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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '79200.f', 'ambient_counter': 6, 'ambient_order': 79200, 'ambient_tex': 'C_5\\times \\SL(2,11):D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1320, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '79200.f.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, '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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2640.l', 'subgroup_hash': 6650082401052208970, 'subgroup_order': 2640, 'subgroup_tex': '\\SL(2,11):C_2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '79200.f', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3960.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.a1.a1', '330.t1.b1', '330.t1.b2', '360.e1.a1', '1650.p1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8672, -1, 2305, -1, 2940, -1, 2831, -1], 'generators': [22487585023125458, 3867401643996858, 2302403905865206, 41772741070013040], 'label': '79200.f.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1320.134'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 660, 'aut_gen_orders': [3, 10, 2], 'aut_gens': [[12415902285472309, 20659006479455967, 6422340100995270, 41772741070013040], [25363221240922668, 10697216649811470, 6422340100995270, 41772741070013040], [26788536624352311, 35358918625935699, 44087814079863762, 41772741070013040], [24923480054318037, 34383787735293824, 6422340100995270, 41772741070013040]], 'aut_group': '2640.a', 'aut_hash': 9195845394065659656, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2640, 'aut_permdeg': 112, 'aut_perms': [14161315091339446276594134958579903721294537397907723089830906279421423353157399683715538546601346149725145810962738745354098199427367403449422941989304523097594542846132063351649, 1773530199196374893570621812614280842506832183296205686204803957888926965497171799411905949104054186595727842934708337325088068635958296341931686938253091678043710081138284320809168, 9434249306230380602667017605569117752459909740181211292563834948019191568565853133158924691992908946935382625137574616817568187784121525169465545824145085672382949754432744756950], 'aut_phi_ratio': 4.125, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 1, 1], [3, 110, 1, 1], [4, 1, 2, 1], [4, 110, 1, 1], [5, 132, 1, 2], [6, 110, 1, 1], [6, 110, 2, 1], [10, 132, 1, 2], [11, 60, 2, 1], [12, 110, 1, 2], [12, 110, 2, 1], [20, 132, 2, 2], [22, 60, 2, 1], [44, 60, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\PGL(2,11)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '1320.133', 'autcentquo_hash': 133, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 110, 1], [3, 110, 1], [4, 1, 2], [4, 110, 1], [5, 132, 2], [6, 110, 3], [10, 132, 2], [11, 60, 2], [12, 110, 4], [20, 132, 4], [22, 60, 2], [44, 60, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '660.13', 'commutator_count': 1, 'commutator_label': '1320.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '660.13'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 1, 1], [3, 110, 1, 1], [4, 1, 2, 1], [4, 110, 1, 1], [5, 132, 2, 1], [6, 110, 1, 1], [6, 110, 2, 1], [10, 132, 2, 1], [11, 60, 2, 1], [12, 110, 2, 2], [20, 132, 4, 1], [22, 60, 2, 1], [44, 60, 4, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 1524, 'exponent': 660, 'exponents_of_order': [4, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[6, 0, 4], [10, 0, 6], [12, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1320.134', 'hash': 6650082401052208970, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [3, 2, 1, 1], 'inner_gens': [[12415902285472309, 2302403905865206, 6422340100995270, 41772741070013040], [9397373410040085, 20659006479455967, 6422340100995270, 41772741070013040], [12415902285472309, 20659006479455967, 6422340100995270, 41772741070013040], [12415902285472309, 20659006479455967, 6422340100995270, 41772741070013040]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 660, 'inner_split': True, 'inner_tex': '\\PSL(2,11)', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 