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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8957952.v', 'ambient_counter': 22, 'ambient_order': 8957952, 'ambient_tex': 'C_3^6.(C_2^9.S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2239488, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8957952.v.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2239488.cu', 'subgroup_hash': 8844530158515779307, 'subgroup_order': 2239488, 'subgroup_tex': 'C_3^6.(C_2^8.A_4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '8957952.v', 'aut_centralizer_order': None, 'aut_label': '4.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '4.B', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [430, 21283345968220455445409469508230868570030, 79911221005670326272000, 79911222869106300672000, 26584437368957250479984869523445504719, 52864572147861871005328188251583579037009, 26584437368957358332962686576240230423, 21283345986536340497831345732514535258183, 116679368657922135640085292378822002938297, 42522206388174474676759940280169562230625, 21283345968220455445409469508230780672430, 2789706124823, 329453219281976597370835277207308309593000, 25903229683158424396800, 350727881731125799846231011378169366652737, 22584401678233640190097958400, 10341839506843610994084987257487360000127], 'label': '8957952.v.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.B', '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': '6.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[9791113975746922324648197582332, 27496508770297206692611802252482, 18948328095604092152941829382250], [27604902967747182790297755210696, 144073055334421410414822103891519, 134207493285283678189285861018087], [9791113978048447624383298659450, 11020843976774660785691990486359, 125968233300801606601629721196839], [9791113978033722225100323842250, 27496508771433371863913214086002, 18948390709203237861927583950010], [28704273628201225171530636388172, 11042620447790390464411970380399, 134207461694050973676529958766007], [9812890474877389188440794006650, 27474730410947961850236125382079, 19568992414505013843611603507047], [11020842710013548083053296641532, 28726051369403587171751516146882, 125986396850217815906839945427050], [11042619827356707721805322506256, 28704272388418684482663203870119, 125365663722228054679830552225202], [27496508149860969402896174003242, 9791112735961827088672535225618, 18948358498702089066359693598092], [9791113975746922324648611709896, 27496508770297206692611759392319, 18948328095604092152941873613287], [9791113975746922324648208529860, 27496508770297206692611799328490, 18948328095604092152941833677122], [9791113975746922324648197582332, 27496508770297206692611802252482, 18948328095604092152941829382250], [28726950862175616842709384193532, 11021246000363547711683866354882, 18948389488470313117924866515050], [9791112737100527669006257614332, 27474730412071968980387442418882, 134809989640883419065505849273450], [9791112737100527669006257614332, 27496508150984970134422484108482, 18948390762019126763247660294250], [11021277643231454853397478862332, 28726982505031231489676542143682, 18937501892566249587049718790250], [9922185617141332533882776219132, 27474732299281355366263250674882, 22617954650825444151424049593450], [28094496938978532300666896795132, 143364581459372354585320916108482, 22617893259083217532773931321450], [9812892983683379133478040833532, 27474732299281355366263250674882, 125365694665980255199022242259050], [9791113975746922324648197582332, 27496508770297206692611802252482, 18948328095604092152941873593919], [9791113975746922324648611709896, 27496508770297206692611799328490, 18948328095604092152941829382250], [9791113975746922324648208529860, 27496508770297206692611762355047, 18948328095604092152941829382250], [9791113975746922324648197582332, 27496508770297206692611762355047, 18948328095604092152941869279679], [9791113975746922324648197582332, 27496508770297206692611759392319, 18948328095604092152941873613287], [35490052138119704927314379556590, 70813177942405599508480830784182, 65674036068728508953203582870686]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 143327232, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 192.