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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7776.dy', 'ambient_counter': 103, 'ambient_order': 7776, 'ambient_tex': 'C_6^3.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 162, 'counter': 315, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '7776.dy.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '7776.dy', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.a1', '24.r1', '24.w1', '24.bh1'], 'contains': ['96.a1', '144.c1', '144.bz1', '144.cc1', '144.cd1'], 'core': '48.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [702, 2808, 4862, 36, 5400], 'label': '7776.dy.48.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1', 'normal_contained_in': ['12.d1', '24.a1'], 'normal_contains': ['96.a1', '144.c1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '7776.dy', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '18.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [3, 2, 3, 3, 3, 2], 'aut_gens': [[736, 2918, 757, 1027], [736, 3431, 757, 1027], [736, 2918, 784, 973], [736, 2972, 757, 1027], [736, 2918, 973, 1027], [5107, 5111, 757, 1027], [733, 2918, 757, 1027]], 'aut_group': '20736.pd', 'aut_hash': 2986519587559918118, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 17, 'aut_perms': [176625221068800, 4197015660316, 25113582144000, 5331894180480, 37249, 10855], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 8, 1], [3, 2, 4, 1], [3, 2, 32, 1], [6, 9, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '48.29', 'autcent_hash': 29, 'autcent_nilpotent': False, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(2,3)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 1, 8], [3, 2, 36], [6, 9, 8]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '18.4', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 52, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 1], ['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 2, 4], [3, 2, 1, 4], [3, 2, 2, 16], [6, 9, 2, 4]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 91, 'exponent': 6, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '162.52', 'hash': 52, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 3, 3], 'inner_gens': [[736, 2918, 757, 1027], [736, 2918, 784, 1243], [736, 2945, 757, 1027], [736, 3458, 757, 1027]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': False, 'inner_tex': 'C_3:S_3', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 18], [2, 36]], 'label': '162.52', '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': 'C3^2wrC2', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, '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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 54, 'number_divisions': 30, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 23, 'number_subgroup_classes': 160, 'number_subgroups': 344, 'old_label': None, 'order': 162, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 9], [3, 80], [6, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 6, 2, 6, 4, 4], 'outer_gen_pows': [730, 730, 2918, 2918, 730, 730], 'outer_gens': [[733, 5108, 1243, 784], [733, 2921, 1243, 1270], [736, 2918, 1216, 1000], [5110, 731, 1243, 757], [5104, 5105, 757, 1027], [5107, 731, 757, 1027]], 'outer_group': '1152.157461', 'outer_hash': 7371672288863537087, 'outer_nilpotent': False, 'outer_order': 1152, 'outer_permdeg': 12, 'outer_perms': [1, 18594004, 23, 7711327, 303055320, 44352840], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4\\times \\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 12], [4, 16]], 'representations': {'PC': {'code': 14018986071, 'gens': [1, 2, 4, 5], 'pres': [5, -3, -2, -3, -3, -3, 26, 248, 909]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 15477644, 24507118, 2939606, 36731395]}, 'GLZq': {'d': 2, 'q': 9, 'gens': [757, 733, 3220, 737, 2920]}, 'Perm': {'d': 12, 'gens': [40723336, 91451125, 325, 435, 130682595]}}, 'schur_multiplier': [3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2\\wr C_2', 'transitive_degree': 18, 'wreath_data': ['C_3^2', 'C_2', '2T1'], 'wreath_product': True}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 6, 18, 12, 12], 'aut_gens': [[1, 6, 108, 648, 1296], [4213, 1050, 540, 648, 6480], [3913, 7374, 108, 648, 7236], [5161, 1950, 1944, 648, 2484], [685, 4890, 1944, 648, 756], [7189, 3594, 540, 648, 2484]], 'aut_group': None, 'aut_hash': 1593371249671273754, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15552, 'aut_permdeg': 129, 'aut_perms': [1773627207703082596686470975923924290975379087304467751819443670168672136345623656132056443072526903250517788501480380807610575869566201221047962160883256973318449486475078821026398394084219014588187445387276028772773, 6868538516395908097279239603941297003583031907948520036648635620951324722194614985608957850049001219263564628952551382809351346695624979160391438066275911373547902509052207225432735167672283914481865099342494218603117, 10056705141416362122666801203460368418204231691039575877750871369222626393877913894197539882481756678750766619434309390813271165103888578669071132155429641395609062109420573893423516145791041038769071542144278929296383, 32184864366229146101521021601068132341695915084347260897442623674436363168686102878321407820284607676490105695307368617595256012155613820531484339990143218716000148959422220918670213578954221384694572305536209697483268, 11194096134512955129093436057751545540551174310309464143357057508388965369751991191217332231134325374142889692803614885547424225290189121551633321284090697695002922077204023579746148182737581697108605681840651396126008], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 9, 2, 1], [2, 27, 2, 1], [2, 54, 2, 2], [3, 2, 1, 2], [3, 3, 1, 2], [3, 4, 1, 1], [3, 6, 1, 5], [3, 12, 1, 3], [4, 54, 2, 2], [6, 2, 1, 2], [6, 3, 1, 6], [6, 4, 1, 1], [6, 6, 1, 23], [6, 12, 1, 33], [6, 18, 2, 1], [6, 27, 2, 4], [6, 54, 2, 7], [6, 108, 2, 6], [9, 72, 1, 3], [9, 144, 1, 3], [12, 54, 2, 4], [12, 108, 2, 6], [18, 72, 1, 3], [18, 144, 1, 3], [18, 216, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6^2.C_3^3.