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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '14.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 812, 'aut_gen_orders': [28, 29], 'aut_gens': [[1, 14], [1, 252], [57, 14]], 'aut_group': '812.7', 'aut_hash': 7, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 812, 'aut_permdeg': 29, 'aut_perms': [187879291521476314292527925029, 8536873649127988094042112000000], 'aut_phi_ratio': 4.833333333333333, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 29, 1, 1], [7, 29, 1, 6], [14, 29, 1, 6], [29, 14, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{29}', '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': 812, 'autcentquo_group': '812.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 812, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{29}', 'cc_stats': [[1, 1, 1], [2, 29, 1], [7, 29, 6], [14, 29, 6], [29, 14, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '406.1', 'commutator_count': 1, 'commutator_label': '29.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '7.1', '29.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 29, 1, 1], [7, 29, 6, 1], [14, 29, 6, 1], [29, 14, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 406, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 7, 29], 'factors_of_order': [2, 7, 29], 'faithful_reps': [[14, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '406.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 406, 'inner_gen_orders': [14, 29], 'inner_gens': [[1, 182], [239, 14]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 406, 'inner_split': False, 'inner_tex': 'C_{29}:C_{14}', 'inner_used': [1, 2], 'irrC_degree': 14, 'irrQ_degree': 28, 'irrQ_dim': 28, 'irrR_degree': 14, 'irrep_stats': [[1, 14], [14, 2]], 'label': '406.1', 'linC_count': 2, 'linC_degree': 14, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 28, 'linQ_degree_count': 1, 'linQ_dim': 28, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C29:C14', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 16, 'number_divisions': 5, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 92, 'old_label': None, 'order': 406, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 29], [7, 174], [14, 174], [29, 28]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [1], 'outer_gens': [[1, 140]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2], [28, 1]], 'representations': {'PC': {'code': 2666644510823, 'gens': [1, 3], 'pres': [3, -2, -7, -29, 6, 1640, 1517]}, 'GLFp': {'d': 2, 'p': 29, 'gens': [24419, 146354]}, 'Perm': {'d': 29, 'gens': [304888344611713860501503999999, 164390733002593674353574020533, 8536873649127988094042112000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [14], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{29}:C_{14}', 'transitive_degree': 29, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 110137900
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 406, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
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id: 110137908
{'aut_label': '2A', 'centralizer': '29.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 406, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 315, 'size': 29}
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id: 110137909
{'aut_label': '7A1', 'centralizer': '29.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 406, 'label': '7A1', 'order': 7, 'powers': [5, 7, 1, 3], 'representative': 278, 'size': 29}
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id: 110137910
{'aut_label': '7A-1', 'centralizer': '29.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 406, 'label': '7A-1', 'order': 7, 'powers': [6, 8, 1, 4], 'representative': 114, 'size': 29}
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id: 110137911
{'aut_label': '7A2', 'centralizer': '29.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 406, 'label': '7A2', 'order': 7, 'powers': [8, 4, 1, 5], 'representative': 304, 'size': 29}
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id: 110137912
{'aut_label': '7A-2', 'centralizer': '29.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 406, 'label': '7A-2', 'order': 7, 'powers': [7, 3, 1, 6], 'representative': 368, 'size': 29}
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id: 110137913
{'aut_label': '7A3', 'centralizer': '29.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 406, 'label': '7A3', 'order': 7, 'powers': [4, 5, 1, 7], 'representative': 134, 'size': 29}
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id: 110137914
{'aut_label': '7A-3', 'centralizer': '29.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 406, 'label': '7A-3', 'order': 7, 'powers': [3, 6, 1, 8], 'representative': 328, 'size': 29}
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id: 110137915
{'aut_label': '14A1', 'centralizer': '29.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 406, 'label': '14A1', 'order': 14, 'powers': [3, 11, 2, 9], 'representative': 405, 'size': 29}
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id: 110137901
{'aut_label': '14A-1', 'centralizer': '29.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 406, 'label': '14A-1', 'order': 14, 'powers': [4, 12, 2, 10], 'representative': 183, 'size': 29}
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id: 110137902
{'aut_label': '14A3', 'centralizer': '29.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 406, 'label': '14A3', 'order': 14, 'powers': [7, 14, 2, 11], 'representative': 361, 'size': 29}
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id: 110137903
{'aut_label': '14A-3', 'centralizer': '29.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 406, 'label': '14A-3', 'order': 14, 'powers': [8, 13, 2, 12], 'representative': 17, 'size': 29}
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id: 110137904
{'aut_label': '14A5', 'centralizer': '29.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 406, 'label': '14A5', 'order': 14, 'powers': [6, 9, 2, 13], 'representative': 205, 'size': 29}
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id: 110137905
{'aut_label': '14A-5', 'centralizer': '29.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 406, 'label': '14A-5', 'order': 14, 'powers': [5, 10, 2, 14], 'representative': 47, 'size': 29}
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id: 110137906
{'aut_label': '29A1', 'centralizer': '14.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 406, 'label': '29A1', 'order': 29, 'powers': [16, 16, 15, 1], 'representative': 14, 'size': 14}
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id: 110137907
{'aut_label': '29A1', 'centralizer': '14.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 406, 'label': '29A2', 'order': 29, 'powers': [15, 15, 16, 1], 'representative': 28, 'size': 14}
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gps_qchar • Show schema
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id: 4531638
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '406.1', 'group_order': 406, 'image': None, 'label': '406.1.1a', '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}
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id: 4531639
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '406.1', 'group_order': 406, 'image': None, 'label': '406.1.1b', '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}
