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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.4656', 'ambient_counter': 4656, 'ambient_order': 960, 'ambient_tex': 'C_2\\times C_{30}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.4656.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.60', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 60, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.4656', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.f1.a1', '120.g1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.b1.c1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 480], 'label': '960.4656.240.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1'], 'normal_contains': ['480.b1.a1', '480.b1.c1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', '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': 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]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': '80.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 4, 12, 4, 4, 12, 12, 12], 'aut_gens': [[1, 4, 32], [481, 164, 354], [17, 340, 752], [489, 6, 370], [489, 190, 624], [25, 182, 354], [505, 492, 240], [497, 188, 34], [497, 812, 48], [507, 180, 242]], 'aut_group': None, 'aut_hash': 7714637356874725850, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 68, 'aut_perms': [742973484890006729131960506157445022987864351060347017852721123833349405385454465591619067629546, 1110964534086740907442082273593628335057163012655776361989119785825462546622194123114577895866352, 936099832311306409691809023897268461842067606267982292961040131095092684362624026274128148421411, 922890045500578578366959552748377866111214682681418424595726504668961742580849161579407551226898, 1131024067047135920069000847617491084733799700585496751480807799315560686032202347768857269288276, 1739156889202860984848129528994232755482617324124522637829542880479822182031897780239611763195038, 1654932123801562553514719552260801399844436618773835439683652318997994775574086681795128023226585, 1654902610487106582660597071970146636820010990601969967354767123261310915632525274686027058170979, 2169868347734496613352062210564749374560829513304650278874352063362167448465786285089883189011736], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 4, 1], [4, 12, 4, 1], [5, 1, 4, 1], [6, 2, 1, 3], [6, 2, 4, 1], [8, 6, 8, 1], [10, 1, 4, 3], [10, 1, 16, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 4, 8, 1], [15, 2, 4, 1], [20, 2, 4, 2], [20, 2, 8, 1], [20, 4, 16, 1], [20, 12, 16, 1], [30, 2, 4, 3], [30, 2, 16, 1], [40, 6, 32, 1], [60, 4, 4, 2], [60, 4, 8, 1], [60, 4, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^5.C_2^6.C_2^2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 7177616586376182635, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5.C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 12, 4], [5, 1, 4], [6, 2, 7], [8, 6, 8], [10, 1, 28], [12, 4, 12], [15, 2, 4], [20, 2, 16], [20, 4, 16], [20, 12, 16], [30, 2, 28], [40, 6, 32], [60, 4, 48]], 'center_label': '40.14', 'center_order': 40, 'central_product': True, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4656, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1], ['96.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 2, 1, 1], [4, 2, 1, 4], [4, 4, 2, 2], [4, 12, 2, 2], [5, 1, 4, 1], [6, 2, 1, 7], [8, 6, 2, 4], [10, 1, 4, 7], [12, 4, 1, 4], [12, 4, 4, 2], [15, 2, 4, 1], [20, 2, 4, 4], [20, 4, 8, 2], [20, 12, 8, 2], [30, 2, 4, 7], [40, 6, 8, 4], [60, 4, 4, 4], [60, 4, 16, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10416, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.45', 'hash': 4656, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 28, 32], [9, 4, 352], [1, 644, 32]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 80], [2, 140], [4, 20]], 'label': '960.4656', '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': 'C2*C30.D8', 'ngens': 8, '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': 40, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 240, 'number_divisions': 68, 'number_normal_subgroups': 158, 'number_subgroup_autclasses': 152, 'number_subgroup_classes': 260, 'number_subgroups': 560, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 72], [5, 4], [6, 14], [8, 48], [10, 28], [12, 48], [15, 8], [20, 288], [30, 56], [40, 192], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 4, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 8, 8], 'outer_gens': [[505, 22, 626], [507, 6, 242], [3, 500, 242], [25, 6, 226], [25, 502, 226], [25, 20, 626], [25, 4, 626]], 'outer_group': None, 'outer_hash': 9087809238134369064, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 18, 'outer_perms': [127382520, 377917979459767, 377924246380936, 1067062411663921, 377917979806222, 753220523064240, 753220523064247], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6.C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 22], [8, 12], [16, 14]], 'representations': {'PC': {'code': 13014065602267708714086920924598954164231, 'gens': [1, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 16, 674, 66, 771, 91, 4245, 141, 9878, 222]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [15673879, 683409, 806761, 2233789, 6133257, 685345, 49875609, 44295745]}, 'Perm': {'d': 22, 'gens': [53780336661602074320, 3669840, 51597817679544151680, 33, 3669120, 109750244591699712000, 163613728419837696000, 6706022400]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{30}.D_8', 'transitive_degree': 960, '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': '20.5', '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, 4, 12], 'aut_gens': [[1, 2, 16], [5, 6, 16], [1, 10, 16], [1, 2, 176], [1, 2, 208], [13, 162, 64]], 'aut_group': '384.18344', 'aut_hash': 18344, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 13, 'aut_perms': [6, 1, 39916801, 811566, 518918694], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 4, 2, 1], [8, 6, 2, 1], [10, 1, 4, 1], [10, 4, 4, 1], [10, 12, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [20, 2, 4, 1], [30, 2, 4, 1], [30, 4, 8, 1], [40, 6, 8, 1], [60, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times D_4\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 1], [2, 12, 1], [3, 2, 1], [4, 2, 1], [5, 1, 4], [6, 2, 1], [6, 4, 2], [8, 6, 2], [10, 1, 4], [10, 4, 4], [10, 12, 4], [12, 4, 1], [15, 2, 4], [20, 2, 4], [30, 2, 4], [30, 4, 8], [40, 6, 8], [60, 4, 4]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 60, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['48.15', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 4, 2, 1], [8, 6, 2, 1], [10, 1, 4, 1], [10, 4, 4, 1], [10, 12, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [20, 2, 4, 1], [30, 2, 4, 1], [30, 4, 8, 1], [40, 6, 8, 1], [60, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 120, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '60.11', 'hash': 60, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 14, 16], [5, 2, 176], [1, 82, 16]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 20], [2, 35], [4, 5]], 'label': '240.60', 'linC_count': 196, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 64, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:D8', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 60, 'number_divisions': 20, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 44, 'number_subgroup_classes': 44, 'number_subgroups': 112, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 17], [3, 2], [4, 2], [5, 4], [6, 10], [8, 12], [10, 68], [12, 4], [15, 8], [20, 8], [30, 40], [40, 48], [60, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 4, 0], 'outer_gens': [[1, 10, 16], [13, 2, 16], [1, 2, 208]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 7], [8, 3], [16, 3]], 'representations': {'PC': {'code': 27575784872951778074631, 'gens': [1, 2, 5], 'pres': [6, -2, -2, -2, -2, -3, -5, 169, 31, 218, 50, 2650, 118]}, 'GLZN': {'d': 2, 'p': 62, 'gens': [238389, 11201463, 359446, 14538069, 7573951, 1052508]}, 'Perm': {'d': 16, 'gens': [87178296556, 2813, 522910080, 13307, 19342, 1394852659200]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:D_8', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
