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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4608.v', 'ambient_counter': 22, 'ambient_order': 4608, 'ambient_tex': 'D_{24}.C_{96}', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': True, 'core_order': 24, 'counter': 375, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4608.v.192._.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.175', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 175, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{96}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4608.v', 'aut_centralizer_order': 1536, 'aut_label': None, 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '2._.F', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64._.H', '96._.H', '96._.M', '96._.R'], 'contains': ['384._.F', '576._.D'], 'core': '192._.M', 'coset_action_label': None, 'count': 1, 'diagramx': [9938, 583, 7788, 8282, 8902, 1646, 9766, 8452], 'generators': [395398321, 776418240, 783607298, 934577459], 'label': '4608.v.192._.M', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192._.M', 'normal_contained_in': ['64._.H', '96._.H', '96._.M', '96._.R'], 'normal_contains': ['384._.F', '576._.D'], 'normalizer': '1.a1.a1', 'old_label': '192.k1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.2', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192._.M', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '24.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2, 2], 'aut_gens': [[1], [17], [13], [19]], 'aut_group': '8.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 6, 'aut_perms': [1, 6, 120], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [24, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3', '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': 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, 1], [3, 1, 2], [4, 1, 2], [6, 1, 2], [8, 1, 4], [12, 1, 4], [24, 1, 8]], 'center_label': '24.2', 'center_order': 24, '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', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [24, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 24, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '4.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 2, 'irrep_stats': [[1, 24]], 'label': '24.2', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C24', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 24, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [8, 4], [12, 4], [24, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[17], [13], [19]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [8, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 1]], 'representations': {'PC': {'code': 5357681, 'gens': [1], 'pres': [4, -2, -2, -2, -3, 8, 21, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [108470311826960419]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [584]}, 'Perm': {'d': 11, 'gens': [27760320, 4, 11614560, 3669864]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [24], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}', 'transitive_degree': 24, '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': '384.5547', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 48, 'aut_gen_orders': [16, 24, 24, 16, 8, 48, 48, 8], 'aut_gens': [[37442, 395398321, 35945290], [6882766, 115025093, 913010366], [481149, 395398321, 158159276], [287377, 992089873, 833930728], [37442, 992089873, 71890580], [343540, 1301219333, 1250896092], [4039104, 395398321, 862686960], [3187202, 395398321, 1049602468], [5622862, 1272463101, 589502756]], 'aut_group': None, 'aut_hash': 2675128990628703738, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 58, 'aut_perms': [1209836495979212660927431096201921996793240735553015761880256400263328622580693, 460404172012635887940176008295548619537204047757590778225083279146513706895115, 174652649647282533900418686626609112483306293175539093391243115546255472235550, 1597639767924934956743718311830340876443831605492568598712822068395741430687228, 1765178233114510148290555356882976171987611967425069352141110052884293477525307, 1074154375750739599809226010366626104094520919021880789240330648703660255467695, 2331923544139373031937616687423484820025328957153845510685169469375855377795222, 460087216947899050909888636323091739061296835940936754624644615139315293135174], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 4, 1], [4, 12, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 12, 4, 1], [8, 1, 4, 1], [8, 2, 2, 3], [8, 12, 4, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 