-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 1640, 'aut_gen_orders': [40, 41], 'aut_gens': [[1, 5], [1, 110], [31, 5]], 'aut_group': '1640.47', 'aut_hash': 47, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1640, 'aut_permdeg': 41, 'aut_perms': [29313887403177185229066573544696381698321866316956, 12865133555059837560152831460106004181239386686674], 'aut_phi_ratio': 10.25, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 41, 1, 4], [41, 5, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{41}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1640, 'autcentquo_group': '1640.47', 'autcentquo_hash': 47, 'autcentquo_nilpotent': False, 'autcentquo_order': 1640, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{41}', 'cc_stats': [[1, 1, 1], [5, 41, 4], [41, 5, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '205.1', 'commutator_count': 1, 'commutator_label': '41.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['5.1', '41.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 41, 4, 1], [41, 5, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 205, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 5, 41], 'factors_of_order': [5, 41], 'faithful_reps': [[5, 0, 8]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '205.1', 'hash': 1, 'hyperelementary': 5, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 205, 'inner_gen_orders': [5, 41], 'inner_gens': [[1, 50], [161, 5]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 205, 'inner_split': True, 'inner_tex': 'C_{41}:C_5', 'inner_used': [1, 2], 'irrC_degree': 5, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 10, 'irrep_stats': [[1, 5], [5, 8]], 'label': '205.1', 'linC_count': 8, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 40, 'linQ_degree_count': 1, 'linQ_dim': 40, 'linQ_dim_count': 1, 'linR_count': 4, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C41:C5', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 13, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 44, 'old_label': None, 'order': 205, 'order_factorization_type': 11, 'order_stats': [[1, 1], [5, 164], [41, 40]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [8], 'outer_gen_pows': [4], 'outer_gens': [[1, 35]], 'outer_group': '8.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 8, 'outer_perms': [5913], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_8', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 41, 'pgroup': 0, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [40, 1]], 'representations': {'PC': {'code': 60959, 'gens': [1, 2], 'pres': [2, -5, -41, 201]}, 'GLFp': {'d': 2, 'p': 41, 'gens': [68963, 1240615]}, 'Perm': {'d': 41, 'gens': [193380446544193151050670286765040239042532465176, 32636611329915909373824450783844635770880000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{41}:C_5', 'transitive_degree': 41, 'wreath_data': None, 'wreath_product': False}
-
gps_conj_classes • Show schema
Hide schema
-
id: 109205867
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 205, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
-
id: 109205872
{'aut_label': '5A1', 'centralizer': '41.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 205, 'label': '5A1', 'order': 5, 'powers': [4, 1, 2], 'representative': 116, 'size': 41}
-
id: 109205873
{'aut_label': '5A-1', 'centralizer': '41.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 205, 'label': '5A-1', 'order': 5, 'powers': [5, 1, 3], 'representative': 54, 'size': 41}
-
id: 109205874
{'aut_label': '5A2', 'centralizer': '41.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 205, 'label': '5A2', 'order': 5, 'powers': [3, 1, 4], 'representative': 37, 'size': 41}
-
id: 109205875
{'aut_label': '5A-2', 'centralizer': '41.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 205, 'label': '5A-2', 'order': 5, 'powers': [2, 1, 5], 'representative': 58, 'size': 41}
-
id: 109205876
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 205, 'label': '41A1', 'order': 41, 'powers': [8, 9, 1], 'representative': 5, 'size': 5}
-
id: 109205877
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 205, 'label': '41A-1', 'order': 41, 'powers': [9, 8, 1], 'representative': 20, 'size': 5}
-
id: 109205878
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 205, 'label': '41A2', 'order': 41, 'powers': [7, 6, 1], 'representative': 10, 'size': 5}
-
id: 109205879
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 205, 'label': '41A-2', 'order': 41, 'powers': [6, 7, 1], 'representative': 25, 'size': 5}
-
id: 109205868
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 205, 'label': '41A3', 'order': 41, 'powers': [12, 13, 1], 'representative': 15, 'size': 5}
-
id: 109205869
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 205, 'label': '41A-3', 'order': 41, 'powers': [13, 12, 1], 'representative': 55, 'size': 5}
-
id: 109205870
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 205, 'label': '41A6', 'order': 41, 'powers': [11, 10, 1], 'representative': 30, 'size': 5}
-
id: 109205871
{'aut_label': '41A1', 'centralizer': '5.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 205, 'label': '41A-6', 'order': 41, 'powers': [10, 11, 1], 'representative': 75, 'size': 5}
-
gps_qchar • Show schema
Hide schema
-
id: 4185010
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '205.1', 'group_order': 205, 'image': None, 'label': '205.1.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4185011
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '205.1', 'group_order': 205, 'image': None, 'label': '205.1.1b', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
-
id: 4185012
{'cdim': 5, 'counter': 3, 'faithful': True, 'group': '205.1', 'group_order': 205, 'image': None, 'label': '205.1.5a', 'multiplicity': 8, 'nt': [41, 4], 'qdim': 40, 'qvalues': [40, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
-
gps_char • Show schema
Hide schema
-
id: 6113564
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 205, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 205, 'label': '205.1.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 6113569
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 205, 'counter': 2, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 41, 'label': '205.1.1b1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 6113570
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 205, 'counter': 3, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 41, 'label': '205.1.1b2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 6113571
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 205, 'counter': 4, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 41, 'label': '205.1.1b3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 6113572
