-
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': 3, 'aut_exponent': 40, 'aut_gen_orders': [8, 4, 2, 5, 5, 4, 10], 'aut_gens': [[1, 2, 20], [10, 81, 4], [90, 73, 16], [5, 38, 80], [9, 42, 20], [13, 42, 20], [9, 54, 40], [9, 78, 20]], 'aut_group': '800.1191', 'aut_hash': 1191, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 800, 'aut_permdeg': 10, 'aut_perms': [370090, 2883024, 806992, 1999297, 2085339, 2015705, 2376125], 'aut_phi_ratio': 20.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 5, 2, 1], [2, 25, 1, 1], [5, 2, 4, 1], [5, 4, 4, 1], [10, 10, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5\\wr C_2', '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': 40, 'autcentquo_group': '800.1191', 'autcentquo_hash': 1191, 'autcentquo_nilpotent': False, 'autcentquo_order': 800, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 5, 2], [2, 25, 1], [5, 2, 4], [5, 4, 4], [10, 10, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '100.13', 'commutator_count': 1, 'commutator_label': '25.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['10.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 5, 1, 2], [2, 25, 1, 1], [5, 2, 2, 2], [5, 4, 2, 2], [10, 10, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 10, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[4, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '100.13', 'hash': 13, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 10, 5], 'inner_gens': [[1, 18, 20], [5, 2, 80], [1, 42, 20]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 100, 'inner_split': False, 'inner_tex': 'D_5^2', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 8], [4, 4]], 'label': '100.13', 'linC_count': 20, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 6, 'linQ_dim': 8, 'linQ_dim_count': 6, 'linR_count': 20, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D5^2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 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': 4, 'number_conjugacy_classes': 16, 'number_divisions': 10, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 24, 'number_subgroups': 124, 'old_label': None, 'order': 100, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 35], [5, 24], [10, 40]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 11], 'outer_gens': [[10, 81, 8], [10, 61, 8]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [2, 13], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4], [8, 2]], 'representations': {'PC': {'code': 413139638799, 'gens': [1, 2, 4], 'pres': [4, -2, -2, -5, -5, 145, 21, 194, 647]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [25977, 1644884, 147908, 1594376]}, 'Perm': {'d': 10, 'gens': [2177183, 2045400, 409056, 1451616]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_5^2', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}
-
gps_conj_classes • Show schema
Hide schema
-
id: 108354257
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 13, 'group_order': 100, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
-
id: 108354265
{'aut_label': '2A', 'centralizer': '5.a1.a1', 'counter': 2, 'group_counter': 13, 'group_order': 100, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 10, 'size': 5}
-
id: 108354266
{'aut_label': '2A', 'centralizer': '5.a1.b1', 'counter': 3, 'group_counter': 13, 'group_order': 100, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1, 'size': 5}
-
id: 108354267
{'aut_label': '2C', 'centralizer': '25.a1.a1', 'counter': 4, 'group_counter': 13, 'group_order': 100, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 39, 'size': 25}
-
id: 108354268
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 13, 'group_order': 100, 'label': '5A1', 'order': 5, 'powers': [6, 1], 'representative': 4, 'size': 2}
-
id: 108354269
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 13, 'group_order': 100, 'label': '5A2', 'order': 5, 'powers': [5, 1], 'representative': 8, 'size': 2}
-
id: 108354270
{'aut_label': '5A1', 'centralizer': '2.a1.b1', 'counter': 7, 'group_counter': 13, 'group_order': 100, 'label': '5B1', 'order': 5, 'powers': [8, 1], 'representative': 40, 'size': 2}
-
id: 108354271
{'aut_label': '5A1', 'centralizer': '2.a1.b1', 'counter': 8, 'group_counter': 13, 'group_order': 100, 'label': '5B2', 'order': 5, 'powers': [7, 1], 'representative': 80, 'size': 2}
-
id: 108354272
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 13, 'group_order': 100, 'label': '5C1', 'order': 5, 'powers': [10, 1], 'representative': 24, 'size': 4}
-
id: 108354258
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 10, 'group_counter': 13, 'group_order': 100, 'label': '5C2', 'order': 5, 'powers': [9, 1], 'representative': 48, 'size': 4}
-
id: 108354259
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 13, 'group_order': 100, 'label': '5D1', 'order': 5, 'powers': [12, 1], 'representative': 44, 'size': 4}
-
id: 108354260
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 13, 'group_order': 100, 'label': '5D2', 'order': 5, 'powers': [11, 1], 'representative': 28, 'size': 4}
-
id: 108354261
{'aut_label': '10A1', 'centralizer': '10.b1.a1', 'counter': 13, 'group_counter': 13, 'group_order': 100, 'label': '10A1', 'order': 10, 'powers': [5, 2], 'representative': 2, 'size': 10}
-
id: 108354262
{'aut_label': '10A1', 'centralizer': '10.b1.a1', 'counter': 14, 'group_counter': 13, 'group_order': 100, 'label': '10A3', 'order': 10, 'powers': [6, 2], 'representative': 6, 'size': 10}
-
id: 108354263
{'aut_label': '10A1', 'centralizer': '10.b1.b1', 'counter': 15, 'group_counter': 13, 'group_order': 100, 'label': '10B1', 'order': 10, 'powers': [7, 3], 'representative': 21, 'size': 10}
-
id: 108354264
{'aut_label': '10A1', 'centralizer': '10.b1.b1', 'counter': 16, 'group_counter': 13, 'group_order': 100, 'label': '10B3', 'order': 10, 'powers': [8, 3], 'representative': 41, 'size': 10}
-
gps_qchar • Show schema
Hide schema
-
id: 3838407
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 3838409
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
-
id: 3838410
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 3838411
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 3838412
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.2a', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
-
id: 3838413
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.2b', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -1, -1, 4, 4, -1, -1, -1, -1, 0, 0, -1, -1], 'schur_index': 1}
-
id: 3838414
