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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4096.ol', 'ambient_counter': 376, 'ambient_order': 4096, 'ambient_tex': 'C_4^4.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2048, 'characteristic': False, 'core_order': 8, 'counter': 2606, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4096.ol.512.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '512.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '512.6277208', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8928800377295992974, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 512, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^3.C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4096.ol', 'aut_centralizer_order': None, 'aut_label': '512.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.E', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['256.BP', '256.DI', '256.EZ', '256.FJ', '256.FP', '256.FS', '256.FW', '256.OH', '256.OM'], 'contains': ['1024.BC', '1024.BE', '1024.BG'], 'core': '512.DM', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [295705, 573441], 'label': '4096.ol.512.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '512.DM', 'normal_contained_in': ['256.BP', '256.DI', '256.EZ', '256.FJ', '256.FP', '256.FS', '256.FW'], 'normal_contains': ['1024.BC', '1024.BE', '1024.BG'], 'normalizer': '1.a1', 'old_label': '512.dm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.DM', '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1, 2], [1, 3], [5, 3]], 'aut_group': '8.3', 'aut_hash': 3, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 4, 'aut_perms': [1, 22], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', '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], [4, 1, 4]], 'center_label': '8.2', 'center_order': 8, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '2.1', '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, 8]], 'label': '8.2', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 4, 'linQ_dim': 3, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C4', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 8, 'number_divisions': 6, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 4]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 3], [5, 3]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2]], 'representations': {'PC': {'code': 34, 'gens': [1, 2], 'pres': [3, -2, 2, -2, 16]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [3362, 16426]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [251, 504]}, 'Perm': {'d': 6, 'gens': [22, 120, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4', 'transitive_degree': 8, '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': '512.6249624', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[508551, 446601, 235785, 303385, 295705, 1015839], [573833, 708993, 305431, 41489, 295705, 492063], [1033119, 635279, 576015, 57873, 835849, 1032719], [304001, 176769, 768793, 844569, 312089, 1032735], [963473, 254599, 522257, 1024543, 312089, 1016335], [754319, 979329, 776457, 516639, 295705, 507919], [971417, 33417, 59407, 565265, 835849, 1016351], [692889, 238223, 822023, 762119, 819465, 1016335], [193425, 753799, 43535, 40961, 295705, 492047], [754079, 103055, 313607, 320281, 819465, 1016351], [778631, 168833, 252169, 778519, 819465, 1016351], [168593, 492183, 821511, 254727, 835849, 492063]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 17179869184, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 8388608.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 4], [2, 1, 4, 1], [2, 1, 16, 1], [2, 8, 16, 1], [4, 1, 4, 2], [4, 1, 8, 3], [4, 1, 16, 2], [4, 1, 32, 1], [4, 2, 2, 2], [4, 2, 4, 1], [4, 2, 8, 3], [4, 2, 16, 2], [4, 2, 32, 2], [4, 2, 64, 1], [4, 8, 16, 1], [4, 8, 32, 1], [8, 2, 64, 2], [8, 4, 64, 1], [8, 4, 256, 1], [8, 8, 64, 1], [8, 8, 128, 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, 31], [2, 8, 16], [4, 1, 96], [4, 2, 192], [4, 8, 48], [8, 2, 128], [8, 4, 320], [8, 8, 192]], 'center_label': '128.2150', 'center_order': 128, 'central_product': True, 'central_quotient': '32.46', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, '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'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 376, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['2048.uc', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 31], [2, 8, 1, 16], [4, 1, 2, 48], [4, 2, 1, 48], [4, 2, 2, 72], [4, 8, 2, 24], [8, 2, 4, 32], [8, 4, 4, 80], [8, 8, 4, 48]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [12], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '128.997', 'frattini_quotient': '32.51', 'hash': 6956102936927258547, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [4, 4, 2, 2, 2, 1], 'inner_gens': [[508551, 971417, 514049, 303385, 295705, 1015839], [1032343, 446601, 1022481, 303385, 295705, 1015839], [770463, 693121, 235785, 844553, 819465, 1015839], [508551, 446601, 776985, 303385, 295705, 1015839], [508551, 446601, 760601, 303385, 295705, 1015839], [508551, 446601, 235785, 303385, 295705, 1015839]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 32, 'inner_split': None, 'inner_tex': 'C_2^2\\times D_4', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 512], [2, 384], [4, 128]], 'label': '4096.ol', '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': 'C4^4.C2^4', 'ngens': 5, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [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': 38, 'number_characteristic_subgroups': 71, 'number_conjugacy_classes': 1024, 'number_divisions': 400, 'number_normal_subgroups': 11867, 'number_subgroup_autclasses': 2756, 'number_subgroup_classes': 67115, 'number_subgroups': 