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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 20, 5], 'aut_gens': [[1, 4, 20], [1, 12, 20], [13, 4, 60], [21, 4, 20]], 'aut_group': '400.205', 'aut_hash': 205, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 400, 'aut_permdeg': 10, 'aut_perms': [18, 50515, 454320], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [4, 25, 1, 2], [5, 2, 2, 1], [5, 4, 1, 1], [5, 4, 4, 1], [10, 10, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_5^2', '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': 20, 'autcentquo_group': '400.205', 'autcentquo_hash': 205, 'autcentquo_nilpotent': False, 'autcentquo_order': 400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5^2', 'cc_stats': [[1, 1, 1], [2, 5, 1], [4, 25, 2], [5, 2, 2], [5, 4, 5], [10, 10, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '100.10', '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': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [4, 25, 2, 1], [5, 2, 2, 1], [5, 4, 1, 1], [5, 4, 4, 1], [10, 10, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 20, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '100.10', 'hash': 10, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [4, 5, 5], 'inner_gens': [[1, 8, 80], [17, 4, 20], [41, 4, 20]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 100, 'inner_split': True, 'inner_tex': 'C_5:F_5', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 4], [4, 5]], 'label': '100.10', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C5:F5', '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': 8, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 13, 'number_divisions': 7, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 13, 'number_subgroup_classes': 13, 'number_subgroups': 56, 'old_label': None, 'order': 100, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 5], [4, 50], [5, 24], [10, 20]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[1, 4, 60]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 3], [16, 1]], 'representations': {'PC': {'code': 1970081001743, 'gens': [1, 3, 4], 'pres': [4, -2, -2, -5, -5, 8, 98, 102, 1283]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [118869, 517634, 1786579, 851419]}, 'Perm': {'d': 10, 'gens': [46087, 90720, 37, 493920]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5:F_5', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 108354234
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10, 'group_order': 100, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 108354239
{'aut_label': '2A', 'centralizer': '5.a1.a1', 'counter': 2, 'group_counter': 10, 'group_order': 100, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2, 'size': 5}
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id: 108354240
{'aut_label': '4A1', 'centralizer': '25.a1.a1', 'counter': 3, 'group_counter': 10, 'group_order': 100, 'label': '4A1', 'order': 4, 'powers': [2, 3], 'representative': 97, 'size': 25}
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id: 108354241
{'aut_label': '4A-1', 'centralizer': '25.a1.a1', 'counter': 4, 'group_counter': 10, 'group_order': 100, 'label': '4A-1', 'order': 4, 'powers': [2, 4], 'representative': 95, 'size': 25}
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id: 108354242
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 10, 'group_order': 100, 'label': '5A1', 'order': 5, 'powers': [6, 1], 'representative': 40, 'size': 2}
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id: 108354243
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 10, 'group_order': 100, 'label': '5A2', 'order': 5, 'powers': [5, 1], 'representative': 80, 'size': 2}
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id: 108354244
{'aut_label': '5B', 'centralizer': '4.a1.a1', 'counter': 7, 'group_counter': 10, 'group_order': 100, 'label': '5B', 'order': 5, 'powers': [7, 1], 'representative': 4, 'size': 4}
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id: 108354245
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 8, 'group_counter': 10, 'group_order': 100, 'label': '5C1', 'order': 5, 'powers': [10, 1], 'representative': 24, 'size': 4}
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id: 108354246
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 10, 'group_order': 100, 'label': '5C-1', 'order': 5, 'powers': [11, 1], 'representative': 28, 'size': 4}
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id: 108354235
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 10, 'group_counter': 10, 'group_order': 100, 'label': '5C2', 'order': 5, 'powers': [9, 1], 'representative': 64, 'size': 4}
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id: 108354236
{'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 10, 'group_order': 100, 'label': '5C-2', 'order': 5, 'powers': [8, 1], 'representative': 44, 'size': 4}
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id: 108354237
{'aut_label': '10A1', 'centralizer': '10.b1.a1', 'counter': 12, 'group_counter': 10, 'group_order': 100, 'label': '10A1', 'order': 10, 'powers': [5, 2], 'representative': 22, 'size': 10}
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id: 108354238
{'aut_label': '10A1', 'centralizer': '10.b1.a1', 'counter': 13, 'group_counter': 10, 'group_order': 100, 'label': '10A3', 'order': 10, 'powers': [6, 2], 'representative': 42, 'size': 10}
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gps_qchar • Show schema
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id: 3838393
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 3838394
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 3838395
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
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id: 3838396
{'cdim': 2, 'counter': 4, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.2a', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -1, -1, -1, -1, 4, -1, -1, -1, -1], 'schur_index': 1}
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id: 3838397
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.2b', 'multiplicity': 2, 'nt': [20, 2], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -1, -1, -1, -1, 4, -1, -1, 1, 1], 'schur_index': 2}
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id: 3838398
{'cdim': 4, 'counter': 6, 'faithful': False, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
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id: 3838399
{'cdim': 4, 'counter': 7, 'faithful': True, 'group': '100.10', 'group_order': 100, 'image': None, 'label': '100.10.4b', 'multiplicity': 4, 'nt': [20, 26], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -4, -4, 1, 1, -4, 1, 1, 0, 0], 'schur_index': 1}
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gps_char • Show schema
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id: 5261931
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 100, 'label': '100.10.1a', '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]]]}
