836535081500212, 368563939425543630867275124304626743457685085802994062057817623702714106704472747319741320242175874180028268912164631274472840450741684865302906469292752194070299553068079798553399219003432770991252955655693105205902913819092767355466880705806992366115861434807673619718591909288221497], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 2, 4, 1], [2, 4, 2, 3], [2, 8, 1, 1], [2, 12, 8, 1], [3, 2, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 16, 4, 1], [4, 24, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 4, 1, 2], [6, 4, 4, 2], [6, 8, 2, 3], [8, 48, 4, 1], [12, 8, 2, 2], [12, 16, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^7.C_2^6.C_2^2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '1536.408498090', 'autcentquo_hash': 631692073767964252, 'autcentquo_nilpotent': False, 'autcentquo_order': 1536, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times C_4^2:C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 6], [2, 8, 1], [2, 12, 8], [3, 2, 1], [4, 4, 2], [4, 8, 1], [4, 16, 4], [4, 24, 4], [6, 2, 3], [6, 4, 10], [6, 8, 6], [8, 48, 4], [12, 8, 4], [12, 16, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '192.513', 'commutator_count': 1, 'commutator_label': '48.52', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 85027, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 6], [2, 8, 1, 1], [2, 12, 1, 8], [3, 2, 1, 1], [4, 4, 1, 2], [4, 8, 1, 1], [4, 16, 2, 2], [4, 24, 1, 4], [6, 2, 1, 3], [6, 4, 1, 6], [6, 4, 2, 2], [6, 8, 1, 4], [6, 8, 2, 1], [8, 48, 2, 2], [12, 8, 1, 2], [12, 8, 2, 1], [12, 16, 4, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '32.46', 'frattini_quotient': '24.14', 'hash': 85027, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 2, 2, 2, 1, 2, 2, 1, 3], 'inner_gens': [[89214089064, 180747304081, 1560, 205662965760, 1680, 2446577280, 270160934400, 288848891520, 3], [362724728424, 19200345361, 264, 193198078080, 1680, 27390222720, 25434259200, 288848891520, 4], [89214090744, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [437328501864, 19200345361, 264, 193198078080, 1680, 287404588800, 25434259200, 288848891520, 3], [89214089064, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [89214089064, 31661644561, 264, 649138654080, 1680, 2446577280, 25434259200, 288848891520, 3], [456060327144, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [89214089064, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [89214089064, 19200345365, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3]], 'inner_hash': 513, 'inner_nilpotent': False, 'inner_order': 192, 'inner_split': False, 'inner_tex': 'C_2^3.D_{12}', 'inner_used': [1, 2, 3, 9], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 28], [4, 24], [8, 4]], 'label': '768.85027', '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': '(D6*C2^4):C4', 'ngens': 9, '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': 29, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 72, 'number_divisions': 58, 'number_normal_subgroups': 123, 'number_subgroup_autclasses': 524, 'number_subgroup_classes': 2508, 'number_subgroups': 15156, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 143], [3, 2], [4, 176], [6, 94], [8, 192], [12, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 4, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 25434260760], 'outer_gens': [[89214089064, 295076597761, 288848893080, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3], [89214089064, 295076597761, 270160935960, 193198078080, 288848893200, 2446577280, 25434259200, 288848891520, 3], [89214089064, 295076598025, 25434259464, 193198079760, 288848893200, 2446577280, 25434259200, 288848891520, 3], [88227378024, 19200345361, 264, 636677354880, 1680, 2446577280, 25434259200, 288848891520, 4], [89214089064, 295076599441, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 4], [89214089064, 19200343681, 288848891784, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 4], [88227379440, 19200343681, 288848891784, 636677354880, 1680, 2446578960, 25434259200, 288848891520, 3]], 'outer_group': '512.10482065', 'outer_hash': 2448485374602736457, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 14, 'outer_perms': [14964049, 46663465087, 32732870094, 1, 126, 13905647406, 13905647695], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 22], [8, 8]], 'representations': {'PC': {'code': '1290160561327314358889220094794645375193229314', 'gens': [1, 2, 3, 5, 7, 9], 'pres': [9, -2, -2, 2, -2, -2, -2, 2, -3, -2, 164, 74, 6682, 301, 130, 5639, 1536, 3561, 2814, 186, 1195]}, 'Perm': {'d': 15, 'gens': [89214089064, 19200345361, 264, 193198078080, 1680, 2446577280, 25434259200, 288848891520, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(D_6\\times C_2^4):C_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