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.2c', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -1, -1, 4, 4, -1, -1, -1, -1, 0, 0, 1, 1], 'schur_index': 1}
-
id: 3838415
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.2d', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
-
id: 3838416
{'cdim': 4, 'counter': 9, 'faithful': True, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.4a', 'multiplicity': 2, 'nt': [10, 9], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -2, -2, -2, -2, -2, 3, -2, 3, 0, 0, 0, 0], 'schur_index': 1}
-
id: 3838408
{'cdim': 4, 'counter': 10, 'faithful': True, 'group': '100.13', 'group_order': 100, 'image': None, 'label': '100.13.4b', 'multiplicity': 2, 'nt': [10, 9], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -2, -2, -2, -2, 3, -2, 3, -2, 0, 0, 0, 0], 'schur_index': 1}
-
gps_char • Show schema
Hide schema
-
id: 5261954
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 100, 'label': '100.13.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5261962
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 50, 'label': '100.13.1b', 'nt': [2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 5261963
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 50, 'label': '100.13.1c', 'nt': [2, 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]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 5261964
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 50, 'label': '100.13.1d', 'nt': [2, 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]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5261965
{'center': '10.a1.b1', 'center_index': 10, 'center_order': 10, 'counter': 5, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.b1', 'kernel_order': 10, 'label': '100.13.2a1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
-
id: 5261966
{'center': '10.a1.b1', 'center_index': 10, 'center_order': 10, 'counter': 6, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.b1', 'kernel_order': 10, 'label': '100.13.2a2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
-
id: 5261967
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 7, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 10, 'label': '100.13.2b1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
-
id: 5261968
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 8, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 10, 'label': '100.13.2b2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
-
id: 5261969
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 9, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.b1', 'kernel_order': 5, 'label': '100.13.2c1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
-
id: 5261955
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 10, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.b1', 'kernel_order': 5, 'label': '100.13.2c2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
-
id: 5261956
{'center': '10.a1.b1', 'center_index': 10, 'center_order': 10, 'counter': 11, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 5, 'label': '100.13.2d1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
-
id: 5261957
{'center': '10.a1.b1', 'center_index': 10, 'center_order': 10, 'counter': 12, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 5, 'label': '100.13.2d2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
-
id: 5261958
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.13.4a1', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5261959
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.13.4a2', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5261960
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.13.4b1', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5261961
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '100.13', 'group_counter': 13, 'group_order': 100, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.13.4b2', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
gps_subgroup_search • Show schema
Hide schema
-
id: 60452017
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 100, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '100.13.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 60452028
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 50, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '100.13.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452034
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 50, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '100.13.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 50, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '100.13.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452036
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': True, 'core_order': 25, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '100.13.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
-
id: 60452037
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 60452038
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.5.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.b1', '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': 5, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 60452039
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '100.13.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452040
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': False, 'core_order': 10, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '100.13.10.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452018
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.b1.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': 10, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 60452019
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.b1.b1', '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': 10, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 60452020
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.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': 10, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452021
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.b1', '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': 10, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452022
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.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': 10, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452023
