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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '27648.ed', 'ambient_counter': 108, 'ambient_order': 27648, 'ambient_tex': '(C_2^2\\times D_6).S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '27648.ed.24.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.it1', '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': 24, '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': '1152.99269', 'subgroup_hash': 279433580542087119, 'subgroup_order': 1152, 'subgroup_tex': 'C_2^3.D_6^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '27648.ed', 'aut_centralizer_order': None, 'aut_label': '24.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13824.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '288.C', 'coset_action_label': None, 'count': 12, 'diagramx': [236, -1, 3537, -1], 'generators': [87185911680, 9258, 87178291603, 47537280, 25181, 1680, 269, 174356582400, 32794], 'label': '27648.ed.24.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '24.it1', 'projective_image': '13824.fy', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IX', 'subgroup_fusion': None, 'weyl_group': '1152.134261'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 12, 12, 4, 6], 'aut_gens': [[6398703487, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 304, 59], [6438625650, 7625520, 13902013440, 6314117606, 83467440, 20757824640, 6314117040, 576, 103], [32695856370, 6310483200, 25916970240, 6314117309, 6234641280, 20797746480, 6314117040, 576, 103], [32655934739, 46678428720, 40451402880, 339, 32776415280, 32736493440, 6314117040, 576, 506], [20677265999, 7625520, 13902013440, 6314117309, 6234641280, 20757824640, 6314117040, 356, 103], [20677265695, 25920604080, 13905647280, 6314117159, 20757824640, 20797746480, 6314117040, 557, 506], [6438625650, 40451402880, 40364311680, 6314117309, 32736493440, 20757824640, 6314117040, 304, 59]], 'aut_group': None, 'aut_hash': 8539866400945060701, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 55296, 'aut_permdeg': 60, 'aut_perms': [834694599667499958706684615156853470347897385180109816252731228640252783967398597, 72942805682298146122678064070933438481197642662569309878510675233778716532267038, 3022912320571070585900603562321117968017396153676757341975815917050821793758035155, 854216858700868189439284711344021681896750671323615776843324490212343422250696648, 3420733490364256100519508208620331231007744744916296423073113808314551798994871255, 7621556305836889212703771511567901850672062642062343317646972675358014567467645111], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 4, 3, 1], [2, 9, 2, 1], [2, 12, 4, 1], [2, 18, 3, 1], [2, 36, 3, 1], [3, 2, 2, 1], [3, 4, 1, 1], [4, 4, 3, 1], [4, 24, 6, 1], [4, 36, 3, 1], [6, 2, 2, 1], [6, 4, 1, 1], [6, 4, 6, 1], [6, 8, 3, 1], [6, 8, 6, 2], [6, 24, 4, 1], [12, 8, 6, 2], [12, 48, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.(C_2^4\\times A_4).C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '3456.hx', 'autcentquo_hash': 6465188289485321743, 'autcentquo_nilpotent': False, 'autcentquo_order': 3456, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times D_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 3], [2, 9, 2], [2, 12, 4], [2, 18, 3], [2, 36, 3], [3, 2, 2], [3, 4, 1], [4, 4, 3], [4, 24, 6], [4, 36, 3], [6, 2, 2], [6, 4, 7], [6, 8, 15], [6, 24, 4], [12, 8, 12], [12, 48, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '576.7409', 'commutator_count': 1, 'commutator_label': '72.50', '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', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 