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 2, 1], [2, 108, 2, 1], [2, 216, 2, 1], [2, 243, 1, 4], [2, 243, 2, 2], [2, 324, 2, 1], [2, 324, 8, 1], [2, 972, 2, 1], [2, 972, 4, 1], [2, 1944, 2, 1], [3, 8, 2, 1], [3, 12, 1, 2], [3, 16, 2, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 48, 1, 2], [3, 48, 2, 2], [3, 96, 1, 1], [3, 96, 2, 1], [3, 20736, 2, 1], [4, 216, 2, 1], [4, 432, 2, 1], [4, 1944, 2, 1], [4, 3888, 2, 1], [4, 11664, 2, 2], [4, 11664, 4, 1], [6, 8, 2, 1], [6, 12, 1, 6], [6, 12, 2, 4], [6, 16, 2, 1], [6, 24, 1, 6], [6, 24, 2, 8], [6, 24, 8, 1], [6, 32, 1, 1], [6, 48, 1, 6], [6, 48, 2, 17], [6, 48, 4, 5], [6, 48, 8, 4], [6, 96, 1, 5], [6, 96, 2, 7], [6, 96, 4, 14], [6, 96, 8, 5], [6, 96, 16, 4], [6, 432, 2, 2], [6, 432, 4, 2], [6, 648, 2, 2], [6, 648, 4, 1], [6, 648, 8, 1], [6, 648, 16, 1], [6, 864, 2, 2], [6, 864, 4, 3], [6, 972, 1, 8], [6, 972, 2, 4], [6, 1296, 2, 2], [6, 1296, 4, 2], [6, 1296, 8, 1], [6, 1296, 16, 2], [6, 1728, 2, 1], [6, 1728, 4, 2], [6, 1944, 2, 2], [6, 1944, 8, 1], [6, 3888, 2, 1], [6, 3888, 4, 2], [6, 7776, 2, 1], [6, 20736, 2, 1], [6, 62208, 4, 1], [9, 20736, 4, 1], [9, 41472, 2, 1], [9, 41472, 4, 1], [12, 432, 2, 2], [12, 432, 4, 1], [12, 864, 2, 6], [12, 864, 4, 4], [12, 1728, 2, 6], [12, 1728, 4, 6], [12, 1728, 8, 1], [12, 3888, 4, 1], [12, 7776, 2, 3], [12, 15552, 2, 1], [12, 23328, 2, 2], [12, 23328, 4, 1], [18, 20736, 4, 1], [18, 41472, 2, 1], [18, 41472, 4, 1], [18, 62208, 8, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 2], [2, 108, 2], [2, 216, 2], [2, 243, 8], [2, 324, 10], [2, 972, 6], [2, 1944, 2], [3, 8, 2], [3, 12, 2], [3, 16, 2], [3, 24, 2], [3, 32, 1], [3, 48, 6], [3, 96, 3], [3, 20736, 2], [4, 216, 2], [4, 432, 2], [4, 1944, 2], [4, 3888, 2], [4, 11664, 8], [6, 8, 2], [6, 12, 14], [6, 16, 2], [6, 24, 30], [6, 32, 1], [6, 48, 92], [6, 96, 179], [6, 432, 12], [6, 648, 32], [6, 864, 16], [6, 972, 16], [6, 1296, 52], [6, 1728, 10], [6, 1944, 12], [6, 3888, 10], [6, 7776, 2], [6, 20736, 2], [6, 62208, 4], [9, 20736, 4], [9, 41472, 6], [12, 432, 8], [12, 864, 28], [12, 1728, 44], [12, 3888, 4], [12, 7776, 6], [12, 15552, 2], [12, 23328, 8], [18, 20736, 4], [18, 41472, 6], [18, 62208, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 2, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 17, 'conjugacy_classes_known': False, 'counter': 73, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 2], [2, 108, 1, 2], [2, 216, 1, 2], [2, 243, 1, 8], [2, 324, 1, 10], [2, 972, 1, 6], [2, 1944, 1, 2], [3, 8, 2, 1], [3, 12, 1, 2], [3, 16, 2, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 48, 1, 4], [3, 48, 2, 1], [3, 96, 1, 1], [3, 96, 2, 1], [3, 20736, 2, 1], [4, 216, 1, 2], [4, 432, 1, 2], [4, 1944, 1, 2], [4, 3888, 1, 2], [4, 11664, 1, 8], [6, 8, 2, 1], [6, 12, 1, 14], [6, 16, 2, 1], [6, 24, 1, 26], [6, 24, 2, 2], [6, 32, 1, 1], [6, 48, 1, 58], [6, 48, 2, 17], [6, 96, 1, 53], [6, 96, 2, 63], [6, 432, 1, 8], [6, 432, 2, 2], [6, 648, 1, 32], [6, 864, 1, 12], [6, 864, 2, 2], [6, 972, 1, 16], [6, 1296, 1, 32], [6, 1296, 2, 10], [6, 1728, 1, 6], [6, 1728, 2, 2], [6, 1944, 1, 12], [6, 3888, 1, 10], [6, 7776, 1, 2], [6, 20736, 2, 1], [6, 62208, 2, 2], [9, 20736, 2, 2], [9, 41472, 2, 3], [12, 432, 1, 8], [12, 864, 1, 24], [12, 864, 2, 2], [12, 1728, 1, 24], [12, 1728, 2, 10], [12, 3888, 1, 4], [12, 7776, 1, 6], [12, 15552, 1, 2], [12, 23328, 1, 8], [18, 20736, 2, 2], [18, 41472, 2, 3], [18, 62208, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [10, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 16], [24, 1, 44], [48, 0, 48], [48, 1, 64], [96, 0, 40], [96, 1, 20]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '279936.kq', 'hash': 8844530158515779307, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [9, 3, 6], 'inner_gens': [[9791113975746922324648197582332, 28824050599860974104817837526330, 125365699708238306304550905424658], [11140635811030223209183732002559, 27496508770297206692611802252482, 134196567868881378856376806041199], [142733723795058569653732082778802, 143365278170369365273689601364407, 18948328095604092152941829382250]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 1119744, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 6], [3, 10], [4, 6], [6, 24], [8, 6], [12, 78], [16, 24], [24, 122], [32, 12], [48, 224], [96, 176]], 'label': '2239488.cu', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.