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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20480.bj', 'ambient_counter': 36, 'ambient_order': 20480, 'ambient_tex': 'C_2^{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20480.bj.1280._.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1280.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1280.1116446', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1280, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^6:D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': None, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '20480.bj', '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': [229973444527448188128, 229243427677346148750, 52374799658685381174, 384854479513500414], 'label': '20480.bj.1280._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1280.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1280._.C', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 420, 'aut_gen_orders': [6, 3], 'aut_gens': [[1, 2, 4, 8], [12, 4, 5, 3], [10, 14, 7, 5]], 'aut_group': '20160.a', 'aut_hash': 3764836782182912467, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20160, 'aut_permdeg': 8, 'aut_perms': [5193, 5760], 'aut_phi_ratio': 2520.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 15, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_8', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 420, 'autcent_group': '20160.a', 'autcent_hash': 3764836782182912467, 'autcent_nilpotent': False, 'autcent_order': 20160, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'A_8', '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, 15]], 'center_label': '16.14', 'center_order': 16, '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', '2.1', '2.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 4]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [4], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '16.14', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8]], '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, 16]], 'label': '16.14', 'linC_count': 840, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 840, 'linQ_dim': 4, 'linQ_dim_count': 840, 'linR_count': 840, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^4', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 16, 'number_divisions': 16, 'number_normal_subgroups': 67, 'number_subgroup_autclasses': 5, 'number_subgroup_classes': 67, 'number_subgroups': 67, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 15]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 420, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[12, 4, 5, 3], [10, 14, 7, 5]], 'outer_group': '20160.a', 'outer_hash': 3764836782182912467, 'outer_nilpotent': False, 'outer_order': 20160, 'outer_permdeg': 8, 'outer_perms': [5193, 5760], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'A_8', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4], 'pres': [4, -2, 2, 2, 2]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7233746, 7115648, 35812976, 7115160]}, 'GLFp': {'d': 4, 'p': 2, 'gens': [33837, 18465, 27183, 18467]}, 'Perm': {'d': 8, 'gens': [5040, 120, 6, 1]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4', 'transitive_degree': 16, '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [8, 4, 6, 6, 12], 'aut_gens': [[166215333127394381401, 112044398840756943847, 59038978458658401031], [283263282543036340489, 337634052975460939104, 261443492510456210400], [283263283049341121670, 59199494178178056655, 826766051519316520080], [806025645097503430351, 637625558717555287248, 494569012266721710240], [906694692158232565950, 260387031797780802720, 789411305782915655425], [453823739564900798401, 337697975828036206824, 59942344743234385470]], 'aut_group': '19683.bc', 'aut_hash': 1001787406301949890, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 29491200, 'aut_permdeg': 324, 'aut_perms': [171504285211828908002528551908781905932301635259538797363970519200667469968234107919656953710263231732341131902543594078801044924788949999352231280183962895392966156401071631968584513869427983403417699716019789360735270250992824613493571614901023134297858999286513347018012006512841568116737481414143212063376114876099664339909923257679461752420293132756651233158979890243582891410687421760181193524716865829575500382094523225106393192093268658781201729313543792191657091214274195828438606929125907280533559062701162732253432637295340849832293517452825969235240606903214952213626713563157676724797914944574794220511887696012569659141986194946209168452928274935400075856264776, 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1328603155379756017970706263565982933658832386228101127780882803376904574253413466615111354204324853427770457748989754572746979944492529496611011643330305187217720579742122443429019432991485230318683777446307853115835583357274359681764636370110419303817395577319292436956199847231576706094536564798812200004058072545078645057819872467002473093122808952211004813080163208877206168402344837793607893529361463562084184580276065405660025852095050630349613245616708415371758778836565804182664982412462785792837173915745498389069283380310142605800757192829440332833753290675388656989985208699436096914523069519281350402497892846515166026245702113215602289704891740830586626213167], 'aut_phi_ratio': 3600.