99269, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 3], [2, 9, 1, 2], [2, 12, 1, 4], [2, 18, 1, 3], [2, 36, 1, 3], [3, 2, 1, 2], [3, 4, 1, 1], [4, 4, 1, 3], [4, 24, 1, 6], [4, 36, 1, 3], [6, 2, 1, 2], [6, 4, 1, 7], [6, 8, 1, 15], [6, 24, 1, 4], [12, 8, 1, 12], [12, 48, 1, 6]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9085440, 'exponent': 12, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 1]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '144.192', 'hash': 99269, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 2, 2, 2, 1, 3, 3], 'inner_gens': [[6398703487, 87091200, 46591337520, 16, 83467440, 20797746480, 6314117040, 304, 278], [6438625327, 7625520, 13905647280, 16, 83467440, 32736493440, 6314117040, 304, 59], [32695856047, 7625520, 13905647280, 16, 6234641280, 20797746480, 6314117040, 304, 59], [6398703487, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 576, 103], [6398703487, 7625520, 25916970240, 16, 83467440, 20797746480, 6314117040, 304, 59], [6398703487, 6310483200, 13905647280, 16, 83467440, 20797746480, 6314117040, 304, 59], [6398703487, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 304, 59], [6398703487, 7625520, 13905647280, 592, 83467440, 20797746480, 6314117040, 304, 59], [6398703810, 7625520, 13905647280, 119, 83467440, 20797746480, 6314117040, 304, 59]], 'inner_hash': 7409, 'inner_nilpotent': False, 'inner_order': 576, 'inner_split': True, 'inner_tex': 'C_2^4:S_3^2', 'inner_used': [1, 2, 3, 4, 8, 9], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 28], [4, 32], [8, 4], [16, 1]], 'label': '1152.99269', '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.D6^2', '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 81, 'number_divisions': 81, 'number_normal_subgroups': 178, 'number_subgroup_autclasses': 493, 'number_subgroup_classes': 2485, 'number_subgroups': 19734, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 247], [3, 8], [4, 264], [6, 248], [12, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 2, 3], 'outer_gen_pows': [0, 0, 16, 0, 0, 16], 'outer_gens': [[6398703487, 13902013440, 13905647280, 16, 32776415280, 20797746480, 6314117040, 304, 59], [6398703487, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 576, 506], [6398703503, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 557, 506], [6398703487, 7625520, 13905647280, 6314117056, 83467440, 20797746480, 6314117040, 576, 103], [204387247, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 576, 103], [6398703487, 13902013440, 7625520, 16, 32776415280, 83467440, 6314117040, 576, 103]], 'outer_group': '96.209', 'outer_hash': 209, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 9, 'outer_perms': [5040, 120, 5, 127, 16, 45360], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 28], [4, 32], [8, 4], [16, 1]], 'representations': {'PC': {'code': '347552882444306049056900441586673588912168693187828475405714696201', 'gens': [1, 2, 3, 5, 7], 'pres': [9, 2, 2, 2, 2, 2, 3, 2, 2, 3, 173, 74, 3604, 13333, 7402, 130, 3461, 887, 30246, 2796, 5325, 186, 69127, 4633, 214, 62216, 8450]}, 'Perm': {'d': 14, 'gens': [6398703487, 7625520, 13905647280, 16, 83467440, 20797746480, 6314117040, 304, 59]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], '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_6^2', '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 6, 6, 6, 12, 6, 2, 6], 'aut_gens': [[47537280, 87178291200, 180631154019, 127370880, 174436804061, 174436813184, 93529087126, 174356582400, 7620480, 93412951822, 40279680, 7286095, 87261786394], [83825280, 180583635994, 87262153494, 87091200, 93525095072, 