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '3888.fl', 'autcentquo_hash': 3044566718417071494, 'autcentquo_nilpotent': False, 'autcentquo_order': 3888, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.(C_6\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 9, 2], [2, 27, 2], [2, 54, 4], [3, 2, 2], [3, 3, 2], [3, 4, 1], [3, 6, 5], [3, 12, 3], [4, 54, 4], [6, 2, 2], [6, 3, 6], [6, 4, 1], [6, 6, 23], [6, 12, 33], [6, 18, 2], [6, 27, 8], [6, 54, 14], [6, 108, 12], [9, 72, 3], [9, 144, 3], [12, 54, 8], [12, 108, 12], [18, 72, 3], [18, 144, 3], [18, 216, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '3888.fl', 'commutator_count': 1, 'commutator_label': '324.59', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 103, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3888.fl', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 2], [2, 27, 1, 2], [2, 54, 1, 4], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 1, 1], [3, 6, 2, 2], [3, 12, 1, 1], [3, 12, 2, 1], [4, 54, 1, 4], [6, 2, 1, 2], [6, 3, 2, 3], [6, 4, 1, 1], [6, 6, 1, 7], [6, 6, 2, 8], [6, 12, 1, 7], [6, 12, 2, 13], [6, 18, 1, 2], [6, 27, 2, 4], [6, 54, 1, 2], [6, 54, 2, 6], [6, 108, 1, 4], [6, 108, 2, 4], [9, 72, 1, 1], [9, 72, 2, 1], [9, 144, 1, 1], [9, 144, 2, 1], [12, 54, 2, 4], [12, 108, 1, 4], [12, 108, 2, 4], [18, 72, 1, 1], [18, 72, 2, 1], [18, 144, 1, 1], [18, 144, 2, 1], [18, 216, 1, 2], [18, 216, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 7076160, 'exponent': 36, 'exponents_of_order': [5, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 8], [12, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '864.4690', 'hash': 1798508750155658558, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 18, 6, 1, 6], 'inner_gens': [[1, 4890, 1944, 648, 756], [3973, 6, 1944, 648, 2484], [7237, 7242, 108, 648, 1296], [1, 6, 108, 648, 1296], [2485, 762, 108, 648, 1296]], 'inner_hash': 3044566718417071494, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': True, 'inner_tex': 'C_3^3.(C_6\\times S_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 24], [3, 24], [4, 6], [6, 52], [12, 38]], 'label': '7776.dy', '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': True, 'name': 'C6^3.S3^2', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 131, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 168, 'number_divisions': 112, 'number_normal_subgroups': 96, 'number_subgroup_autclasses': 1794, 'number_subgroup_classes': 2722, 'number_subgroups': 48914, 'old_label': None, 'order': 7776, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 295], [3, 80], [4, 216], [6, 2864], [9, 648], [12, 1728], [18, 1944]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[649, 654, 108, 648, 1296], [1, 654, 540, 648, 6480]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [3, 8], [4, 10], [6, 28], [8, 2], [12, 26], [24, 14]], 'representations': {'PC': {'code': '18953224405134942158315723211279615683168348738539633708186991917455599538614801019556186541038313412017513', 'gens': [1, 3, 6, 8, 9], 'pres': [10, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 20, 48611, 146702, 58962, 82, 41283, 21133, 153, 3604, 116645, 19465, 9215, 175, 181446, 30266, 17676, 68048, 37288, 8948, 268, 21609, 50429, 3639]}, 'Perm': {'d': 24, 'gens': [55239539857503286014720, 2452858939489884556344, 28202584576981040837407]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^3.S_3^2', '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': '4.2', '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, 3, 2, 2], 'aut_gens': [[143, 127, 576, 126, 121], [719, 127, 304, 126, 7], [16, 127, 576, 126, 121], [719, 127, 576, 7, 126], [143, 127, 702, 126, 121], [136, 127, 583, 126, 121]], 'aut_group': '48.48', 'aut_hash': 48, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 6, 'aut_perms': [269, 450, 244, 94, 444], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 2, 1], [3, 8, 1, 1], [4, 6, 2, 1], [6, 8, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 2], [3, 8, 1], [4, 6, 2], [6, 8, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '12.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 48, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.12', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 2], [3, 8, 1, 1], [4, 6, 1, 2], [6, 8, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '48.48', 'hash': 48, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 3, 2, 2], 'inner_gens': [[143, 127, 304, 121, 126], [143, 127, 576, 126, 121], [415, 127, 576, 121, 7], [136, 127, 697, 126, 121], [136, 127, 583, 126, 121]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 3, 4], 'irrC_degree': 3, 'irrQ_degree': 3, 'irrQ_dim': 3, 'irrR_degree': 3, 'irrep_stats': [[1, 4], [2, 2], [3, 4]], 'label': '48.48', 'linC_count': 2, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 2, 'linQ_dim': 3, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*S4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, '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': 8, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 10, 'number_divisions': 10, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 33, 'number_subgroups': 98, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 19], [3, 8], [4, 12], [6, 8]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[16, 127, 576, 126, 121]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 6, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4]], 'representations': {'PC': {'code': 44643202623812656708, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -3, -2, 2, 101, 26, 122, 483, 248, 193, 304, 459, 89]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [10320, 9038]}, 'Lie': [{'d': 3, 'q': 3, 'gens': [1557, 1699, 13205], 'family': 'GO'}, {'d': 3, 'q': 3, 'gens': [1557, 1699, 13205], 'family': 'CO'}], 'GLFp': {'d': 3, 'p': 3, 'gens': [16120, 18391, 13286, 6922, 13843]}, 'Perm': {'d': 6, 'gens': [143, 127, 576, 126, 121]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times S_4', 'transitive_degree': 6, 'wreath_data': ['24.b1.a1', '8.b1.a1', '24.d1.a1', '3T2'], 'wreath_product': True}