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.13.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.b1', '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': 10, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452024
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 5, 'counter': 16, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '100.13.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452025
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 5, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '100.13.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 60452026
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.b1.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': 20, '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': 0}
-
id: 60452027
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.b1.b1', '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': 20, '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': 0}
-
id: 60452029
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '100.13.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25.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': 25, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
-
id: 60452030
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, '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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 60452031
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.50.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.a1.b1', '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': 50, '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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 60452032
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.13.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.b1.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': 50, '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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 60452033
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.13', 'ambient_counter': 13, 'ambient_order': 100, 'ambient_tex': 'D_5^2', 'central': True, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '100.13.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '100.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], '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: 60452017
{'ambient': '100.13', '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': '100.a1.a1', 'complements': ['100.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '5.a1.a1', '5.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3947, 6218, 5502, 5000, 5156, 5508, 5902, 5000], 'generators': [1, 4, 20, 10], 'label': '100.13.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '100.13', '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': '100.13'}
-
id: 60452018
{'ambient': '100.13', 'aut_centralizer_order': 20, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '10.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '50.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [857, -1, 8227, -1, 778, -1, 6326, -1], 'generators': [10, 4], 'label': '100.13.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452019
{'ambient': '100.13', 'aut_centralizer_order': 20, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '10.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '5.a1.b1'], 'contains': ['20.a1.b1', '50.a1.b1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [857, -1, 5807, -1, 778, -1, 8581, -1], 'generators': [1, 20], 'label': '100.13.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.b1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452020
{'ambient': '100.13', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '50.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '50.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6446, -1, 7249, -1, 5978, -1, 4310, -1], 'generators': [3, 4], 'label': '100.13.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452021
{'ambient': '100.13', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '50.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.b1'], 'contains': ['20.a1.b1', '50.b1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [6446, -1, 3019, -1, 5978, -1, 2268, -1], 'generators': [3, 20], 'label': '100.13.10.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.c1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452022
{'ambient': '100.13', 'aut_centralizer_order': 2, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['20.b1.a1', '50.b1.a1'], 'core': '100.a1.a1', 'coset_action_label': '10T9', 'count': 10, 'diagramx': [9143, -1, 1675, -1, 9400, -1, 1313, -1], 'generators': [3, 24], 'label': '100.13.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1.a1', 'old_label': '10.d1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452023
{'ambient': '100.13', 'aut_centralizer_order': 2, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['20.b1.b1', '50.b1.a1'], 'core': '100.a1.a1', 'coset_action_label': '10T9', 'count': 10, 'diagramx': [9143, -1, 330, -1, 9400, -1, 358, -1], 'generators': [3, 44], 'label': '100.13.10.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1.b1', 'old_label': '10.d1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452024
{'ambient': '100.13', 'aut_centralizer_order': 100, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '2.a1.a1', 'complements': ['5.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.b1', '10.b1.a1', '10.c1.a1'], 'contains': ['100.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3505, 3825, 7249, 3567, 4378, 4610, 5371, 3968], 'generators': [4], 'label': '100.13.20.a1.a1', 'mobius_quo': -1, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.b1'], 'normal_contains': ['100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452025
{'ambient': '100.13', 'aut_centralizer_order': 100, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '2.a1.b1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.b1', '10.c1.b1'], 'contains': ['100.a1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3505, 3825, 3692, 5631, 4378, 4610, 4417, 6032], 'generators': [20], 'label': '100.13.20.a1.b1', 'mobius_quo': -1, 'mobius_sub': -10, 'normal_closure': '20.a1.b1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.b1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452026
{'ambient': '100.13', 'aut_centralizer_order': 50, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.d1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': '20T28', 'count': 2, 'diagramx': [7795, -1, 1002, -1, 7689, -1, 2507, -1], 'generators': [24], 'label': '100.13.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452027