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id: 4531640
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '406.1', 'group_order': 406, 'image': None, 'label': '406.1.1c', 'multiplicity': 6, 'nt': [7, 1], 'qdim': 6, 'qvalues': [6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6], 'schur_index': 1}
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id: 4531641
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '406.1', 'group_order': 406, 'image': None, 'label': '406.1.1d', 'multiplicity': 6, 'nt': [14, 1], 'qdim': 6, 'qvalues': [6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 6, 6], 'schur_index': 1}
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id: 4531642
{'cdim': 14, 'counter': 5, 'faithful': True, 'group': '406.1', 'group_order': 406, 'image': None, 'label': '406.1.14a', 'multiplicity': 2, 'nt': [29, 5], 'qdim': 28, 'qvalues': [28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
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gps_char • Show schema
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id: 7045359
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 406, 'label': '406.1.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 7045367
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 203, 'label': '406.1.1b', '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]]]}
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id: 7045368
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 3, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c1', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, 0]], [[1, 0]]]}
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id: 7045369
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 4, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c2', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, 0]], [[1, 0]]]}
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id: 7045370
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 5, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c3', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, 0]], [[1, 0]]]}
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id: 7045371
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 6, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c4', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 0]], [[1, 0]]]}
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id: 7045372
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 7, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c5', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 0]], [[1, 0]]]}
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id: 7045373
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 8, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 58, 'label': '406.1.1c6', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 3]], [[1, -3]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 0]], [[1, 0]]]}
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id: 7045374
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 9, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d1', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, 1]], [[1, 0]], [[1, 0]]]}
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id: 7045360
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 10, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d2', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, -1]], [[1, 0]], [[1, 0]]]}
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id: 7045361
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 11, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d3', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 3]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -3]], [[-1, 2]], [[-1, 3]], [[1, 0]], [[1, 0]]]}
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id: 7045362
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 12, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d4', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -3]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 3]], [[-1, -2]], [[-1, -3]], [[1, 0]], [[1, 0]]]}
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id: 7045363
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 13, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d5', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, -2]], [[-1, 3]], [[-1, -3]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, 0]], [[1, 0]]]}
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id: 7045364
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 406, 'counter': 14, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 29, 'label': '406.1.1d6', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 3]], [[1, -3]], [[1, 2]], [[-1, -3]], [[-1, 3]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, 0]], [[1, 0]]]}
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id: 7045365
{'center': '406.a1.a1', 'center_index': 406, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 29, 'dim': 14, 'faithful': True, 'field': [-7, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '406.1', 'image_order': 406, 'indicator': 1, 'kernel': '406.a1.a1', 'kernel_order': 1, 'label': '406.1.14a1', 'nt': [29, 5], 'q_character': None, 'values': [[[14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 3], [1, 8], [1, 10], [1, 11], [1, 12], [1, 14], [1, -14], [1, -12], [1, -11], [1, -10], [1, -8], [1, -3], [1, -2]], [[-1, 0], [-1, 2], [-1, 3], [-1, 8], [-1, 10], [-1, 11], [-1, 12], [-1, 14], [-1, -14], [-1, -12], [-1, -11], [-1, -10], [-1, -8], [-1, -3], [-1, -2]]]}
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id: 7045366
{'center': '406.a1.a1', 'center_index': 406, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 29, 'dim': 14, 'faithful': True, 'field': [-7, -1, 1], 'group': '406.1', 'group_counter': 1, 'group_order': 406, 'image': None, 'image_isoclass': '406.1', 'image_order': 406, 'indicator': 1, 'kernel': '406.a1.a1', 'kernel_order': 1, 'label': '406.1.14a2', 'nt': [29, 5], 'q_character': None, 'values': [[[14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 2], [-1, 3], [-1, 8], [-1, 10], [-1, 11], [-1, 12], [-1, 14], [-1, -14], [-1, -12], [-1, -11], [-1, -10], [-1, -8], [-1, -3], [-1, -2]], [[1, 2], [1, 3], [1, 8], [1, 10], [1, 11], [1, 12], [1, 14], [1, -14], [1, -12], [1, -11], [1, -10], [1, -8], [1, -3], [1, -2]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 66427697
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 406, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 406, 'label': '406.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '406.1', 'subgroup_hash': 1, 'subgroup_order': 406, 'subgroup_tex': 'C_{29}:C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 66427698
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 203, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 203, 'label': '406.1.2.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '203.1', 'subgroup_hash': 1, 'subgroup_order': 203, 'subgroup_tex': 'C_{29}:C_7', 'supersolvable': True, 'sylow': 0}
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id: 66427699