93525080212, 174440080955, 93405312000, 123742080, 174480326160, 40279680, 47562461, 180587232000], [123379200, 87178291200, 180707010633, 87091200, 174400514496, 174400502082, 93488779520, 174356582400, 395674, 93405680639, 127370880, 7259280, 87218208000], [120113280, 6227020800, 87298419577, 87091200, 174400519375, 174400510769, 93412965526, 174356582400, 123742080, 93529059839, 40279680, 123410576, 6230682394], [120113280, 180583635994, 87298432713, 127370880, 93452519072, 93452507711, 174480325224, 93405312000, 39949594, 174396500880, 87091200, 79846675, 180583998874], [43545600, 180583603200, 87221875110, 127370880, 93485539856, 93485522284, 174360237271, 93405312000, 39916800, 174396500880, 87091200, 47556622, 180583998874], [3991680, 87178291200, 180587621817, 127370880, 174403793699, 174403791104, 93408975952, 174356582400, 7620480, 93412946973, 40279680, 120118770, 87261786394], [43545600, 87178291200, 6270581974, 87091200, 93525075475, 93525099049, 174440078338, 93405312000, 3661594, 174360238015, 40279680, 4024352, 87302033280], [7257600, 87178291200, 6234315414, 40279680, 93532320269, 93532342722, 174356946024, 93405312000, 7620480, 174364233994, 127370880, 47562461, 87261786394]], 'aut_group': None, 'aut_hash': 4266983194254145422, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 663552, 'aut_permdeg': 42, 'aut_perms': [553734556803020682903997429345550855824525581565330, 11467630172795441064983174865057949147397897508606, 85120542988069329050007146239769418388970921160641, 78650706381075332394963392054834255754844427314119, 1001336658675171067156507409460829072153881096215379, 804336417380391979026383775125876676553135064973176, 928724691154120098742162970098115207069993737887583, 561899461680538415708088501200063258544303563132198], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 2, 1], [2, 6, 3, 1], [2, 9, 2, 1], [2, 12, 2, 1], [2, 18, 2, 1], [2, 18, 3, 2], [2, 36, 2, 2], [2, 36, 3, 1], [2, 54, 3, 1], [2, 72, 2, 1], [2, 108, 2, 1], [2, 108, 3, 1], [2, 216, 2, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 64, 1, 1], [3, 256, 1, 1], [3, 512, 1, 1], [4, 6, 2, 1], [4, 12, 1, 1], [4, 18, 2, 1], [4, 24, 3, 1], [4, 36, 1, 2], [4, 36, 3, 1], [4, 72, 1, 2], [4, 72, 2, 1], [4, 72, 3, 2], [4, 108, 1, 1], [4, 108, 3, 1], [4, 144, 3, 2], [4, 216, 1, 2], [4, 216, 2, 1], [4, 216, 3, 1], [4, 432, 3, 2], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 12, 2, 1], [6, 12, 3, 1], [6, 16, 1, 1], [6, 24, 2, 2], [6, 32, 1, 1], [6, 36, 3, 1], [6, 48, 3, 1], [6, 64, 1, 1], [6, 72, 2, 1], [6, 72, 3, 1], [6, 96, 1, 2], [6, 96, 2, 2], [6, 96, 3, 1], [6, 144, 2, 1], [6, 144, 3, 1], [6, 192, 1, 2], [6, 192, 2, 2], [6, 256, 1, 1], [6, 288, 2, 2], [6, 384, 2, 1], [6, 512, 1, 1], [6, 576, 2, 1], [6, 768, 2, 1], [12, 12, 2, 1], [12, 24, 1, 1], [12, 48, 3, 1], [12, 72, 1, 1], [12, 72, 3, 1], [12, 96, 1, 1], [12, 144, 1, 2], [12, 144, 2, 1], [12, 144, 3, 1], [12, 192, 1, 1], [12, 192, 2, 1], [12, 192, 3, 1], [12, 288, 1, 1], [12, 288, 3, 2], [12, 384, 2, 1], [12, 384, 3, 1], [12, 576, 2, 1], [12, 576, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3\\times A_4\\wr C_2.C_2\\times S_4\\times S_3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '82944.ga', 'autcentquo_hash': 4719265760670157792, 'autcentquo_nilpotent': False, 'autcentquo_order': 82944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6.S_3^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 4], [2, 6, 5], [2, 9, 2], [2, 12, 2], [2, 18, 8], [2, 36, 7], [2, 54, 3], [2, 72, 2], [2, 108, 5], [2, 216, 2], [3, 2, 1], [3, 8, 1], [3, 16, 1], [3, 32, 1], [3, 64, 1], [3, 256, 1], [3, 