{'ambient': '100.13', 'aut_centralizer_order': 50, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 200, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.d1.b1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': '20T28', 'count': 2, 'diagramx': [7795, -1, 1883, -1, 7689, -1, 1552, -1], 'generators': [44], 'label': '100.13.20.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '20.b1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 60452028
{'ambient': '100.13', 'aut_centralizer_order': 5, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '80.30', 'aut_weyl_index': 10, 'centralizer': '20.a1.a1', 'complements': ['50.a1.b1', '50.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.a1', '10.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1790, 2543, 4426, 8296, 5156, 2813, 4403, 8295], 'generators': [10, 20, 4], 'label': '100.13.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 60452029
{'ambient': '100.13', 'aut_centralizer_order': 16, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.a1.b1'], 'contains': ['50.a1.a1', '50.a1.b1', '50.b1.a1'], 'core': '100.a1.a1', 'coset_action_label': '25T12', 'count': 25, 'diagramx': [4976, -1, 5685, -1, 2667, -1, 7454, -1], 'generators': [1, 10], 'label': '100.13.25.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 60452030
{'ambient': '100.13', 'aut_centralizer_order': 80, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 800, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.b1.a1', '25.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2157, -1, 5623, -1, 2733, -1, 6326, -1], 'generators': [10], 'label': '100.13.50.a1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 60452031
{'ambient': '100.13', 'aut_centralizer_order': 80, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 800, 'centralizer': '5.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.b1', '10.b1.b1', '25.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2157, -1, 6504, -1, 2733, -1, 8011, -1], 'generators': [1], 'label': '100.13.50.a1.b1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '50.a1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 60452032
{'ambient': '100.13', 'aut_centralizer_order': 32, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '10.c1.b1', '10.d1.a1', '10.d1.b1', '25.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5711, -1, 2885, -1, 5978, -1, 3462, -1], 'generators': [3], 'label': '100.13.50.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 60452033
{'ambient': '100.13', 'aut_centralizer_order': None, 'aut_label': '100.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': ['20.a1.a1', '20.a1.b1', '20.b1.a1', '20.b1.b1', '50.a1.a1', '50.a1.b1', '50.b1.a1'], 'contains': [], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4976, 3825, 3558, 4599, 5178, 4610, 4417, 5000], 'generators': [], 'label': '100.13.100.a1.a1', 'mobius_quo': 1, 'mobius_sub': 50, 'normal_closure': '100.a1.a1', 'normal_contained_in': ['20.a1.a1', '20.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 60452034
{'ambient': '100.13', 'aut_centralizer_order': 5, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '80.30', 'aut_weyl_index': 10, 'centralizer': '20.a1.b1', 'complements': ['50.a1.a1', '50.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.b1', '10.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1790, 2543, 6944, 1704, 5156, 2813, 8581, 1705], 'generators': [1, 4, 20], 'label': '100.13.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 60452035
{'ambient': '100.13', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 1, 'centralizer': '100.a1.a1', 'complements': ['50.a1.a1', '50.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.c1.a1', '10.c1.b1', '10.d1.a1', '10.d1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7475, 7457, 2995, 5000, 7711, 8251, 2573, 5000], 'generators': [3, 20, 4], 'label': '100.13.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 60452036
{'ambient': '100.13', 'aut_centralizer_order': 25, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 25, 'centralizer': '4.a1.a1', 'complements': ['25.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['20.a1.a1', '20.a1.b1', '20.b1.a1', '20.b1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6078, 5106, 3692, 5000, 7689, 6454, 3289, 5000], 'generators': [4, 20], 'label': '100.13.4.a1.a1', 'mobius_quo': 1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['20.a1.a1', '20.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 60452037
{'ambient': '100.13', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '50.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.b1', '10.b1.a1', '10.c1.a1', '25.a1.a1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3358, -1, 8387, -1, 2644, -1, 7082, -1], 'generators': [1, 4, 10], 'label': '100.13.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452038
{'ambient': '100.13', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '50.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.b1', '10.c1.b1', '25.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3358, -1, 5208, -1, 2644, -1, 5902, -1], 'generators': [1, 20, 10], 'label': '100.13.5.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '5.a1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452039
{'ambient': '100.13', 'aut_centralizer_order': 20, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '10.a1.b1', 'complements': ['10.a1.b1', '10.c1.a1', '10.d1.a1', '10.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.b1'], 'contains': ['20.a1.b1', '50.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2819, 2628, 4364, 7006, 4378, 2813, 5265, 7751], 'generators': [10, 20], 'label': '100.13.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 60452040
{'ambient': '100.13', 'aut_centralizer_order': 20, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 40, 'centralizer': '10.a1.a1', 'complements': ['10.a1.a1', '10.c1.b1', '10.d1.a1', '10.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '50.a1.b1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2819, 2628, 9670, 2307, 4378, 2813, 9642, 2249], 'generators': [1, 4], 'label': '100.13.10.a1.b1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.b1', 'normal_contained_in': ['2.a1.b1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.b1', 'projective_image': '100.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