(C2^8.A4)', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 220, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 688, 'number_divisions': 554, 'number_normal_subgroups': 43, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 2239488, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 15583], [3, 42200], [4, 106272], [6, 530600], [9, 331776], [12, 383616], [18, 829440]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '128.2163', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 128, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^4:D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 2], [3, 10], [4, 2], [6, 24], [8, 2], [12, 78], [16, 3], [24, 112], [32, 14], [48, 141], [64, 5], [96, 98], [192, 61]], 'representations': {'PC': {'code': '4847428681200764740992277024579624454357608234584168986868291058449624301608979779970101829971305500714537754954662214379807501329273965578740500018897061090657840823881160232988331157594208456807787336147529503488661454762743273070753179303299877391135734367856908787689140520311628340093359718488088877063482355886935365013751636741607678806985711032188818654815308658844919645072838936089815127581516167719395718086406257275107483299878730981090732378703282196992410430441650279962912935810218', 'gens': [1, 3, 4, 6, 8, 11, 13, 15, 17], 'pres': [17, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 34, 59573918, 39061990, 29412, 75907587, 55360928, 10842093, 190, 33782404, 37087221, 718, 75550181, 94841662, 64911, 15976316, 294, 149705814, 74758679, 40024, 3909921, 199216615, 66864696, 28504553, 14976922, 120027, 1082924, 20101, 398, 277610552, 128633857, 4814051, 450, 14104569, 318266, 10624380, 155263492, 108210195, 8563148, 8805517, 3406487, 491548, 873045, 82052, 81508, 554, 418960523, 70061788, 38776365, 538690, 22230, 5616948, 93109097, 5728366, 10883871, 938939, 54548, 658, 269857741, 44416542, 4935215, 68676, 5895, 145423454, 144419791, 46084, 762, 5646735, 2820128, 39353, 486158128, 81276081]}, 'Perm': {'d': 30, 'gens': [9791113975746922324648197582332, 27496508770297206692611802252482, 18948328095604092152941829382250]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 8, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(C_2^8.A_4)', 'transitive_degree': 36, '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': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[74183738529785082139235290714848666109417, 297827481065425439401871709517055720850905, 10351040863297636169573164779521768221439], [74183738548078382844038018890187535805145, 276570719534573941260950217312570437178649, 10351040863297636169573164779521854505809], [74183738539247494234339739044246438637225, 286912542595740243873286339438388961517734, 10351040863297636169573164779521854505809], [234003458832246439737266666826795479230792, 371975433755948271117087153714456345486718, 26584437368957278421864833754997276743], [255313958122426235709467742273834340141750, 340385516117965661412276492929680414285447, 21256761576313350190657458214244218332743], [74165845651200349336057264141148133603529, 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'aut_nilpotent': None, 'aut_order': 573308928, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 192.