2, 8, 2], [12, 2, 16, 1], [12, 12, 4, 1], [16, 1, 8, 1], [16, 2, 4, 1], [16, 2, 8, 1], [16, 12, 8, 1], [24, 1, 8, 1], [24, 2, 4, 7], [24, 2, 8, 4], [24, 12, 8, 1], [32, 1, 16, 1], [32, 2, 8, 1], [32, 2, 16, 1], [32, 12, 16, 1], [48, 1, 16, 1], [48, 2, 8, 3], [48, 2, 16, 4], [48, 2, 32, 1], [48, 12, 16, 1], [64, 1, 32, 1], [64, 2, 16, 1], [64, 2, 32, 1], [64, 12, 32, 1], [96, 1, 32, 1], [96, 2, 16, 3], [96, 2, 32, 4], [96, 2, 64, 1], [96, 12, 32, 1], [192, 1, 64, 1], [192, 2, 32, 3], [192, 2, 64, 4], [192, 2, 128, 1], [192, 12, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:((C_4\\times C_8).C_2^6.C_2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '256.55608', 'autcent_hash': 55608, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{16}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.38', 'autcentquo_hash': 38, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 12, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 5], [4, 12, 2], [6, 1, 2], [6, 2, 11], [6, 12, 4], [8, 1, 4], [8, 2, 6], [8, 12, 4], [12, 1, 4], [12, 2, 46], [12, 12, 4], [16, 1, 8], [16, 2, 12], [16, 12, 8], [24, 1, 8], [24, 2, 60], [24, 12, 8], [32, 1, 16], [32, 2, 24], [32, 12, 16], [48, 1, 16], [48, 2, 120], [48, 12, 16], [64, 1, 32], [64, 2, 48], [64, 12, 32], [96, 1, 32], [96, 2, 240], [96, 12, 32], [192, 1, 64], [192, 2, 480], [192, 12, 64]], 'center_label': '192.2', 'center_order': 192, 'central_product': True, 'central_quotient': '24.6', 'commutator_count': 1, 'commutator_label': '12.2', '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', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 22, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1536.10843710', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 2, 2], [4, 12, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 12, 2, 2], [8, 1, 4, 1], [8, 2, 2, 3], [8, 12, 2, 2], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 10], [12, 12, 2, 2], [16, 1, 8, 1], [16, 2, 4, 1], [16, 2, 8, 1], [16, 12, 4, 2], [24, 1, 8, 1], [24, 2, 4, 7], [24, 2, 8, 4], [24, 12, 4, 2], [32, 1, 16, 1], [32, 2, 8, 1], [32, 2, 16, 1], [32, 12, 8, 2], [48, 1, 16, 1], [48, 2, 8, 3], [48, 2, 16, 6], [48, 12, 8, 2], [64, 1, 32, 1], [64, 2, 16, 1], [64, 2, 32, 1], [64, 12, 16, 2], [96, 1, 32, 1], [96, 2, 16, 3], [96, 2, 32, 6], [96, 12, 16, 2], [192, 1, 64, 1], [192, 2, 32, 3], [192, 2, 64, 6], [192, 12, 32, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 2236416, 'exponent': 192, 'exponents_of_order': [9, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 256]], 'familial': False, 'frattini_label': '64.50', 'frattini_quotient': '72.48', 'hash': 1280522339947909588, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 12, 1], 'inner_gens': [[37442, 1337164657, 35945290], [1850291, 395398321, 35945290], [37442, 395398321, 35945290]], 'inner_hash': 6, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': False, 'inner_tex': 'D_{12}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 128, 'irrQ_dim': 128, 'irrR_degree': None, 'irrep_stats': [[1, 384], [2, 1056]], 'label': '4608.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': True, 'metacyclic': False, 'monomial': True, 'name': 'D24.C96', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 88, 'number_characteristic_subgroups': 138, 'number_conjugacy_classes': 1440, 'number_divisions': 110, 'number_normal_subgroups': 202, 'number_subgroup_autclasses': 351, 'number_subgroup_classes': 495, 'number_subgroups': 1178, 'old_label': None, 'order': 4608, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 27], [3, 8], [4, 36], [6, 72], [8, 64], [12, 144], [16, 128], [24, 224], [32, 256], [48, 448], [64, 512], [96, 896], [192, 1792]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 16, 'outer_gen_orders': [16, 8, 16, 8, 4, 8], 'outer_gen_pows': [776418240, 7189058, 7189058, 776418240, 611069953, 7189058], 'outer_gens': [[4039104, 992089873, 366641958], [5622862, 1272463101, 589502756], [4851827, 1301219333, 381020074], [630917, 1272463101, 323507610], [2084593, 86268861, 1200572686], [7188864, 115025093, 1171816454]], 'outer_group': '512.10493039', 'outer_hash': 3046548263559564634, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 512, 'outer_perms': 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\times C_{16}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 134, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 32, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 19], [8, 19], [16, 17], [32, 13], [64, 8], [128, 8]], 