212187, 'old_label': None, 'order': 4096, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 159], [4, 864], [8, 3072]], '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': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 536870912, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 8, 8], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 80], [4, 176], [8, 112]], 'representations': {'PC': {'code': '6746569087339958082211710580228697601623861136345908295473955938971', 'gens': [1, 4, 7, 8, 10, 12], 'pres': [12, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 24, 61, 49539, 135, 172, 48390, 45714, 8778, 5766, 655, 283, 2961, 357]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [32777, 33025, 32785, 102791, 32897, 294921, 100361, 33281, 709505, 557073, 573953, 828161]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 8, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^4.C_2^4', 'transitive_degree': 2048, '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': '256.53038', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 8, 32, 64, 256], [127, 408, 48, 212, 260], [235, 410, 416, 448, 388], [489, 414, 308, 68, 272], [121, 270, 416, 468, 388], [87, 200, 372, 468, 260], [59, 200, 368, 464, 256], [493, 408, 436, 84, 404], [149, 412, 436, 468, 384]], 'aut_group': None, 'aut_hash': 1279073005126419346, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 8388608, 'aut_permdeg': 96, 'aut_perms': [699286954173727460883769491127627312018727080797504221267782205464217401490447893649662260006757441611719906968594758770687487689543293780838352502447, 219464301979510479444433215062437009102921088242446043115521471708834357189665127015781677984422437111643428520303808556929853184026894232856915760350, 448803147468672022523331088782424401639082095798107399225385316055898194006214413351750656349976879626263936933746402914043229870643663528983179052673, 448809504180883492065697406342697264567585292094167733650989373392059194776972500203868714184734166759227598036932475448839199412450486984841647869567, 344357093706418562943538100365137361815918877722938242518635728384398177396077365017582450817532456826271777271447287608167369089666606264086896489647, 730754902951213643650246516788652439533799924259193958618346700618751813471661306809062060419729681205100460010537978561318956040718433294006624253440, 970710017381589346171426917501759721678501826865900007275135649459850847008725551396047216213026345437923476037730771348763440979447453323000089484223, 480202589971878494255696035708453020333788045233045172636372884238907768619896255332081404831325099814176105040098447485310499882169645223862852502750], 'aut_phi_ratio': 32768.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [2, 1, 8, 1], [2, 2, 16, 1], [4, 1, 4, 2], [4, 1, 8, 1], [4, 1, 32, 1], [4, 2, 8, 2], [4, 2, 16, 2], [4, 2, 32, 1], [8, 1, 64, 1], [8, 2, 32, 1], [8, 2, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{14}.C_2^6.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 8, 'autcent_group': None, 'autcent_hash': 6280121446071870734, 'autcent_nilpotent': True, 'autcent_order': 4194304, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{12}.C_2^6.C_2^4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 15], [2, 2, 16], [4, 1, 48], [4, 2, 80], [8, 1, 64], [8, 2, 96]], 'center_label': '128.1601', 'center_order': 128, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', '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', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 6277208, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1], ['8.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [2, 2, 1, 16], [4, 1, 2, 24], [4, 2, 1, 8], [4, 2, 2, 36], [8, 1, 4, 16], [8, 2, 4, 24]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1249920, 'exponent': 8, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '32.51', 'hash': 6277208, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2, 1], 'inner_gens': [[1, 136, 32, 192, 256], [129, 8, 160, 192, 256], [1, 136, 32, 192, 256], [129, 136, 160, 64, 256], [1, 8, 32, 64, 256]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 256], [2, 64]], 'label': '512.6277208', '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': 'C4^3.C2^3', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 30, 'number_conjugacy_classes': 320, 'number_divisions': 140, 'number_normal_subgroups': 2618, 'number_subgroup_autclasses': 350, 'number_subgroup_classes': 4430, 'number_subgroups': 6242, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 47], [4, 208], [8, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [4, 4, 4, 4, 4, 4, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[127, 408, 48, 212, 260], [87, 200, 372, 468, 260], [149, 412, 436, 468, 384], [59, 200, 368, 464, 256], [493, 408, 436, 84, 404], [121, 270, 416, 468, 388], [489, 414, 308, 68, 272], [107, 410, 288, 320, 388]], 'outer_group': None, 'outer_hash': 8748338138142181001, 'outer_nilpotent': True, 'outer_order': 2097152, 'outer_permdeg': 512, 'outer_perms': 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^9.C_2^5.C_2^6.C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 4, 8], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 56], [4, 44], [8, 8]], 'representations': {'PC': {'code': '166478653092435712611241314855429195', 'gens': [1, 4, 6, 7, 9], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 46, 4899, 102, 1112, 12102, 1545, 429, 186]}, 'Perm': {'d': 18, 'gens': [401736287272447, 798996224315575, 1171856857691808, 401736287559888, 1174609, 288, 1171856858422320, 1552384830492720, 1552384829318400]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^3.C_2^3', 'transitive_degree': 256, 'wreath_data': None, 'wreath_product': False}