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 2, 1], [2, 6, 2, 1], [2, 12, 1, 3], [2, 108, 4, 1], [2, 216, 2, 1], [2, 243, 2, 2], [2, 324, 4, 1], [2, 324, 8, 1], [2, 432, 1, 1], [2, 486, 1, 2], [2, 486, 2, 1], [2, 648, 4, 1], [2, 972, 1, 3], [2, 972, 2, 1], [2, 972, 4, 1], [2, 1296, 4, 1], [2, 1944, 2, 2], [2, 3888, 1, 1], [2, 3888, 4, 1], [3, 12, 1, 2], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 2], [3, 48, 1, 2], [3, 96, 1, 3], [3, 192, 1, 1], [3, 41472, 1, 1], [4, 216, 2, 1], [4, 432, 1, 1], [4, 432, 2, 1], [4, 864, 1, 1], [4, 1296, 4, 1], [4, 1944, 2, 1], [4, 2592, 4, 1], [4, 3888, 1, 1], [4, 3888, 2, 1], [4, 3888, 4, 1], [4, 3888, 8, 1], [4, 7776, 1, 1], [4, 7776, 4, 2], [4, 11664, 4, 2], [4, 11664, 8, 1], [4, 23328, 4, 2], [4, 31104, 2, 1], [4, 93312, 2, 1], [6, 12, 1, 6], [6, 12, 4, 1], [6, 16, 1, 1], [6, 24, 1, 14], [6, 24, 2, 4], 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'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 4, 2], [2, 6, 2], [2, 12, 3], [2, 108, 4], [2, 216, 2], [2, 243, 4], [2, 324, 12], [2, 432, 1], [2, 486, 4], [2, 648, 4], [2, 972, 9], [2, 1296, 4], [2, 1944, 4], [2, 3888, 5], [3, 12, 2], [3, 16, 1], [3, 24, 2], [3, 32, 2], [3, 48, 2], [3, 96, 3], [3, 192, 1], [3, 41472, 1], [4, 216, 2], [4, 432, 3], [4, 864, 1], [4, 1296, 4], [4, 1944, 2], [4, 2592, 4], [4, 3888, 15], [4, 7776, 9], [4, 11664, 16], [4, 23328, 8], [4, 31104, 2], [4, 93312, 2], [6, 12, 10], [6, 16, 1], [6, 24, 22], [6, 32, 6], [6, 48, 45], [6, 64, 2], [6, 96, 131], [6, 192, 157], [6, 432, 4], [6, 648, 16], [6, 864, 14], [6, 972, 12], [6, 1296, 40], [6, 1728, 10], [6, 1944, 16], [6, 2592, 48], [6, 3456, 12], [6, 3888, 17], [6, 5184, 8], [6, 7776, 6], [6, 10368, 8], [6, 15552, 10], [6, 41472, 3], [6, 124416, 4], [8, 31104, 2], [8, 93312, 2], [9, 41472, 2], [9, 82944, 3], [12, 432, 4], [12, 864, 18], [12, 1728, 32], [12, 2592, 4], [12, 3456, 39], [12, 3888, 16], [12, 5184, 20], [12, 7776, 40], [12, 10368, 28], [12, 15552, 34], [12, 23328, 24], [12, 31104, 9], [12, 46656, 4], [12, 62208, 6], [12, 186624, 2], [18, 41472, 6], [18, 82944, 9], [18, 124416, 8], [24, 31104, 4], [24, 62208, 6], [24, 186624, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '1119744.el', 'complements_known': False, 'complete': False, 'complex_characters_known': False, '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', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 19, 'conjugacy_classes_known': False, 'counter': 22, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 6, 1, 2], [2, 12, 1, 3], [2, 108, 1, 4], [2, 216, 1, 2], [2, 243, 1, 4], [2, 324, 1, 12], [2, 432, 1, 1], [2, 486, 1, 4], [2, 648, 1, 4], [2, 972, 1, 9], [2, 1296, 1, 4], [2, 1944, 1, 4], [2, 3888, 1, 5], [3, 12, 1, 2], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 2], [3, 48, 1, 2], [3, 96, 1, 3], [3, 192, 1, 1], [3, 41472, 1, 1], [4, 216, 1, 2], [4, 432, 1, 3], [4, 864, 1, 1], [4, 1296, 1, 4], [4, 1944, 1, 2], [4, 2592, 1, 4], [4, 3888, 1, 15], [4, 7776, 1, 9], [4, 11664, 1, 16], [4, 23328, 1, 8], [4, 31104, 1, 2], [4, 93312, 1, 2], [6, 12, 1, 10], [6, 16, 1, 1], [6, 24, 1, 22], [6, 32, 1, 6], [6, 48, 1, 45], [6, 64, 1, 2], [6, 96, 1, 103], [6, 96, 2, 14], [6, 192, 1, 73], [6, 192, 2, 42], [6, 432, 1, 4], [6, 648, 1, 16], [6, 864, 1, 14], [6, 972, 1, 12], [6, 1296, 1, 40], [6, 1728, 1, 10], [6, 1944, 1, 16], [6, 2592, 1, 40], [6, 2592, 2, 4], [6, 3456, 1, 12], [6, 3888, 1, 17], [6, 5184, 1, 8], [6, 7776, 1, 6], [6, 10368, 1, 8], [6, 15552, 1, 10], [6, 41472, 1, 3], [6, 124416, 1, 4], [8, 31104, 1, 2], [8, 93312, 1, 2], [9, 41472, 1, 2], [9, 82944, 1, 3], [12, 432, 1, 4], [12, 864, 1, 18], [12, 1728, 1, 28], [12, 1728, 2, 2], [12, 2592, 1, 4], [12, 3456, 1, 27], [12, 3456, 2, 6], [12, 3888, 2, 8], [12, 5184, 1, 20], [12, 7776, 1, 16], [12, 7776, 2, 12], [12, 10368, 1, 20], [12, 10368, 2, 4], [12, 15552, 1, 26], [12, 15552, 2, 4], [12, 23328, 1, 16], [12, 23328, 2, 4], [12, 31104, 1, 5], [12, 31104, 2, 2], [12, 46656, 1, 4], [12, 62208, 1, 2], [12, 62208, 2, 2], [12, 186624, 1, 2], [18, 41472, 1, 6], [18, 82944, 1, 9], [18, 124416, 1, 8], [24, 31104, 2, 2], [24, 62208, 1, 2], [24, 62208, 2, 2], [24, 186624, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [12, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 32], [24, 1, 32], [48, 1, 70], [96, 0, 24], [96, 1, 96], [192, 0, 36], [192, 1, 20]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '1119744.jy', 'hash': 8980566156622874911, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [6, 24, 6], 