'representations': {'PC': {'code': '329680630424262361155756325310135021435345469787175764357129', 'gens': [1, 2, 9], 'pres': [11, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 56, 90, 124, 158, 192, 226, 446696, 294, 443529, 328, 371722]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [37442, 395398321, 35945290]}, 'Perm': {'d': 134, 'gens': [15436099512715775457938543278326507815845689574710838830107688810017577763733977450011984164779589723803741620601164288034107911637534346484885657452980049119193810696159407465763620684673469402907159176922987348319091426457781, 30416434948139670563396958516244672379826467384532234219099342505013084076009486586160473368904038175732413567608632246792986883477085494093187563011904349788641140966404643730495870381169235744223786385631570991923106233357116, 45407757218969033080556801194086373207428069848356286463199006820714443992346660515070374613771350849450635387299016895487662001532848635142300672322084731362248726798354717938598556493694381906621611206288096414946036257045493]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 96], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{24}.C_{96}', 'transitive_degree': 384, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '192.175', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 2, 8], 'aut_gens': [[1, 2], [1, 94], [1, 130], [97, 15], [97, 62], [1, 74]], 'aut_group': '128.2303', 'aut_hash': 2303, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 128, 'aut_permdeg': 20, 'aut_perms': [669291327396131063, 16, 618072310285003447, 759143329715554680, 411395174969804760], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 1, 2, 2], [6, 1, 2, 1], [6, 1, 4, 1], [8, 1, 4, 2], [12, 1, 4, 2], [16, 1, 8, 2], [24, 1, 8, 2], [32, 1, 32, 1], [48, 1, 16, 2], [96, 1, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_8.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 8, 'autcent_group': '128.2303', 'autcent_hash': 2303, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_8.C_2^4', '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], [3, 1, 2], [4, 1, 4], [6, 1, 6], [8, 1, 8], [12, 1, 8], [16, 1, 16], [24, 1, 16], [32, 1, 32], [48, 1, 32], [96, 1, 64]], 'center_label': '192.175', 'center_order': 192, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 175, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['32.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 2], [6, 1, 2, 3], [8, 1, 4, 2], [12, 1, 4, 2], [16, 1, 8, 2], [24, 1, 8, 2], [32, 1, 16, 2], [48, 1, 16, 2], [96, 1, 32, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 96, 'exponent': 96, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '12.5', 'hash': 175, '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, 192]], 'label': '192.175', 'linC_count': 6144, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 4, 'linQ_dim': 18, 'linQ_dim_count': 4, 'linR_count': 64, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C96', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 26, 'number_conjugacy_classes': 192, 'number_divisions': 24, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 34, 'number_subgroups': 34, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [8, 8], [12, 8], [16, 16], [24, 16], [32, 32], [48, 32], [96, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 2, 8], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 94], [1, 130], [97, 15], [97, 62], [1, 74]], 'outer_group': '128.2303', 'outer_hash': 2303, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 20, 'outer_perms': [669291327396131063, 16, 618072310285003447, 759143329715554680, 411395174969804760], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_8.C_2^4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 37, 'pgroup': 0, 'primary_abelian_invariants': [2, 32, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [8, 4], [16, 4], [32, 2]], 'representations': {'PC': {'code': 23715291945026723585, 'gens': [1, 2], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 36, 58, 80, 102, 124]}, 'GLFp': {'d': 2, 'p': 97, 'gens': [15515447, 87616704]}, 'Perm': {'d': 37, 'gens': [9420320787564833044042482448295657472000, 371993326789901217467999448150835200000000, 4, 4553316871647675141030596900032688179200, 2119814913695370483408246361737529456320, 903065845799780519864142501070727825760, 295496195434689904216526716510628258664]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 96], '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_{96}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