12, 'irrep_stats': [[1, 2], [5, 4], [6, 4], [10, 10], [11, 2], [12, 8]], 'label': '2640.l', 'linC_count': 4, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,11):C2', 'ngens': 4, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 30, 'number_divisions': 16, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 44, 'number_subgroup_classes': 52, 'number_subgroups': 2574, 'old_label': None, 'order': 2640, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 111], [3, 110], [4, 112], [5, 264], [6, 330], [10, 264], [11, 120], [12, 440], [20, 528], [22, 120], [44, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [6052347071692345, 4177274107001304], 'outer_gens': [[34606509070527979, 18571808815089020, 6422340100995270, 41772741070013040], [38125662136079015, 20659006479455967, 44087814079863762, 41772741070013040]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 48, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [10, 6], [11, 2], [20, 1], [24, 3], [40, 1], [48, 1]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [12415902285472309, 20659006479455967, 6422340100995270, 41772741070013040]}, 'Perm': {'d': 48, 'gens': [275498137939564867243117935231960667818428360675401975655761, 539996405648161088148639090121438123669905530990861566993821, 804228661802683289240822518897947753394336217817017271292418, 1068489615632911821954143950392518853656430819665656837307160]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,11):C_2', 'transitive_degree': 48, '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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 44, 12, 4, 30, 4], 'aut_gens': [[12531822321003912, 2934716565033418, 44126476888948032, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [16709096428005216, 27966380576706138, 39810077106306952, 25047920183746949, 14164265598316791, 24456129884550084, 29240918749009128], [37595466963011736, 11775046123494139, 22696522587771439, 20369903018230733, 20278855777548780, 31897979080935279, 8354548214002608], [37595466963011736, 22233924720624028, 45860275281136793, 8579635851927536, 21911298838890817, 18646723749506926, 8354548214002608], [20886370535006520, 15572233229542685, 10566613700840654, 15642504638026605, 19366156759931367, 13251566580699389, 25063644642007824], [12531822321003912, 34248322234204240, 1819062460863418, 34558586257723293, 40860042266609549, 38925579311070212, 33418192856010432], [20886370535006520, 32693114333341282, 24185707265661236, 14327398256267393, 6114901428503014, 37293136249742816, 25063644642007824]], 'aut_group': None, 'aut_hash': 3236943272440868389, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 253440, 'aut_permdeg': 126, 'aut_perms': [22674973287027425427258076226424247928420832554328452366315822356389202547572026234952422730855972135021901804698066058373424221752485113183710409402494685555586945368637420276484599197533584886212020814168355013, 21032798004514492670756152578322546847041669350681130680304310697453440225154258341901902922853928181704465732135064663268947476117974537919773922506207482325747403154099474102153581702854393402854521236495345831, 14275404826394017375124779324521800840551162837910131362039167672567053502136840277670244327991779760047027059418629015958376726877711878410523954738427666016592557036775695793113761775774070307158524231752900677, 13283781489173500224286873911117111068201432742501895366242756864459010054578138672492642134754942620463518557969399710825514037351673857343865359182043947879483481399037000624389054290221490121351105576634618674, 22211509450564483848377309888138574039856834599199834406577455668918275668742603985125919489868897601192942671196561334226262618178313465702166007017779737161885818030404196071951748770863599877273723567224446371, 20245099593200212131751603166156233904819408174289507504708918128508599778881793656215546305243147868440870069338510235461735814550465671228342830998278549192675981614827088321799074063777856103404890090190105180], 'aut_phi_ratio': 13.2, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 