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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46903', 'ambient_counter': 46903, 'ambient_order': 1728, 'ambient_tex': 'C_6^2:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 561, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46903.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.46903', 'aut_centralizer_order': 144, 'aut_label': '48.e1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 432, 'centralizer': '48.a1.a1', 'complements': ['36.w1.a1', '36.v1.a1', '36.dr1.a1', '36.z1.a1', '36.do1.a1', '36.w1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.b1', '24.cf1.b1', '24.cw1.b1', '24.cy1.b1', '24.cy1.e1', '24.da1.b1', '24.dd1.b1'], 'contains': ['144.e1.a1', '144.g1.b1', '144.cw1.b1', '192.b1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [178, 2740, 3035, 1897, 385, 3252, 685, 2774], 'generators': [4555816, 8046913, 25489843, 892585], 'label': '1728.46903.48.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.e1.b1', 'normal_contained_in': ['16.a1.a1', '24.c1.b1'], 'normal_contains': ['144.e1.a1', '144.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.b1', 'projective_image': '1728.46903', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '9.2', '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, 3, 2, 2], 'aut_gens': [[1, 3, 6], [13, 3, 30], [2, 18, 15], [1, 21, 27], [25, 3, 6], [22, 3, 6], [19, 3, 6]], 'aut_group': '144.183', 'aut_hash': 183, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 144, 'aut_permdeg': 7, 'aut_perms': [1, 120, 144, 3, 744, 1680], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 1, 2, 1], [3, 4, 6, 1], [6, 3, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times S_4', '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': 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, 3, 1], [3, 1, 2], [3, 4, 6], [6, 3, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '12.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 11, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 1, 2, 1], [3, 4, 2, 3], [6, 3, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4, 'exponent': 6, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '36.11', 'hash': 11, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 2, 2], 'inner_gens': [[1, 21, 27], [19, 3, 6], [22, 3, 6]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'A_4', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 9], [3, 3]], 'label': '36.11', 'linC_count': 2, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 3, 'linQ_dim': 5, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3*A4', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 12, 'number_divisions': 7, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 14, 'number_subgroups': 30, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [3, 26], [6, 6]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[2, 18, 27], [26, 18, 15]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [7, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 4], [3, 1], [6, 1]], 'representations': {'PC': {'code': 107356617, 'gens': [1, 2, 3], 'pres': [4, -3, -2, 2, -3, 169, 326, 34]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [706461792882, 48233911639]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [16247572, 34591248, 17540971, 23068812]}, 'Perm': {'d': 7, 'gens': [147, 3, 744, 1680]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times A_4', 'transitive_degree': 12, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 6, 6, 12, 2, 6, 6], 'aut_gens': [[594539, 31671377, 35456684, 4403503, 7751737], [25492769, 10417733, 35161508, 4403503, 7749385], [596891, 31671377, 5020679, 4403503, 32641735], [7706999, 31671377, 43885901, 32943967, 4705735], [38382884, 10417733, 5315855, 29593381, 32941615], [7711703, 31671377, 43969229, 4403503, 32646439], [743303, 31671377, 6627764, 4703383, 32939263], [25488065, 31671377, 42360968, 4403503, 7749385]], 'aut_group': None, 'aut_hash': 4497091926293446014, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 44, 'aut_perms': [1649097481739674138774890356162714568261959310904859058, 1170445641534250623987654218773733747089527309626347726, 2104781815748018619358662369500964740151598102696474265, 1299247415059279002814968609199487075610286533659245873, 2234059504695561892477724071384375485961809084018062225, 1589128904095310272093216601505988072313390564861667508, 588769029700997255207879372285809359573057848844427866], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 2], [2, 18, 1, 1], [2, 18, 2, 1], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 3, 1], [3, 16, 3, 1], [4, 6, 1, 1], [4, 18, 1, 1], [4, 18, 2, 1], [4, 36, 1, 1], [4, 108, 1, 3], [6, 2, 1, 2], [6, 2, 2, 1], [6, 4, 1, 2], [6, 4, 2, 1], [6, 6, 1, 4], [6, 6, 2, 1], [6, 8, 3, 1], [6, 12, 1, 4], [6, 12, 2, 1], [6, 16, 3, 2], [6, 16, 6, 1], [6, 36, 1, 1], [6, 36, 2, 2], [6, 48, 3, 1], [12, 12, 1, 1], [12, 36, 1, 1], [12, 36, 2, 2], [12, 48, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_6^2.C_2^4', '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': '2592.jb', 'autcentquo_hash': 6898096242996517164, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 2], [2, 18, 3], [2, 36, 1], [2, 108, 1], [3, 2, 2], [3, 4, 1], [3, 8, 3], [3, 16, 3], [4, 6, 1], [4, 18, 3], [4, 36, 1], [4, 108, 3], [6, 2, 4], [6, 4, 4], [6, 6, 6], [6, 8, 3], [6, 12, 6], [6, 16, 12], [6, 36, 5], [6, 48, 3], [12, 12, 1], [12, 36, 5], [12, 48, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '864.4692', 'commutator_count': 1, 'commutator_label': '216.173', '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', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46903, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.8', 1], ['72.43', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 2], [2, 18, 1, 3], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 1, 3], [3, 16, 1, 3], [4, 6, 1, 1], [4, 18, 1, 3], [4, 36, 1, 1], [4, 108, 1, 3], [6, 2, 1, 2], [6, 2, 2, 1], [6, 4, 1, 2], [6, 4, 2, 1], [6, 6, 1, 4], [6, 6, 2, 1], [6, 8, 1, 3], [6, 12, 1, 4], [6, 12, 2, 1], [6, 16, 1, 6], [6, 16, 2, 3], [6, 36, 1, 3], [6, 36, 2, 1], [6, 48, 1, 3], [12, 12, 1, 1], [12, 36, 1, 3], [12, 36, 2, 1], [12, 48, 1, 3]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 40320, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4692', 'hash': 46903, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 6, 6], 'inner_gens': [[594539, 31671377, 47610623, 4403503, 32646439], [594539, 31671377, 6925292, 4403503, 7751737], [38382884, 10417733, 35456684, 7754089, 4701031], [594539, 31671377, 10652366, 4403503, 7751737], [25492769, 31671377, 42360968, 4403503, 7751737]], 'inner_hash': 4692, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': 'S_3\\times C_6:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 26], [3, 8], [4, 20], [6, 14], [12, 5]], 'label': '1728.46903', 'linC_count': 432, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 1152, 'linQ_dim': 9, 'linQ_dim_count': 1152, 'linR_count': 1152, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:(C2*S4)', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 52, 'number_characteristic_subgroups': 59, 'number_conjugacy_classes': 81, 'number_divisions': 72, 'number_normal_subgroups': 90, 'number_subgroup_autclasses': 920, 'number_subgroup_classes': 1310, 'number_subgroups': 17536, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 219], [3, 80], [4, 420], [6, 672], [12, 336]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [592705, 592705, 592705], 'outer_gens': [[594539, 31671377, 35456684, 32943967, 29598085], [594539, 31671377, 47610623, 4403503, 32641735], [7706999, 31671377, 35461388, 4403503, 7751737]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 22], [3, 8], [4, 14], [6, 10], [8, 4], [12, 5], [24, 1]], 'representations': {'PC': {'code': 2362315213057807382612637065800565756284382605137202126419572189841676309, 'gens': [1, 2, 3, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 542, 389, 74, 1443, 102, 1444, 12983, 6188, 3605, 158, 3048, 107143, 9529, 11698, 1987, 214, 101096, 15578]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [892585, 7072411, 596891, 595057, 31672385, 25782667, 1042546, 29300557, 7705165]}, 'Perm': {'d': 14, 'gens': [997960320, 745, 264, 1680, 518918400, 403200, 3, 6266937600, 13412044800]}}, 'schur_multiplier': [2, 2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:(C_2\\times S_4)', 'transitive_degree': 72, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 3], 'aut_gens': [[1, 2, 4], [1, 2, 20], [25, 2, 4], [1, 2, 28], [1, 38, 28], [1, 26, 4], [17, 2, 4]], 'aut_group': '96.209', 'aut_hash': 209, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 9, 'aut_perms': [5040, 127, 16, 126, 7, 45360], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 3, 2, 1], [2, 6, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 4, 2, 1], [12, 4, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times D_6', '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': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 3, 2], [2, 6, 2], [3, 2, 1], [4, 2, 1], [4, 6, 1], [6, 2, 1], [6, 4, 2], [12, 4, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '6.2', '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': 38, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 3, 1, 2], [2, 6, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 4, 1, 2], [12, 4, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.14', 'hash': 38, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 6], 'inner_gens': [[1, 2, 20], [1, 2, 28], [33, 26, 4]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 6], [4, 1]], 'label': '48.38', 'linC_count': 9, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 9, 'linQ_dim': 4, 'linQ_dim_count': 9, 'linR_count': 9, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'S3*D4', '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': 11, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 15, 'number_divisions': 15, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 34, 'number_subgroup_classes': 54, 'number_subgroups': 120, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 8], [6, 10], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [12, 0], 'outer_gens': [[1, 14, 4], [25, 2, 4]], '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': 3, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1]], 'representations': {'PC': {'code': 537262988737921, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -3, 302, 217, 42, 803, 58, 804]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16563488, 35931400, 7233337]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [1305911, 24677712, 16278362, 16118845, 16002800]}, 'Perm': {'d': 7, 'gens': [1, 264, 744, 1680, 3]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times D_4', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