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 5, 15, 2], [2, 5, 30, 1], [2, 10, 18, 2], [2, 10, 30, 1], [2, 10, 36, 1], [2, 10, 72, 1], [2, 160, 2, 1], [4, 160, 2, 1], [4, 160, 30, 2], [5, 512, 2, 1], [10, 512, 2, 1], [10, 512, 4, 1], [10, 512, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_9^3.(C_3\\times C_9)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '921600.m', 'autcentquo_hash': 8437111023814810970, 'autcentquo_nilpotent': False, 'autcentquo_order': 921600, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^8.\\GL(2,4):F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 5, 60], [2, 10, 174], [2, 160, 2], [4, 160, 62], [5, 512, 2], [10, 512, 14]], 'center_label': '4.2', 'center_order': 4, 'central_product': None, 'central_quotient': '5120.g', 'commutator_count': 2, 'commutator_label': '2560.o', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 36, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 5, 1, 60], [2, 10, 1, 174], [2, 160, 1, 2], [4, 160, 1, 62], [5, 512, 2, 1], [10, 512, 2, 3], [10, 512, 4, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 20, 'exponents_of_order': [12, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '10240.i', 'hash': 1554416458128650330, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [10, 4, 2], 'inner_gens': [[166215333127394381401, 911419269499099610305, 637452703607549893945], [501567218377222042831, 112044398840756943847, 788950510945439655145], [943022811551958885631, 426152039608243396255, 59038978458658401031]], 'inner_hash': 3413195323342073849, 'inner_nilpotent': False, 'inner_order': 5120, 'inner_split': False, 'inner_tex': 'C_2^8.D_{10}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 18], [5, 120], [10, 174]], 'label': '20480.bj', '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': 'C2^10.D10', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 3, 3, 0, 1, 0, 5, 0, 15, 0, 15, 0, 5, 0, 1, 0, 3, 0, 3, 1, 1, 3, 0, 7, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 320, 'number_divisions': 310, 'number_normal_subgroups': 75, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 20480, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 2367], [4, 9920], [5, 1024], [10, 7168]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [10, 6, 4, 4, 30], 'outer_gen_pows': [0, 0, 0, 0, 52092350732538751974], 'outer_gens': [[166183303715903563320, 537736795142022181687, 564119688233136357000], [315981209396041002984, 260706927105297570966, 562948225422766848055], [732881887105647023665, 261443492999034173329, 191614406105387368369], [517640024919441363390, 538178358926630118288, 427112545170919590295], [314501777672741378185, 537877644814581464328, 59212307755026196110]], 'outer_group': '19683.v', 'outer_hash': 1871348800534618884, 'outer_nilpotent': False, 'outer_order': 5760, 'outer_permdeg': 18, 'outer_perms': [1464595307169120, 1068369973665169, 20925203040007, 44551544053735, 1464596371012368], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_9\\wr C_3:C_9', 'pc_rank': None, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 4], [5, 120], [8, 2], [10, 174]], 'representations': {'PC': {'code': '1545282833998233191482512152266938958141608851213519710435169381048239368421641537215087919049106113934488355646793736885508830607145778412732331243759416342943088049805676044615680', 'gens': [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 'pres': [13, -2, -2, -5, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 203840, 2549, 66, 226826, 574083, 287056, 223629, 210604, 415367, 7505, 719165, 359598, 162271, 1235786, 1839, 290777, 784167, 1056660, 384313, 769868, 356871, 359224, 772209, 386122, 267835, 1398550, 699293, 248856, 1216811, 1009344, 421237, 3403672, 1052895, 850953]}, 'Perm': {'d': 22, 'gens': [166215333127394381401, 112044398840756943847, 59038978458658401031]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 16, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_2^{10}.D_{10}', '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [8, 4, 20, 4, 6], 'aut_gens': [[999094447, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [13413219247, 28037364600, 12419280, 12944332800, 12945463200, 1967535360, 14382387376, 14382387374, 16], [999821663, 28026851160, 14382386640, 1959916440, 11291160, 1968262560, 14382387360, 14382387374, 16], [32152263127, 7785752520, 1959916440, 14375134800, 11291160, 12419280, 14382387376, 14382387374, 16], [50433521767, 45328238640, 12419280, 1961009280, 1968262560, 12934540800, 14382387376, 14382387365, 16], [50437151287, 38422108920, 14381661720, 1498320, 12419280, 12945463200, 14382387360, 14, 16]], 'aut_group': None, 'aut_hash': 