1, 1], [2, 330, 2, 1], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [4, 2, 1, 1], [4, 6, 2, 1], [4, 110, 1, 1], [5, 1, 4, 1], [5, 132, 1, 2], [5, 132, 4, 2], [6, 2, 1, 1], [6, 110, 1, 1], [6, 220, 1, 3], [6, 220, 2, 1], [6, 660, 2, 1], [10, 1, 4, 1], [10, 110, 4, 1], [10, 132, 1, 2], [10, 132, 4, 2], [10, 330, 8, 1], [11, 60, 2, 1], [12, 2, 2, 1], [12, 110, 1, 2], [12, 220, 1, 4], [12, 220, 2, 1], [12, 660, 2, 1], [15, 2, 4, 1], [15, 110, 4, 1], [15, 220, 4, 1], [15, 264, 1, 2], [15, 264, 4, 2], [20, 2, 4, 1], [20, 6, 8, 1], [20, 110, 4, 1], [20, 264, 1, 2], [20, 264, 4, 2], [20, 792, 2, 2], [20, 792, 8, 2], [22, 60, 2, 1], [30, 2, 4, 1], [30, 110, 4, 1], [30, 220, 4, 3], [30, 220, 8, 1], [30, 264, 1, 2], [30, 264, 4, 2], [30, 660, 8, 1], [33, 120, 2, 1], [44, 120, 2, 1], [44, 360, 4, 1], [55, 60, 8, 1], [60, 2, 8, 1], [60, 110, 4, 2], [60, 220, 4, 4], [60, 220, 8, 1], [60, 264, 2, 2], [60, 264, 8, 2], [60, 660, 8, 1], [66, 120, 2, 1], [110, 60, 8, 1], [132, 120, 4, 1], [165, 120, 8, 1], [220, 120, 8, 1], [220, 360, 16, 1], [330, 120, 8, 1], [660, 120, 16, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_4\\times S_3\\times D_4).\\PSL(2,11).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': None, 'autcentquo_hash': 2842205202387851101, 'autcentquo_nilpotent': False, 'autcentquo_order': 15840, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times \\PSL(2,11).C_2\\times S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 110, 1], [2, 330, 2], [3, 2, 1], [3, 110, 1], [3, 220, 1], [4, 2, 1], [4, 6, 2], [4, 110, 1], [5, 1, 4], [5, 132, 10], [6, 2, 1], [6, 110, 1], [6, 220, 5], [6, 660, 2], [10, 1, 4], [10, 110, 4], [10, 132, 10], [10, 330, 8], [11, 60, 2], [12, 2, 2], [12, 110, 2], [12, 220, 6], [12, 660, 2], [15, 2, 4], [15, 110, 4], [15, 220, 4], [15, 264, 10], [20, 2, 4], [20, 6, 8], [20, 110, 4], [20, 264, 10], [20, 792, 20], [22, 60, 2], [30, 2, 4], [30, 110, 4], [30, 220, 20], [30, 264, 10], [30, 660, 8], [33, 120, 2], [44, 120, 2], [44, 360, 4], [55, 60, 8], [60, 2, 8], [60, 110, 8], [60, 220, 24], [60, 264, 20], [60, 660, 8], [66, 120, 2], [110, 60, 8], [132, 120, 4], [165, 120, 8], [220, 120, 8], [220, 360, 16], [330, 120, 8], [660, 120, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '3960.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '660.13'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['15840.j', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 1, 1], [2, 330, 1, 2], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 110, 1, 1], [5, 1, 4, 1], [5, 132, 2, 1], [5, 132, 4, 2], [6, 2, 1, 1], [6, 110, 1, 1], [6, 220, 1, 5], [6, 660, 1, 2], [10, 1, 4, 1], [10, 110, 4, 1], [10, 132, 2, 1], [10, 132, 4, 2], [10, 330, 4, 2], [11, 60, 2, 1], [12, 2, 2, 1], [12, 110, 2, 1], [12, 220, 1, 2], [12, 220, 2, 2], [12, 660, 1, 2], [15, 2, 4, 1], [15, 110, 4, 1], [15, 220, 4, 1], [15, 264, 2, 1], [15, 264, 4, 2], [20, 2, 4, 1], [20, 6, 4, 2], [20, 110, 4, 1], [20, 264, 2, 1], [20, 264, 4, 2], [20, 792, 2, 2], [20, 792, 4, 4], [22, 60, 2, 1], [30, 2, 4, 1], [30, 110, 4, 1], [30, 220, 4, 5], [30, 264, 2, 1], [30, 264, 4, 2], [30, 660, 4, 2], [33, 120, 2, 1], [44, 120, 2, 1], [44, 360, 2, 2], [55, 60, 8, 1], [60, 2, 8, 1], [60, 110, 8, 1], [60, 220, 4, 2], [60, 220, 8, 2], [60, 264, 4, 1], [60, 264, 8, 2], [60, 660, 4, 2], [66, 120, 2, 1], [110, 60, 8, 1], [132, 120, 4, 1], [165, 120, 8, 1], [220, 120, 8, 1], [220, 360, 8, 2], [330, 120, 8, 1], [660, 120, 16, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 4572, 'exponent': 660, 'exponents_of_order': [5, 2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[12, 0, 16], [20, 0, 24], [24, 0, 16]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 7062763148763119674, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [1, 2, 6, 6, 3, 2, 1], 'inner_gens': [[12531822321003912, 2934716565033418, 44126476888948032, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 13312816156708455, 13838847548013561, 22216482884836568, 38925579311070212, 33418192856010432], [12531822321003912, 