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 205, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 41, 'label': '205.1.1b4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 6113573
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a1', 'nt': [41, 4], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]]]}
-
id: 6113574
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a2', 'nt': [41, 8], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]]]}
-
id: 6113575
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a3', 'nt': [41, 4], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]]]}
-
id: 6113576
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a4', 'nt': [41, 8], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]]]}
-
id: 6113565
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a5', 'nt': [41, 4], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]]]}
-
id: 6113566
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a6', 'nt': [41, 8], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]]]}
-
id: 6113567
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a7', 'nt': [41, 4], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]]]}
-
id: 6113568
{'center': '205.a1.a1', 'center_index': 205, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 41, 'dim': 5, 'faithful': True, 'field': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'group': '205.1', 'group_counter': 1, 'group_order': 205, 'image': None, 'image_isoclass': '205.1', 'image_order': 205, 'indicator': 0, 'kernel': '205.a1.a1', 'kernel_order': 1, 'label': '205.1.5a8', 'nt': [41, 8], 'q_character': None, 'values': [[[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, 8], [1, 9], [1, -20], [1, -2]], [[1, 1], [1, 10], [1, 16], [1, 18], [1, -4]], [[1, 11], [1, 12], [1, -13], [1, -7], [1, -3]], [[1, 15], [1, -19], [1, -17], [1, -14], [1, -6]], [[1, 3], [1, 7], [1, 13], [1, -12], [1, -11]], [[1, 4], [1, -18], [1, -16], [1, -10], [1, -1]], [[1, 6], [1, 14], [1, 17], [1, 19], [1, -15]], [[1, 2], [1, 20], [1, -9], [1, -8], [1, -5]]]}
-
gps_subgroup_search • Show schema
Hide schema
-
id: 63772774
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '205.1', 'ambient_counter': 1, 'ambient_order': 205, 'ambient_tex': 'C_{41}:C_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 205, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 205, 'label': '205.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '205.1', 'subgroup_hash': 1, 'subgroup_order': 205, 'subgroup_tex': 'C_{41}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 63772775
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '205.1', 'ambient_counter': 1, 'ambient_order': 205, 'ambient_tex': 'C_{41}:C_5', 'central': False, 'central_factor': False, 'centralizer_order': 41, 'characteristic': True, 'core_order': 41, 'counter': 2, 'cyclic': True, 'direct': False, 'hall': 41, 'label': '205.1.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': True, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '41.1', 'subgroup_hash': 1, 'subgroup_order': 41, 'subgroup_tex': 'C_{41}', 'supersolvable': True, 'sylow': 41}
-
id: 63772776
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '205.1', 'ambient_counter': 1, 'ambient_order': 205, 'ambient_tex': 'C_{41}:C_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '205.1.41.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '41.a1.a1', 'outer_equivalence': False, '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': 41, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
-
id: 63772777
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '205.1', 'ambient_counter': 1, 'ambient_order': 205, 'ambient_tex': 'C_{41}:C_5', 'central': True, 'central_factor': False, 'centralizer_order': 205, 'characteristic': True, 'core_order': 1, 'counter': 4, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '205.1.205.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '205.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '205.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 205, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{41}:C_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C2'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
-
gps_subgroup_data • Show schema
Hide schema
-
id: 63772774
{'ambient': '205.1', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '205.a1.a1', 'complements': ['205.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1', '41.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3557, 5000, 4073, 5000, 5282, 5000, 4718, 5000], 'generators': [1, 5], 'label': '205.1.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '205.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '205.1'}
-
id: 63772775
{'ambient': '205.1', 'aut_centralizer_order': 41, 'aut_label': '5.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '40.2', 'aut_weyl_index': 41, 'centralizer': '5.a1.a1', 'complements': ['41.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['205.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2852, 5000, 7460, 5000, 2465, 5000, 7535, 5000], 'generators': [5], 'label': '205.1.5.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['205.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '205.1', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
-
id: 63772776
{'ambient': '205.1', 'aut_centralizer_order': 40, 'aut_label': '41.a1', 'aut_quo_index': None, 'aut_stab_index': 41, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1640, 'centralizer': '41.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['205.a1.a1'], 'core': '205.a1.a1', 'coset_action_label': '41T4', 'count': 41, 'diagramx': [7148, -1, 2540, -1, 8099, -1, 1901, -1], 'generators': [1], 'label': '205.1.41.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '41.a1.a1', 'old_label': '41.a1.a1', 'projective_image': '205.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '41.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 63772777
{'ambient': '205.1', 'aut_centralizer_order': None, 'aut_label': '205.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '41.a1.a1'], 'contains': [], 'core': '205.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6162, 5000, 4879, 5000, 5282, 5000, 4718, 5000], 'generators': [], 'label': '205.1.205.a1.a1', 'mobius_quo': 1, 'mobius_sub': 41, 'normal_closure': '205.a1.a1', 'normal_contained_in': ['5.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '205.a1.a1', 'projective_image': '205.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '205.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