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 58, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 58, 'label': '406.1.7.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '58.1', 'subgroup_hash': 1, 'subgroup_order': 58, 'subgroup_tex': 'D_{29}', 'supersolvable': True, 'sylow': 0}
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id: 66427700
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 29, 'characteristic': True, 'core_order': 29, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 29, 'label': '406.1.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '29.1', 'subgroup_hash': 1, 'subgroup_order': 29, 'subgroup_tex': 'C_{29}', 'supersolvable': True, 'sylow': 29}
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id: 66427701
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': True, 'direct': None, 'hall': 14, 'label': '406.1.29.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '29.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': 29, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 66427702
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '406.1.58.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '58.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': 58, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
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id: 66427703
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '406.1.203.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '203.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': 203, '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': 2}
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id: 66427704
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '406.1', 'ambient_counter': 1, 'ambient_order': 406, 'ambient_tex': 'C_{29}:C_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 406, 'characteristic': True, 'core_order': 1, 'counter': 8, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '406.1.406.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '406.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '406.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 406, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{29}:C_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C3'], '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: 66427697
{'ambient': '406.1', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '406.a1.a1', 'complements': ['406.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '7.a1.a1', '29.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3463, 4897, 8430, 4897, 5538, 4605, 5547, 4605], 'generators': [7, 2, 14], 'label': '406.1.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '7.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '406.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '406.1'}
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id: 66427698
{'ambient': '406.1', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '812.7', 'aut_weyl_index': 1, 'centralizer': '406.a1.a1', 'complements': ['203.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '58.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6537, 7569, 4395, 7569, 1810, 7342, 1813, 7342], 'generators': [2, 14], 'label': '406.1.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '406.1', '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': '406.1'}
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id: 66427699
{'ambient': '406.1', 'aut_centralizer_order': 1, 'aut_label': '7.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '812.7', 'aut_weyl_index': 1, 'centralizer': '406.a1.a1', 'complements': ['58.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '203.a1.a1'], 'core': '7.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3774, 2431, 8430, 2431, 8727, 1868, 5547, 1868], 'generators': [7, 14], 'label': '406.1.7.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '406.1', 'quotient_action_image': '7.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '406.1'}
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id: 66427700
{'ambient': '406.1', 'aut_centralizer_order': 29, 'aut_label': '14.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '28.2', 'aut_weyl_index': 29, 'centralizer': '14.a1.a1', 'complements': ['29.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['406.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8637, 4760, 1570, 4760, 5251, 4605, 2531, 4605], 'generators': [14], 'label': '406.1.14.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1', '7.a1.a1'], 'normal_contains': ['406.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '406.1', 'quotient_action_image': '14.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '14.2'}
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id: 66427701
{'ambient': '406.1', 'aut_centralizer_order': 28, 'aut_label': '29.a1', 'aut_quo_index': None, 'aut_stab_index': 29, 'aut_weyl_group': '1.1', 'aut_weyl_index': 812, 'centralizer': '29.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['58.a1.a1', '203.a1.a1'], 'core': '406.a1.a1', 'coset_action_label': '29T5', 'count': 29, 'diagramx': [1363, -1, 7220, -1, 5538, -1, 8743, -1], 'generators': [7, 2], 'label': '406.1.29.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '29.a1.a1', 'old_label': '29.a1.a1', 'projective_image': '406.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '29.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66427702
{'ambient': '406.1', 'aut_centralizer_order': 28, 'aut_label': '58.a1', 'aut_quo_index': None, 'aut_stab_index': 29, 'aut_weyl_group': '1.1', 'aut_weyl_index': 812, 'centralizer': '29.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '29.a1.a1'], 'contains': ['406.a1.a1'], 'core': '406.a1.a1', 'coset_action_label': None, 'count': 29, 'diagramx': [6031, -1, 4574, -1, 2384, -1, 5404, -1], 'generators': [2], 'label': '406.1.58.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '29.a1.a1', 'old_label': '58.a1.a1', 'projective_image': '406.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '58.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66427703
{'ambient': '406.1', 'aut_centralizer_order': 28, 'aut_label': '203.a1', 'aut_quo_index': None, 'aut_stab_index': 29, 'aut_weyl_group': '1.1', 'aut_weyl_index': 812, 'centralizer': '29.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '29.a1.a1'], 'contains': ['406.a1.a1'], 'core': '406.a1.a1', 'coset_action_label': None, 'count': 29, 'diagramx': [3813, -1, 7220, -1, 8118, -1, 7989, -1], 'generators': [7], 'label': '406.1.203.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '29.a1.a1', 'old_label': '203.a1.a1', 'projective_image': '406.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '203.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66427704
{'ambient': '406.1', 'aut_centralizer_order': None, 'aut_label': '406.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': ['14.a1.a1', '58.a1.a1', '203.a1.a1'], 'contains': [], 'core': '406.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6031, 4760, 4574, 4760, 5251, 4605, 5404, 4605], 'generators': [], 'label': '406.1.406.a1.a1', 'mobius_quo': 1, 'mobius_sub': -29, 'normal_closure': '406.a1.a1', 'normal_contained_in': ['14.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '406.a1.a1', 'projective_image': '406.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '406.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