31763567682754684, 44126476888948032, 14163552244859218, 22216482884836568, 38925579311070212, 33418192856010432], [12531822321003912, 18746586498104348, 36060219064933484, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 20368867936232204, 13312816156708455, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 1625422438811270, 6415087532603292, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 44126476888948032, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432]], 'inner_hash': 3267698946426799616, 'inner_nilpotent': False, 'inner_order': 7920, 'inner_split': True, 'inner_tex': 'D_6.\\PSL(2,11)', 'inner_used': [2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 24, 'irrep_stats': [[1, 20], [2, 10], [5, 40], [10, 60], [11, 20], [12, 70], [20, 65], [22, 10], [24, 50]], 'label': '79200.f', 'linC_count': 16, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 26, 'linQ_degree_count': 8, 'linQ_dim': 26, 'linQ_dim_count': 8, 'linR_count': 48, 'linR_degree': 22, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C5*SL(2,11):D6', 'ngens': 7, '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, 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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 94, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 345, 'number_divisions': 98, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 464, 'number_subgroup_classes': 810, 'number_subgroups': 111004, 'old_label': None, 'order': 79200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 771], [3, 332], [4, 124], [5, 1324], [6, 2532], [10, 4404], [11, 120], [12, 2864], [15, 3968], [20, 18976], [22, 120], [30, 12768], [33, 240], [44, 1680], [55, 480], [60, 16736], [66, 240], [110, 480], [132, 480], [165, 960], [220, 6720], [330, 960], [660, 1920]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [11619123519371993, 30891897937505507, 4177274107001304, 4177274107001304], 'outer_gens': [[12531822321003912, 23166607441639777, 45348108273958908, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 32679949163636774, 14219453376501107, 40860042266609549, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 13312816156708455, 36705855301915694, 22216482884836568, 11619123519371993, 33418192856010432], [20886370535006520, 1002586243376696, 36302406782233822, 22069658221081063, 19366156759931367, 37293136249742816, 25063644642007824]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [5040, 120, 362880, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 104, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [8, 2], [10, 12], [11, 4], [20, 7], [22, 2], [24, 5], [40, 16], [44, 4], [48, 12], [80, 7], [88, 2], [96, 8], [160, 4], [192, 3]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 2934716565033418, 44126476888948032, 20258619725292814, 40860042266609549, 11619123519371993, 33418192856010432]}, 'Perm': {'d': 104, 'gens': [100029102145266306127055557537587000557484473963709770834133122311657379678057035403436002530276680730554269141313114845742816193789783286835187756674069007918488282, 202865907569578627295187346548863910074924314129653007453289875493643596166165043112139268986175375394349233176446898663433178538368592397434485387500989196419261491, 51, 202865907569578627295187346548863910074924314129653007453289875493643596166165043112139268986175375394349233176446898663433178538368592397434485387500989196419255731, 302931305214157051094111224617479822995469679784824827990666312849222947917427362118408400193436130836454631090503605918907073032175726022124695889029710776799052889, 402932015611229697228066501675203596843812038552241851391121367745147871938924168027441898025487038862554048699259946550962289403343741249272831383503534407501514169, 502932000863791122529154534877075147288143064078784243088091852285072711987805298480229395848313152049561056037862155866071910929197718310481927843823973487022912836]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times \\SL(2,11):D_6', 'transitive_degree': 1440, 'wreath_data': None, 'wreath_product': False}
