-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1584.173', 'ambient_counter': 173, 'ambient_order': 1584, 'ambient_tex': 'C_{132}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 132, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1584.173.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.9', 'subgroup_hash': 9, 'subgroup_order': 132, 'subgroup_tex': 'D_{66}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1584.173', 'aut_centralizer_order': 8, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 8, 'centralizer': '132.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '36.b1.a1', '132.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1909, 6027, 2669, 7620, 883, 2574, 883, 2717], 'generators': [15, 16, 144, 24], 'label': '1584.173.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '792.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.5'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [2, 10, 66], 'aut_gens': [[1, 2], [67, 46], [67, 122], [99, 2]], 'aut_group': '1320.142', 'aut_hash': 142, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1320, 'aut_permdeg': 16, 'aut_perms': [6, 834421876561, 2627969828449], 'aut_phi_ratio': 33.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 33, 2, 1], [3, 2, 1, 1], [6, 2, 1, 1], [11, 2, 5, 1], [22, 2, 5, 1], [33, 2, 10, 1], [66, 2, 10, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6\\times F_{11}', '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': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 33, 2], [3, 2, 1], [6, 2, 1], [11, 2, 5], [22, 2, 5], [33, 2, 10], [66, 2, 10]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '66.3', 'commutator_count': 1, 'commutator_label': '33.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [['2.1', 1], ['66.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 33, 1, 2], [3, 2, 1, 1], [6, 2, 1, 1], [11, 2, 5, 1], [22, 2, 5, 1], [33, 2, 10, 1], [66, 2, 10, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 66, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 1, 10]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '132.9', 'hash': 9, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 33], 'inner_gens': [[1, 130], [5, 2]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 66, 'inner_split': True, 'inner_tex': 'D_{33}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 32]], 'label': '132.9', 'linC_count': 10, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 3, 'linQ_dim': 12, 'linQ_dim_count': 3, 'linR_count': 10, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D66', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 36, 'number_divisions': 10, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 20, 'number_subgroups': 152, 'old_label': None, 'order': 132, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 67], [3, 2], [6, 2], [11, 10], [22, 10], [33, 20], [66, 20]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [0, 110], 'outer_gens': [[67, 86], [89, 38]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [40320, 810], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [10, 2], [20, 2]], 'representations': {'PC': {'code': 14239841398380019, 'gens': [1, 2], 'pres': [4, -2, -2, -3, -11, 1041, 21, 1538, 46, 1923]}, 'GLFp': {'d': 2, 'p': 67, 'gens': [4556, 10225944]}, 'Perm': {'d': 16, 'gens': [87660962646, 1, 30, 1482996292560]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{66}', 'transitive_degree': 66, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [10, 30, 30, 10, 30, 10, 30], 'aut_gens': [[1, 2, 48], [13, 1174, 624], [5, 14, 912], [9, 722, 240], [25, 1178, 1248], [17, 1178, 384], [37, 1318, 240], [5, 878, 1392]], 'aut_group': None, 'aut_hash': 6678131497129254218, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10560, 'aut_permdeg': 58, 'aut_perms': [677764223098011788967786438401743856422492786182020353244690313067341570453727, 103159286127620479403124307179047966840830709369316717657417282853147450286775, 603121041646300035793461997144693683455955858854602339230782965605720695518664, 736814387135939412123398943688680005747635173898504611933106835980761073148465, 137274462487256051662990770924931793603929464546359033468050476903535087801552, 327123922748415041116022522863173201521528255945289894360585799362306959193311, 95338408534640141043277335080426255160004958387904407042176503676681023424702], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 66, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 66, 2, 1], [8, 6, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 66, 2, 1], [22, 2, 5, 1], [24, 6, 4, 1], [24, 22, 4, 2], [24, 22, 8, 1], [33, 2, 10, 1], [33, 4, 5, 1], [33, 4, 10, 1], [44, 2, 10, 1], [66, 2, 10, 1], [66, 4, 5, 1], [66, 4, 10, 1], [88, 6, 20, 1], [132, 2, 20, 1], [132, 4, 10, 1], [132, 4, 20, 1], [264, 6, 40, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{33}.