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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '18.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 42, 'aut_gen_orders': [2, 6, 21], 'aut_gens': [[1, 6], [85, 48], [1, 60], [79, 6]], 'aut_group': '252.26', 'aut_hash': 26, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 252, 'aut_permdeg': 10, 'aut_perms': [1, 47064, 2384068], 'aut_phi_ratio': 7.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 1, 2, 1], [3, 7, 3, 2], [6, 7, 2, 1], [6, 7, 3, 2], [7, 6, 1, 1], [21, 6, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3\\times F_7', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '42.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 42, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_7', 'cc_stats': [[1, 1, 1], [2, 7, 1], [3, 1, 2], [3, 7, 6], [6, 7, 8], [7, 6, 1], [21, 6, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '42.1', 'commutator_count': 1, 'commutator_label': '7.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '7.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['42.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 1, 2, 1], [3, 7, 2, 3], [6, 7, 2, 4], [7, 6, 1, 1], [21, 6, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 42, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '126.7', 'hash': 7, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [6, 7], 'inner_gens': [[1, 60], [73, 6]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 42, 'inner_split': True, 'inner_tex': 'F_7', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 18], [6, 3]], 'label': '126.7', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 6, 'linQ_dim': 8, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*F7', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 21, 'number_divisions': 12, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 24, 'number_subgroups': 84, 'old_label': None, 'order': 126, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 7], [3, 44], [6, 56], [7, 6], [21, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[85, 48], [43, 6]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [6, 1], [12, 1]], 'representations': {'PC': {'code': 21911983206086783, 'gens': [1, 3], 'pres': [4, -2, -3, -3, -7, 8, 722, 582, 46, 867, 295]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [351, 1030, 1374]}, 'Perm': {'d': 10, 'gens': [42000, 97227, 4, 486264]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times F_7', 'transitive_degree': 21, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 108633513
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 7, 'group_order': 126, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 108633524
{'aut_label': '2A', 'centralizer': '7.a1.a1', 'counter': 2, 'group_counter': 7, 'group_order': 126, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 3, 'size': 7}
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id: 108633527
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 7, 'group_order': 126, 'label': '3A1', 'order': 3, 'powers': [4, 1, 3], 'representative': 84, 'size': 1}
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id: 108633528
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 7, 'group_order': 126, 'label': '3A-1', 'order': 3, 'powers': [3, 1, 4], 'representative': 42, 'size': 1}
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id: 108633529
{'aut_label': '3B1', 'centralizer': '7.a1.a1', 'counter': 5, 'group_counter': 7, 'group_order': 126, 'label': '3B1', 'order': 3, 'powers': [6, 1, 5], 'representative': 2, 'size': 7}
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id: 108633530
{'aut_label': '3B-1', 'centralizer': '7.a1.a1', 'counter': 6, 'group_counter': 7, 'group_order': 126, 'label': '3B-1', 'order': 3, 'powers': [5, 1, 6], 'representative': 4, 'size': 7}
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id: 108633531
{'aut_label': '3B1', 'centralizer': '7.a1.a1', 'counter': 7, 'group_counter': 7, 'group_order': 126, 'label': '3C1', 'order': 3, 'powers': [8, 1, 7], 'representative': 68, 'size': 7}
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id: 108633532
{'aut_label': '3B-1', 'centralizer': '7.a1.a1', 'counter': 8, 'group_counter': 7, 'group_order': 126, 'label': '3C-1', 'order': 3, 'powers': [7, 1, 8], 'representative': 118, 'size': 7}
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id: 108633533
{'aut_label': '3B1', 'centralizer': '7.a1.a1', 'counter': 9, 'group_counter': 7, 'group_order': 126, 'label': '3D1', 'order': 3, 'powers': [10, 1, 9], 'representative': 8, 'size': 7}
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id: 108633514
{'aut_label': '3B-1', 'centralizer': '7.a1.a1', 'counter': 10, 'group_counter': 7, 'group_order': 126, 'label': '3D-1', 'order': 3, 'powers': [9, 1, 10], 'representative': 106, 'size': 7}
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id: 108633515
{'aut_label': '6A1', 'centralizer': '7.a1.a1', 'counter': 11, 'group_counter': 7, 'group_order': 126, 'label': '6A1', 'order': 6, 'powers': [5, 2, 11], 'representative': 1, 'size': 7}
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id: 108633516
{'aut_label': '6A-1', 'centralizer': '7.a1.a1', 'counter': 12, 'group_counter': 7, 'group_order': 126, 'label': '6A-1', 'order': 6, 'powers': [6, 2, 12], 'representative': 5, 'size': 7}
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id: 108633517
{'aut_label': '6A1', 'centralizer': '7.a1.a1', 'counter': 13, 'group_counter': 7, 'group_order': 126, 'label': '6B1', 'order': 6, 'powers': [7, 2, 13], 'representative': 7, 'size': 7}
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id: 108633518
{'aut_label': '6A-1', 'centralizer': '7.a1.a1', 'counter': 14, 'group_counter': 7, 'group_order': 126, 'label': '6B-1', 'order': 6, 'powers': [8, 2, 14], 'representative': 17, 'size': 7}
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id: 108633519
{'aut_label': '6A1', 'centralizer': '7.a1.a1', 'counter': 15, 'group_counter': 7, 'group_order': 126, 'label': '6C1', 'order': 6, 'powers': [9, 2, 15], 'representative': 13, 'size': 7}
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id: 108633520
{'aut_label': '6A-1', 'centralizer': '7.a1.a1', 'counter': 16, 'group_counter': 7, 'group_order': 126, 'label': '6C-1', 'order': 6, 'powers': [10, 2, 16], 'representative': 11, 'size': 7}
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id: 108633521
{'aut_label': '6D1', 'centralizer': '7.a1.a1', 'counter': 17, 'group_counter': 7, 'group_order': 126, 'label': '6D1', 'order': 6, 'powers': [3, 2, 17], 'representative': 9, 'size': 7}
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id: 108633522
{'aut_label': '6D1', 'centralizer': '7.a1.a1', 'counter': 18, 'group_counter': 7, 'group_order': 126, 'label': '6D-1', 'order': 6, 'powers': [4, 2, 18], 'representative': 15, 'size': 7}
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id: 108633523
{'aut_label': '7A', 'centralizer': '6.a1.a1', 'counter': 19, 'group_counter': 7, 'group_order': 126, 'label': '7A', 'order': 7, 'powers': [19, 19, 1], 'representative': 18, 'size': 6}
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id: 108633525
{'aut_label': '21A1', 'centralizer': '6.a1.a1', 'counter': 20, 'group_counter': 7, 'group_order': 126, 'label': '21A1', 'order': 21, 'powers': [21, 19, 4], 'representative': 6, 'size': 6}
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id: 108633526
{'aut_label': '21A1', 'centralizer': '6.a1.a1', 'counter': 21, 'group_counter': 7, 'group_order': 126, 'label': '21A-1', 'order': 21, 'powers': [20, 19, 3], 'representative': 12, 'size': 6}
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gps_qchar • Show schema
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id: 3950001
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 3950005
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
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id: 3950006
