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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.599', 'ambient_counter': 599, 'ambient_order': 960, 'ambient_tex': '(C_2\\times C_4):C_{120}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.599.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.85', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 85, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}\\times \\OD_{16}', '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': '960.599', 'aut_centralizer_order': 2048, 'aut_label': '240.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '80.c1.b1', '120.a1.a1', '120.g1.b1'], 'contains': ['480.b1.a1', '480.c1.b1', '480.e1.a1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7678, 8271, 3026, 5567, 2315, 7520, 2921, 2528], 'generators': [2, 496], 'label': '960.599.240.c1.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '240.c1.b1', 'normal_contained_in': ['48.c1.b1', '80.c1.b1', '120.a1.a1'], 'normal_contains': ['480.e1.a1', '480.c1.b1', '480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.c1.b1', 'projective_image': '240.85', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.85', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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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': '480.199', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 4, 32], [3, 21, 736], [27, 13, 544], [11, 510, 352], [507, 15, 32], [481, 509, 544], [483, 5, 352], [25, 13, 928]], 'aut_group': None, 'aut_hash': 8378141475050381970, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 38, 'aut_perms': [279081390505661332507597846439845827755159026, 213238580288057117964582644741068966272756438, 3972481994649140320886023666952141298633503, 1597903061244282574927964339297290546268456, 216542647796724067645951606356058798052382707, 518050366355233099515583957599317730136096, 406561756176300230788995379798124055057953173], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [3, 1, 2, 1], [4, 1, 4, 2], [4, 2, 8, 1], [5, 1, 4, 1], [6, 1, 2, 3], [6, 1, 4, 2], [8, 2, 16, 1], [10, 1, 4, 3], [10, 1, 8, 2], [12, 1, 8, 2], [12, 2, 16, 1], [15, 1, 8, 1], [20, 1, 16, 2], [20, 2, 32, 1], [24, 2, 32, 1], [30, 1, 8, 3], [30, 1, 16, 2], [40, 2, 64, 1], [60, 1, 32, 2], [60, 2, 64, 1], [120, 2, 128, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^8.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 9045006922249749083, 'autcent_nilpotent': True, 'autcent_order': 2048, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_4\\times C_2^4.C_2^4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [4, 1, 8], [4, 2, 8], [5, 1, 4], [6, 1, 14], [8, 2, 16], [10, 1, 28], [12, 1, 16], [12, 2, 16], [15, 1, 8], [20, 1, 32], [20, 2, 32], [24, 2, 32], [30, 1, 56], [40, 2, 64], [60, 1, 64], [60, 2, 64], [120, 2, 128]], 'center_label': '240.185', 'center_order': 240, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, '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': 599, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['5.1', 1], ['64.17', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 4], [4, 2, 2, 4], [5, 1, 4, 1], [6, 1, 2, 7], [8, 2, 4, 4], [10, 1, 4, 7], [12, 1, 4, 4], [12, 2, 4, 4], [15, 1, 8, 1], [20, 1, 8, 4], [20, 2, 8, 4], [24, 2, 8, 4], [30, 1, 8, 7], [40, 2, 16, 4], [60, 1, 16, 4], [60, 2, 16, 4], [120, 2, 32, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 72, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '60.13', 'hash': 599, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1], 'inner_gens': [[1, 484, 32], [481, 4, 32], [1, 4, 32]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 480], [2, 120]], 'label': '960.599', '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*C4):C120', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, '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': 52, 'number_conjugacy_classes': 600, 'number_divisions': 80, 'number_normal_subgroups': 164, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 236, 'number_subgroups': 308, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [5, 4], [6, 14], [8, 32], [10, 28], [12, 48], [15, 8], [20, 96], [24, 64], [30, 56], [40, 128], [60, 192], [120, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 4, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 1, 