512, 1], [4, 6, 2], [4, 12, 1], [4, 18, 2], [4, 24, 3], [4, 36, 5], [4, 72, 10], [4, 108, 4], [4, 144, 6], [4, 216, 7], [4, 432, 6], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 12, 5], [6, 16, 1], [6, 24, 4], [6, 32, 1], [6, 36, 3], [6, 48, 3], [6, 64, 1], [6, 72, 5], [6, 96, 9], [6, 144, 5], [6, 192, 6], [6, 256, 1], [6, 288, 4], [6, 384, 2], [6, 512, 1], [6, 576, 2], [6, 768, 2], [12, 12, 2], [12, 24, 1], [12, 48, 3], [12, 72, 4], [12, 96, 1], [12, 144, 7], [12, 192, 6], [12, 288, 7], [12, 384, 5], [12, 576, 5]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '13824.fy', 'commutator_count': 1, 'commutator_label': '3456.qs', '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', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 108, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['192.1493', 1], ['24.12', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 6, 1, 5], [2, 9, 1, 2], [2, 12, 1, 2], [2, 18, 1, 8], [2, 36, 1, 7], [2, 54, 1, 3], [2, 72, 1, 2], [2, 108, 1, 5], [2, 216, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 64, 1, 1], [3, 256, 1, 1], [3, 512, 1, 1], [4, 6, 1, 2], [4, 12, 1, 1], [4, 18, 1, 2], [4, 24, 1, 3], [4, 36, 1, 5], [4, 72, 1, 10], [4, 108, 1, 4], [4, 144, 1, 6], [4, 216, 1, 7], [4, 432, 1, 6], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 12, 1, 5], [6, 16, 1, 1], [6, 24, 1, 4], [6, 32, 1, 1], [6, 36, 1, 3], [6, 48, 1, 3], [6, 64, 1, 1], [6, 72, 1, 5], [6, 96, 1, 9], [6, 144, 1, 5], [6, 192, 1, 6], [6, 256, 1, 1], [6, 288, 1, 4], [6, 384, 1, 2], [6, 512, 1, 1], [6, 576, 1, 2], [6, 768, 1, 2], [12, 12, 1, 2], [12, 24, 1, 1], [12, 48, 1, 3], [12, 72, 1, 4], [12, 96, 1, 1], [12, 144, 1, 7], [12, 192, 1, 6], [12, 288, 1, 7], [12, 384, 1, 5], [12, 576, 1, 5]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 12, 'exponents_of_order': [10, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 4], [48, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '13824.fy', 'hash': 1893477101301930046, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 2, 6, 2, 12, 12, 6, 3, 2, 6, 2, 6, 2], 'inner_gens': [[47537280, 87178291200, 180631154019, 40279680, 174483615581, 174483624704, 93445261846, 174356582400, 123742080, 93529073422, 87091200, 83853775, 87181952794], [47537280, 87178291200, 6274571619, 127370880, 93485533661, 93485542784, 174480357526, 93405312000, 7620480, 174364222222, 40279680, 7286095, 87261786394], [47537280, 6227020800, 180631154019, 40279680, 93532333075, 93532345641, 174396518290, 93405312000, 123742080, 174480343822, 87091200, 83853775, 6230682394], [123379200, 87178291200, 180706995939, 127370880, 174436804061, 174436813184, 93529087126, 174356582400, 83462400, 93488793742, 40279680, 43574095, 87185944474], [43545600, 180583603200, 6270590970, 127370880, 174436804061, 174436814623, 93408959890, 174356582400, 39916800, 93445248142, 87091200, 47574179, 180583998874], [43545600, 180583603200, 6270575658, 127370880, 174436798222, 174436813184, 93408972658, 174356582400, 39916800, 93445255615, 87091200, 47560896, 180583998874], [120113280, 6227020800, 87298431417, 127370880, 174403795379, 174403789054, 93529087126, 174356582400, 39916800, 93445248142, 87091200, 79848093, 6227416474], [47537280, 180583603200, 6274571619, 127370880, 174436804061, 174436813184, 93529087126, 174356582400, 7620480, 93412951822, 40279680, 7286095, 180667098394], [120113280, 87178291200, 180703730019, 40279680, 174444061661, 174444070784, 93445261846, 174356582400, 7620480, 93412951822, 127370880, 4020175, 87261786394], [120113280, 6227020800, 87298418019, 40279680, 174444061661, 174444048407, 93445261846, 