'inner_gens': [[74183738529785082139235290714848666109417, 329479803591145054977653742256859629665342, 26584446244208028597151809824899203534], [170179444647520851001157071582960856453455, 297827481065425439401871709517055720850905, 27145967184966252316991768720225], [63824022590000589071706360333346121376713, 255296065088517635853851345020653681582022, 10351040863297636169573164779521768221439]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 4478976, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 4], [3, 24], [4, 8], [6, 52], [8, 4], [12, 132], [16, 6], [24, 160], [32, 32], [48, 206], [64, 10], [96, 268], [192, 158]], 'label': '8957952.v', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.(C2^9.S4)', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 451, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 1072, 'number_divisions': 964, 'number_normal_subgroups': 82, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 8957952, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 51903], [3, 42200], [4, 772416], [6, 1362600], [8, 248832], [9, 331776], [12, 3286656], [18, 1990656], [24, 870912]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '128.2163', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 128, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^4:D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 4], [3, 24], [4, 8], [6, 52], [8, 4], [12, 116], [16, 6], [24, 128], [32, 32], [48, 206], [64, 10], [96, 222], [192, 102], [384, 42]], 'representations': {'PC': {'code': '757333144795399378329583135816179298483741425729881670695434625247184652450982008864597757924255538505414263031924513992308502568829106598194660110110458522242413503060990380454801937865289331128661401791801831910479755879724760221986764410268370200376869177270421959683375785721129637197042709624441299786549794902860534788979403136398707411951268565053192841931878742028381299599933013879057355146792625298768417751056048391090383264886504975494544168216993255754014039929069265310516190669544059188120571997240895979182033304792673911624277656729440246603737069617995226153867215662083912223141488765876279569094305918720914520992243519746038861852450352007419963944617089829376988156890378143696393920081097101638162238870039836796838162517888233193543967311406987201538206110736191576891596403980263239247774256567863323110973156118887655947453194480375550537783972408914341357432381025879371', 'gens': [1, 2, 4, 5, 7, 8, 10, 12, 14, 17, 19], 'pres': [19, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 3, 58304616, 21962253, 96, 492462674, 14588392, 453874131, 227725054, 113862329, 29887384, 397509473, 40541577, 47278711, 270, 531090437, 156017688, 43382059, 14183524, 1039270518, 243846481, 263011268, 1992422, 16547695, 133892551, 348269114, 307901733, 18913728, 12803955, 1138886, 5302185, 444, 1139689016, 442554867, 96333238, 23877156, 21276607, 5621918, 14011, 478644969, 678067468, 249053567, 50047605, 23643704, 6632643, 5272642, 7571, 560, 485388298, 642850589, 69341232, 274294, 10156, 5159, 1748416187, 334800246, 274654093, 73609431, 870173, 8807328, 20683, 7022, 676, 823280652, 287484319, 194865266, 31015384, 498078, 6864769, 17948, 6111, 1684080061, 106290440, 101813679, 34014022, 38150873, 33324588, 1594550, 143805, 737536, 241218, 58495, 792, 2206761854, 1064529753, 136912912, 4924890, 3324387, 307966, 102785, 850, 933903, 5136418, 481185845, 4202587, 1576084, 262823, 87738, 1939876000, 964976747, 622888758, 33488732, 2790869, 2093208, 697867, 19643, 966, 1838609, 4990500, 255301687, 28366941, 591126, 1773097, 591164, 16680, 1142816274, 179656741, 2633912, 22457220, 5952319, 5614442, 1871613, 52249]}, 'Perm': {'d': 36, 'gens': [74183738529785082139235290714848666109417, 297827481065425439401871709517055720850905, 10351040863297636169573164779521768221439]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 4, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(C_2^9.S_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': '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]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