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id: 5261936
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 50, 'label': '100.10.1b', '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]]]}
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id: 5261937
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 25, 'label': '100.10.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 5261938
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 100, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 25, 'label': '100.10.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 5261939
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 5, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 10, 'label': '100.10.2a1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
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id: 5261940
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 6, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 10, 'label': '100.10.2a2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
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id: 5261941
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 7, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.b1.a1', 'kernel_order': 5, 'label': '100.10.2b1', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
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id: 5261942
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 10, 'counter': 8, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.b1.a1', 'kernel_order': 5, 'label': '100.10.2b2', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
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id: 5261943
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 5, 'counter': 9, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 5, 'label': '100.10.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
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id: 5261932
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '100.10', 'image_order': 100, 'indicator': 0, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.10.4b1', 'nt': [20, 26], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 1], [-1, 2], [1, -2]], [[1, 0], [2, 1], [1, -2]], [[-1, 0]], [[-1, 0], [-2, 1], [-1, 2], [-2, -2]], [[1, 0], [1, 1], [2, 2]], [[0, 0]], [[0, 0]]]}
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id: 5261933
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '100.10', 'image_order': 100, 'indicator': 0, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.10.4b2', 'nt': [20, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[1, 0], [1, 1], [2, 2]], [[-1, 0], [-2, 1], [-1, 2], [-2, -2]], [[-1, 0]], [[1, 0], [2, 1], [1, -2]], [[-1, 1], [-1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
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id: 5261934
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '100.10', 'image_order': 100, 'indicator': 0, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.10.4b3', 'nt': [20, 26], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0], [-2, 1], [-1, 2], [-2, -2]], [[-1, 1], [-1, 2], [1, -2]], [[-1, 0]], [[1, 0], [1, 1], [2, 2]], [[1, 0], [2, 1], [1, -2]], [[0, 0]], [[0, 0]]]}
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id: 5261935
{'center': '100.a1.a1', 'center_index': 100, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '100.10', 'group_counter': 10, 'group_order': 100, 'image': None, 'image_isoclass': '100.10', 'image_order': 100, 'indicator': 0, 'kernel': '100.a1.a1', 'kernel_order': 1, 'label': '100.10.4b4', 'nt': [20, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [2, 1], [1, -2]], [[1, 0], [1, 1], [2, 2]], [[-1, 0]], [[-1, 1], [-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-2, -2]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
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id: 60451988
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 100, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '100.10.1.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': '100.10', 'subgroup_hash': 10, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
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id: 60451993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 50, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '100.10.2.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': ['C1'], 'split': False, '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}
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id: 60451994
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': True, 'core_order': 25, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '100.10.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', '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}
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id: 60451995
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.10.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
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id: 60451996
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 10, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '100.10.5.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 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': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
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id: 60451997
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 10, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '100.10.10.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
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id: 60451998
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.10.10.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}
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id: 60451999
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': True, 'core_order': 5, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '100.10.20.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': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', '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}
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id: 60452000
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': True, 'core_order': 5, 'counter': 9, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '100.10.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:C_4', '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}
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id: 60451989
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.10.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 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}
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id: 60451990
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '100.10.25.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 2}
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id: 60451991