174356582400, 7620480, 93412951822, 127370880, 4028579, 6310515994], [79833600, 87178291200, 180663450339, 127370880, 174403781981, 174403791104, 93408973846, 174356582400, 83462400, 93488793742, 40279680, 83853775, 87185944474], [123379200, 87178291200, 180706995939, 87091200, 174400503955, 174400508692, 93488779756, 174356582400, 362880, 93405680370, 127370880, 7286095, 87218240794], [7257600, 87178291200, 6234291939, 40279680, 93532345181, 93532354304, 174356978326, 93405312000, 7620480, 174364222222, 127370880, 47565775, 87261786394]], 'inner_hash': 5414306939380161149, 'inner_nilpotent': False, 'inner_order': 13824, 'inner_split': True, 'inner_tex': 'C_2^6.S_3^3', 'inner_used': [1, 2, 3, 4, 5, 6, 7], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 12], [3, 32], [4, 14], [6, 36], [8, 13], [9, 24], [12, 20], [16, 6], [18, 16], [24, 9], [32, 1], [36, 2], [48, 2]], 'label': '27648.ed', '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': '(C2^2*D6).S4^2', 'ngens': 13, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 102, 'number_characteristic_subgroups': 67, 'number_conjugacy_classes': 195, 'number_divisions': 195, 'number_normal_subgroups': 122, 'number_subgroup_autclasses': 19892, 'number_subgroup_classes': 89975, 'number_subgroups': 5195190, 'old_label': None, 'order': 27648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1759], [3, 890], [4, 6432], [6, 9014], [12, 9552]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 3], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[47537280, 87178291200, 180631149623, 127370880, 174436810256, 174436814391, 93529087126, 174356582400, 7653274, 93412932749, 40279680, 7286095, 87261753600], [47537280, 87178323994, 180631165050, 127370880, 174436791955, 174436783281, 93529087126, 174356582400, 7653274, 93412937970, 40279680, 7286095, 87261786394], [47537280, 87178323994, 180631165050, 127370880, 174436804061, 174436813184, 93529054483, 174356582400, 7620480, 93412951822, 40279680, 7286095, 87261753600], [47537280, 87178323994, 180631165050, 127370880, 174436791955, 174436783281, 93529054483, 174356582400, 7653274, 93412937970, 40279680, 7286095, 87261786394], [47537280, 87178291200, 180631168713, 127370880, 174436793373, 174436808167, 93529087126, 174356582400, 7620480, 93412938239, 40279680, 7259280, 87261786394]], 'outer_group': '48.51', 'outer_hash': 51, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [41041, 90720, 24, 131784, 3], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 32], [4, 14], [6, 36], [8, 13], [9, 24], [12, 20], [16, 6], [18, 16], [24, 9], [32, 1], [36, 2], [48, 2]], 'representations': {'PC': {'code': '492502891973214553485538894458060370838508486781827974785248648300007893362044882953151403775642722991461454537315507452424172539011111305710364088701835574956148913588516451688344768884084186555049280', 'gens': [1, 2, 4, 6, 8, 9, 11, 12, 13], 'pres': [13, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 624, 1509, 66, 314, 258963, 7192, 19841, 146, 113897, 9416, 1460165, 61794, 26707, 24848, 45219, 226, 1284198, 133269, 66124, 898567, 449300, 235905, 18766, 833984, 492825, 221164, 25319, 801, 346, 34395, 13816, 336971, 572856, 84277, 18796, 2920332, 243411, 8189, 20370]}, 'Perm': {'d': 15, 'gens': [47537280, 87178291200, 180631154019, 127370880, 174436804061, 174436813184, 93529087126, 174356582400, 7620480, 93412951822, 40279680, 7286095, 87261786394]}}, 'schur_multiplier': [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': 36, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times D_6).S_4^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
