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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26620.g', 'ambient_counter': 7, 'ambient_order': 26620, 'ambient_tex': 'C_{11}\\times C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 242, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26620.g.22.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.18', 'subgroup_hash': 18, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:C_{110}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '26620.g', 'aut_centralizer_order': None, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '11.b1'], 'contains': ['44.b1', '110.a1', '242.a1', '242.b1'], 'core': '110.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7911, -1, 7415, -1], 'generators': [13310, 10, 2420, 22], 'label': '26620.g.22.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1', 'old_label': '22.c1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '110.6', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [10, 110], 'aut_gens': [[1, 55], [1, 385], [261, 55]], 'aut_group': '1100.29', 'aut_hash': 29, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1100, 'aut_permdeg': 21, 'aut_perms': [11934801876393871442, 10425726170149285396], 'aut_phi_ratio': 2.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 11, 1, 4], [10, 11, 1, 4], [11, 1, 10, 1], [11, 5, 2, 1], [11, 5, 20, 1], [22, 1, 10, 1], [22, 5, 2, 1], [22, 5, 20, 1], [55, 11, 10, 4], [110, 11, 10, 4]], 'aut_supersolvable': True, 'aut_tex': 'C_{10}\\times F_{11}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [5, 11, 4], [10, 11, 4], [11, 1, 10], [11, 5, 22], [22, 1, 10], [22, 5, 22], [55, 11, 40], [110, 11, 40]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '55.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 18, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1], ['55.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 11, 4, 1], [10, 11, 4, 1], [11, 1, 10, 1], [11, 5, 2, 1], [11, 5, 10, 2], [22, 1, 10, 1], [22, 5, 2, 1], [22, 5, 10, 2], [55, 11, 40, 1], [110, 11, 40, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 864, 'exponent': 110, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[5, 0, 20]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1210.18', 'hash': 18, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 55, 'inner_gen_orders': [5, 11], 'inner_gens': [[1, 495], [771, 55]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 55, 'inner_split': True, 'inner_tex': 'C_{11}:C_5', 'inner_used': [1, 2], 'irrC_degree': 5, 'irrQ_degree': 50, 'irrQ_dim': 50, 'irrR_degree': 10, 'irrep_stats': [[1, 110], [5, 44]], 'label': '1210.18', 'linC_count': 20, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 3, 'linQ_dim': 20, 'linQ_dim_count': 3, 'linR_count': 10, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11:C110', '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': 24, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 154, 'number_divisions': 14, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 20, 'number_subgroups': 76, 'old_label': None, 'order': 1210, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [5, 44], [10, 44], [11, 120], [22, 120], [55, 440], [110, 440]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [53, 0], 'outer_gens': [[21, 275], [41, 1155]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [40320, 753], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 5, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [10, 4], [40, 2], [50, 4]], 'representations': {'PC': {'code': 72593129636373909, 'gens': [1, 3], 'pres': [4, -5, -11, -2, -11, 20, 5942, 34, 15843]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1449881381, 2296050935, 2143735230, 418103038]}, 'Perm': {'d': 24, 'gens': [1, 1233866237413653043200, 522956310, 28258547372470250035200]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [110], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}:C_{110}', 'transitive_degree': 110, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '220.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [10, 20, 10, 10, 10], 'aut_gens': [[1, 110, 1210], [9401, 12540, 15730], [15329, 5610, 18480], [16079, 4950, 25630], [7589, 5060, 11330], [9501, 550, 6050]], 'aut_group': None, 'aut_hash': 7721490425071638488, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 484000, 'aut_permdeg': 494, 'aut_perms': 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'aut_phi_ratio': 50.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 2, 1], [5, 121, 2, 2], [10, 121, 2, 2], [10, 121, 4, 2], [11, 1, 10, 1], [11, 10, 2, 1], [11, 10, 10, 1], [11, 10, 20, 1], [11, 10, 100, 1], [22, 1, 10, 1], [22, 10, 2, 1], [22, 10, 10, 1], [22, 10, 20, 1], [22, 10, 100, 1], [22, 121, 20, 1], [55, 121, 20, 2], [110, 121, 20, 2], [110, 121, 40, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_5.C_{10}^2.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '20.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 20, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [5, 121, 4], [10, 121, 12], [11, 1, 10], [11, 10, 132], [22, 1, 10], [22, 10, 132], [22, 121, 20], [55, 121, 40], [110, 121, 120]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '1210.10', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['1210.10', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [5, 121, 4, 1], [10, 121, 4, 3], [11, 1, 10, 1], [11, 10, 1, 2], [11, 10, 5, 2], [11, 10, 10, 12], [22, 1, 10, 1], [22, 10, 1, 2], [22, 10, 5, 2], [22, 10, 10, 12], [22, 121, 10, 2], [55, 121, 40, 1], [110, 121, 40, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 432, 'exponent': 110, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 0, 100]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '26620.g', 'hash': 2427916003340982652, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11, 11], 'inner_gens': [[1, 2640, 20570], [25301, 110, 1210], [7261, 110, 1210]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 1210, 'inner_split': False, 'inner_tex': 'C_{11}:F_{11}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 100, 'irrQ_dim': 100, 'irrR_degree': 20, 'irrep_stats': [[1, 220], [10, 264]], 'label': '26620.g', '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': 'C11*C22:F11', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 484, 'number_divisions': 48, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 64, 'number_subgroup_classes': 148, 'number_subgroups': 3500, 'old_label': None, 'order': 26620, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [5, 484], [10, 1452], [11, 1330], [22, 3750], [55, 4840], [110, 14520]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10, 10], 'outer_gen_pows': [0, 5, 0, 0], 'outer_gens': [[21, 15620, 1210], [89, 25080, 4180], [13411, 22880, 15730], [1, 19580, 1210]], 'outer_group': '400.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 400, 'outer_permdeg': 18, 'outer_perms': [6227020800, 39916800, 355687428504960, 1307674368037], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4], [10, 8], [40, 4], [50, 4], [100, 24]], 'representations': {'PC': {'code': '528813456519975220209744021034204504538003039909', 'gens': [1, 4, 5], 'pres': [6, -2, -5, -11, -11, -2, -11, 12, 67, 63363, 237609, 617104, 54460, 88, 522725, 130691]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [25960483174700722, 18721992341619836, 20595883671717277, 1754382938723032, 32182222080390795, 41772741070013040]}, 'Perm': {'d': 35, 'gens': [3660370560, 1, 1528272406707723354336080590416745728000, 1182569150567880324329024375814087936000, 70824919749089501245204251625763635200, 296599418055876144539989709234376192001]}}, 'schur_multiplier': [22], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 110], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\times C_{22}:F_{11}', 'transitive_degree': 220, 'wreath_data': None, 'wreath_product': False}