(C_2^5\\times C_{10})', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 66, 1], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 66, 1], [6, 1, 2], [6, 2, 3], [6, 66, 2], [8, 6, 2], [8, 22, 2], [11, 2, 5], [12, 1, 4], [12, 2, 6], [12, 66, 2], [22, 2, 5], [24, 6, 4], [24, 22, 16], [33, 2, 10], [33, 4, 15], [44, 2, 10], [66, 2, 10], [66, 4, 15], [88, 6, 20], [132, 2, 20], [132, 4, 30], [264, 6, 40]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '132.5', 'commutator_count': 1, 'commutator_label': '66.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 173, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['528.10', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 66, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 66, 2, 1], [8, 6, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 66, 2, 1], [22, 2, 5, 1], [24, 6, 4, 1], [24, 22, 4, 2], [24, 22, 8, 1], [33, 2, 10, 1], [33, 4, 5, 1], [33, 4, 10, 1], [44, 2, 10, 1], [66, 2, 10, 1], [66, 4, 5, 1], [66, 4, 10, 1], [88, 6, 20, 1], [132, 2, 20, 1], [132, 4, 10, 1], [132, 4, 20, 1], [264, 6, 40, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 264, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[4, 0, 20]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '396.19', 'hash': 173, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 6, 11], 'inner_gens': [[1, 10, 48], [41, 2, 480], [1, 1154, 48]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'S_3\\times D_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 150], [4, 60]], 'label': '1584.173', 'linC_count': 1940, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 20, 'linQ_dim': 18, 'linQ_dim_count': 20, 'linR_count': 80, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C132.D6', 'ngens': 7, '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': 36, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 234, 'number_divisions': 36, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 88, 'number_subgroup_classes': 88, 'number_subgroups': 700, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 67], [3, 8], [4, 68], [6, 140], [8, 56], [11, 10], [12, 148], [22, 10], [24, 376], [33, 80], [44, 20], [66, 80], [88, 120], [132, 160], [264, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 10], 'outer_gen_pows': [4, 0, 0, 8], 'outer_gens': [[17, 2, 480], [1, 34, 480], [13, 38, 480], [17, 2, 384]], 'outer_group': '80.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 13, 'outer_perms': [720, 479001600, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 6], [8, 3], [10, 2], [16, 1], [20, 5], [40, 5], [80, 2]], 'representations': {'PC': {'code': 1201423665998983284543726003149937354680150000119, 'gens': [1, 2, 6], 'pres': [7, -2, -2, -2, -2, -3, -3, -11, 84, 141, 36, 422, 58, 1123, 80, 1124, 10092, 166, 35293]}, 'GLZN': {'d': 2, 'p': 110, 'gens': [28226989, 30613023, 1332101, 118459089, 30886461, 58043547, 75207551]}, 'Perm': {'d': 25, 'gens': [25903229683152201817200, 7309585, 6706022400, 11745624, 16148160, 3, 672254861098236159744000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{132}.D_6', 'transitive_degree': 528, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '12.2', '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], 'aut_gens': [[1], [5], [7]], 'aut_group': '4.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [1, 6], '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], [12, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2', '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': 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], [12, 1, 4]], 'center_label': '12.2', 'center_order': 12, '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', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4.1', 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], [12, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 12, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '2.1', '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 12]], 'label': '12.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 3, 'linQ_dim': 4, 'linQ_dim_count': 3, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C12', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 12, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5], [7]], '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': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 1]], 'representations': {'PC': {'code': 3865, 'gens': [1], 'pres': [3, -2, -2, -3, 6, 16]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [20970031]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [619]}, 'Perm': {'d': 7, 'gens': [2400, 4, 744]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