7528179241671287496, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 30720, 'aut_permdeg': 84, 'aut_perms': [1224214264156756305972459081385868437016672812413093261051798836245605953527311130834386879978729228414342819090170727218848962, 1665158098409651600076695658128423147137656145211922549327732150829630418356405559120628711136527852522774336446031959471675645, 945483814738970861930924384436175117585197562517691177189895402485685563786570481737703925135273769821341690930267327774246182, 1657803086861279899127916395774633352039724712897823092169918528549773853224565741433188739330867895554153677668931198097968356, 2884011085774047757629368874215186148648504920249310572413221762299850625947569756802100770783574167742891351081751004683261162], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 5, 3, 2], [2, 5, 6, 1], [2, 10, 6, 1], [2, 40, 2, 1], [4, 40, 2, 1], [4, 40, 6, 2], [5, 32, 2, 1], [10, 32, 2, 1], [10, 32, 4, 1], [10, 32, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{16}.C_2^4.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '960.11359', 'autcentquo_hash': 11359, 'autcentquo_nilpotent': False, 'autcentquo_order': 960, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{16}:C_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 5, 12], [2, 10, 6], [2, 40, 2], [4, 40, 14], [5, 32, 2], [10, 32, 14]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '320.1636', 'commutator_count': 1, 'commutator_label': '160.235', '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', '5.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1116446, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['640.21467', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 5, 1, 12], [2, 10, 1, 6], [2, 40, 1, 2], [4, 40, 1, 14], [5, 32, 2, 1], [10, 32, 2, 3], [10, 32, 4, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 21420, 'exponent': 20, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '640.21537', 'hash': 1116446, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 5, 2, 2, 2, 2, 1, 2, 1], 'inner_gens': [[999094447, 18855259920, 12934540800, 14375134800, 12944332800, 1967535360, 14382387360, 14382387374, 16], [25644826087, 7784985720, 1967535360, 14381661720, 1961009280, 12934540800, 14382387360, 14382387365, 16], [999821647, 33096632520, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [2446940287, 34529564280, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [2446940287, 9744860280, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [999094447, 34533193800, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [999094447, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [999094463, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16], [999094447, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16]], 'inner_hash': 1636, 'inner_nilpotent': False, 'inner_order': 320, 'inner_split': False, 'inner_tex': 'C_2\\wr D_5', 'inner_used': [1, 2, 3, 8], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 18], [5, 24], [10, 6]], 'label': '1280.1116446', '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': True, 'name': 'C2^6:D10', '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': 16, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 56, 'number_divisions': 46, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 438, 'number_subgroup_classes': 4827, 'number_subgroups': 46862, 'old_label': None, 'order': 1280, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 207], [4, 560], [5, 64], [10, 448]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 6, 4, 2], 'outer_gen_pows': [999094447, 14382387365, 0, 0], 'outer_gens': [[999094447, 45316590480, 14381661720, 12419280, 1961009280, 1968262560, 14382387376, 5, 16], [14861792287, 7784985720, 14375134800, 11291160, 12419280, 1968262560, 14382387376, 14382387365, 16], [999094447, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387376, 14, 16], [14861792287, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16]], 'outer_group': '96.210', 'outer_hash': 210, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 13, 'outer_perms': [3437250487, 3125253630, 1086190560, 1611308161], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:D_6', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 4], [5, 24], [8, 2], [10, 6]], 'representations': {'PC': {'code': '3926868250457796261799072650750498679059581417775997642558862758595806102272', 'gens': [1, 2, 4, 6, 7, 8, 9], 'pres': [9, -2, -2, -2, -2, -5, -2, 2, 2, 2, 109, 46, 2595, 1308, 102, 2884, 1453, 21605, 10814, 6512, 1391, 50406, 25215, 663, 3822, 4354, 2563, 2465, 5309]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1085736031, 3876913498, 1089034753, 1087243448, 1087431672, 969133475, 1087374465, 1077385976, 1076435457]}, 'Perm': {'d': 14, 'gens': [999094447, 7784985720, 12933044760, 12945463200, 14374039680, 1967535360, 14382387360, 14382387365, 16]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^6:D_{10}', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}