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '100.10.50.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}
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id: 60451992
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '100.10', 'ambient_counter': 10, 'ambient_order': 100, 'ambient_tex': 'C_5:F_5', 'central': True, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 1, 'counter': 13, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '100.10.100.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': '100.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:F_5', '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}
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gps_subgroup_data • Show schema
Hide schema
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id: 60451988
{'ambient': '100.10', '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', '5.a1.a1', '5.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7148, 4763, 2960, 6598, 6551, 4779, 6551, 5147], 'generators': [1, 4, 20, 2], 'label': '100.10.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '100.10', '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': '100.10'}
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id: 60451989
{'ambient': '100.10', 'aut_centralizer_order': 25, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 100, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': '20T26', 'count': 4, 'diagramx': [706, -1, 9080, -1, 854, -1, 854, -1], 'generators': [24], 'label': '100.10.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '100.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 60451990
{'ambient': '100.10', 'aut_centralizer_order': 16, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.b1.a1'], 'contains': ['50.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': '25T11', 'count': 25, 'diagramx': [8456, -1, 1717, -1, 9146, -1, 9146, -1], 'generators': [1], 'label': '100.10.25.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': '100.10', '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'}
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id: 60451991
{'ambient': '100.10', 'aut_centralizer_order': 80, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1.1', 'aut_weyl_index': 400, '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': [6415, -1, 3658, -1, 7690, -1, 7690, -1], 'generators': [2], 'label': '100.10.50.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': '100.10', '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'}
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id: 60451992
{'ambient': '100.10', '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.b1.a1', '20.c1.a1', '50.a1.a1'], 'contains': [], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3534, 6803, 6593, 4286, 4272, 5000, 4272, 5000], 'generators': [], 'label': '100.10.100.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '100.a1.a1', 'normal_contained_in': ['20.a1.a1', '20.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '100.10', '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'}
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id: 60451993
{'ambient': '100.10', 'aut_centralizer_order': 5, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.30', 'aut_weyl_index': 5, 'centralizer': '20.a1.a1', 'complements': [], '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': [4792, 4763, 5225, 6598, 2911, 4779, 2911, 5147], 'generators': [2, 4, 20], 'label': '100.10.2.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': '100.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
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id: 60451994
{'ambient': '100.10', 'aut_centralizer_order': 25, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.2', 'aut_weyl_index': 25, 'centralizer': '4.a1.a1', 'complements': ['25.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2722, 5917, 7189, 4081, 1646, 7647, 1646, 2353], 'generators': [4, 20], 'label': '100.10.4.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '100.10', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
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id: 60451995
{'ambient': '100.10', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '20.3', 'aut_weyl_index': 20, 'centralizer': '50.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.a1', '25.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9294, -1, 920, -1, 6551, -1, 6551, -1], 'generators': [1, 20, 2], 'label': '100.10.5.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': '100.10', '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: 60451996
{'ambient': '100.10', 'aut_centralizer_order': 4, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '20.3', 'aut_weyl_index': 20, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '25.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7148, -1, 2960, -1, 9146, -1, 9146, -1], 'generators': [1, 4, 2], 'label': '100.10.5.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '5.b1.a1', 'projective_image': '100.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 60451997
{'ambient': '100.10', 'aut_centralizer_order': 20, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.3', 'aut_weyl_index': 20, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.a1'], 'contains': ['20.b1.a1', '50.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4713, 1837, 5274, 8164, 6867, 1985, 6867, 8015], 'generators': [2, 4], 'label': '100.10.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '100.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 60451998
{'ambient': '100.10', 'aut_centralizer_order': 20, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.1', 'aut_weyl_index': 100, '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': [6807, -1, 3284, -1, 4335, -1, 4335, -1], 'generators': [2, 20], 'label': '100.10.10.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': '100.10', '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: 60451999
{'ambient': '100.10', 'aut_centralizer_order': 100, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 100, 'centralizer': '2.a1.a1', 'complements': ['5.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.b1.a1'], 'contains': ['100.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4477, 8163, 5498, 1836, 3133, 7647, 3133, 2353], 'generators': [20], 'label': '100.10.20.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '100.10', '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: 60452000
{'ambient': '100.10', 'aut_centralizer_order': 100, 'aut_label': '20.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 100, 'centralizer': '4.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['100.a1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2592, 3265, 7289, 6734, 5411, 2353, 5411, 7647], 'generators': [4], 'label': '100.10.20.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '100.10', 'quotient_action_image': '4.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