0], 'outer_gens': [[1, 14, 928], [507, 7, 352], [1, 22, 544], [27, 6, 736], [483, 21, 32], [491, 494, 352]], 'outer_group': None, 'outer_hash': 6604407904945055806, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 18, 'outer_perms': [3031, 6354062504, 1108907864077015, 754534464747174, 357001369428450, 357001456858833], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6.C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [4, 8, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 14], [4, 20], [8, 20], [16, 16], [32, 6]], 'representations': {'PC': {'code': 40395156529929164659332840488967, 'gens': [1, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 16, 11618, 66, 91, 141, 222]}, 'GLZN': {'d': 2, 'p': 44, 'gens': [2486917, 1959255, 1127105, 766665, 85669, 1487589, 1788885, 86153]}, 'Perm': {'d': 24, 'gens': [28260967468524015012480, 29384968553371851840000, 10080, 96, 56205024193684574208000, 83329461136203646291200, 110310223113171873792000, 2878327872000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 120], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_4):C_{120}', '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': '120.31', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 4, 4], 'aut_gens': [[1, 2], [1, 82], [1, 182], [121, 62], [1, 154], [121, 123]], 'aut_group': '128.2154', 'aut_hash': 2154, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 128, 'aut_permdeg': 12, 'aut_perms': [87096240, 40279681, 87091327, 5335, 119755441], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 1, 2, 1], [6, 2, 2, 1], [8, 2, 4, 1], [10, 1, 4, 1], [10, 2, 4, 1], [12, 1, 4, 1], [12, 2, 2, 1], [15, 1, 8, 1], [20, 1, 8, 1], [20, 2, 4, 1], [24, 2, 8, 1], [30, 1, 8, 1], [30, 2, 8, 1], [40, 2, 16, 1], [60, 1, 16, 1], [60, 2, 8, 1], [120, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.260', 'autcent_hash': 260, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [3, 1, 2], [4, 1, 2], [4, 2, 1], [5, 1, 4], [6, 1, 2], [6, 2, 2], [8, 2, 4], [10, 1, 4], [10, 2, 4], [12, 1, 4], [12, 2, 2], [15, 1, 8], [20, 1, 8], [20, 2, 4], [24, 2, 8], [30, 1, 8], [30, 2, 8], [40, 2, 16], [60, 1, 16], [60, 2, 8], [120, 2, 32]], 'center_label': '60.4', 'center_order': 60, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', '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': 85, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.6', 1], ['3.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 1, 2, 1], [6, 2, 2, 1], [8, 2, 2, 2], [10, 1, 4, 1], [10, 2, 4, 1], [12, 1, 4, 1], [12, 2, 2, 1], [15, 1, 8, 1], [20, 1, 8, 1], [20, 2, 4, 1], [24, 2, 4, 2], [30, 1, 8, 1], [30, 2, 8, 1], [40, 2, 8, 2], [60, 1, 16, 1], [60, 2, 8, 1], [120, 2, 16, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 144, 'exponent': 120, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[2, 0, 16]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '60.13', 'hash': 85, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 122], [121, 2]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 4, 'irrep_stats': [[1, 120], [2, 30]], 'label': '240.85', 'linC_count': 16, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 16, 'linQ_dim': 10, 'linQ_dim_count': 16, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C15*OD16', 'ngens': 6, 'nilpotency_class': 2, 'nilpotent': True, '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': 24, 'number_characteristic_subgroups': 28, 'number_conjugacy_classes': 150, 'number_divisions': 28, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 40, 'number_subgroups': 44, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [5, 4], [6, 6], [8, 8], [10, 12], [12, 8], [15, 8], [20, 16], [24, 16], [30, 24], [40, 32], [60, 32], [120, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 123], [1, 182], [1, 82], [1, 194]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 7], [8, 7], [16, 3], [32, 1]], 'representations': {'PC': {'code': 313553381480705810439, 'gens': [1, 2], 'pres': [6, -2, -2, -2, -2, -3, -5, 1465, 31, 50, 69, 118]}, 'GLFp': {'d': 2, 'p': 61, 'gens': [3843, 11349061, 453964]}, 'Perm': {'d': 16, 'gens': [9703614412800, 40279680, 10080, 96, 4097506694400, 1313941668480]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 60], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}\\times \\OD_{16}', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