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
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id: 3950007
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
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id: 3950008
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1], 'schur_index': 1}
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id: 3950009
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, 2], 'schur_index': 1}
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id: 3950010
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, -1, -1, -1, -1, 2, 2, -2, 1, 1, 1, 1, -2, 1, 1, 2, -1, -1], 'schur_index': 1}
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id: 3950011
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, -1, -1, 2, 2, -1, -1, 1, -2, -2, 1, 1, 1, 1, 1, 2, -1, -1], 'schur_index': 1}
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id: 3950012
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, -2, 1, -2, 1, 2, -1, -1], 'schur_index': 1}
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id: 3950002
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, -2, 1, 1, 1, -2, 2, 2, 2], 'schur_index': 1}
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id: 3950003
{'cdim': 6, 'counter': 11, 'faithful': False, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.6a', 'multiplicity': 1, 'nt': [7, 4], 'qdim': 6, 'qvalues': [6, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
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id: 3950004
{'cdim': 6, 'counter': 12, 'faithful': True, 'group': '126.7', 'group_order': 126, 'image': None, 'label': '126.7.6b', 'multiplicity': 2, 'nt': [21, 9], 'qdim': 12, 'qvalues': [12, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1], 'schur_index': 1}
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gps_char • Show schema
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id: 5541210
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 126, 'label': '126.7.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541221
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 63, 'label': '126.7.1b', '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]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541224
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 42, 'label': '126.7.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541225
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 42, 'label': '126.7.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541226
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 42, 'label': '126.7.1d1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541227
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 42, 'label': '126.7.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541228
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 42, 'label': '126.7.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541229
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 42, 'label': '126.7.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541230
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 42, 'label': '126.7.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541211
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 42, 'label': '126.7.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541212
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 21, 'label': '126.7.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541213
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 21, 'label': '126.7.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541214
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 21, 'label': '126.7.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541215
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 21, 'label': '126.7.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541216
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 21, 'label': '126.7.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
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id: 5541217
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 21, 'label': '126.7.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
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id: 5541218
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 21, 'label': '126.7.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541219
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 126, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 21, 'label': '126.7.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5541220
{'center': '42.a1.a1', 'center_index': 42, 'center_order': 3, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '42.1', 'image_order': 42, 'indicator': 1, 'kernel': '42.a1.a1', 'kernel_order': 3, 'label': '126.7.6a', 'nt': [7, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[6, 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]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 5541222
{'center': '42.a1.a1', 'center_index': 42, 'center_order': 3, 'counter': 20, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '126.7', 'image_order': 126, 'indicator': 0, 'kernel': '126.a1.a1', 'kernel_order': 1, 'label': '126.7.6b1', 'nt': [21, 9], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[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, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
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id: 5541223
{'center': '42.a1.a1', 'center_index': 42, 'center_order': 3, 'counter': 21, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '126.7', 'group_counter': 7, 'group_order': 126, 'image': None, 'image_isoclass': '126.7', 'image_order': 126, 'indicator': 0, 'kernel': '126.a1.a1', 'kernel_order': 1, 'label': '126.7.6b2', 'nt': [21, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[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, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 61491638
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 126, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '126.7.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '126.7', 'subgroup_hash': 7, 'subgroup_order': 126, 'subgroup_tex': 'C_3\\times F_7', 'supersolvable': True, 'sylow': 0}
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id: 61491649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 63, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 21, 'label': '126.7.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': '63.3', 'subgroup_hash': 3, 'subgroup_order': 63, 'subgroup_tex': 'C_{21}:C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491655
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 42, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '126.7.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
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id: 61491656
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': False, 'core_order': 42, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '126.7.3.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
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id: 61491657
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': False, 'core_order': 42, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '126.7.3.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
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id: 61491658
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': False, 'core_order': 42, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '126.7.3.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
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id: 61491659
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 21, 'characteristic': True, 'core_order': 21, 'counter': 7, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '126.7.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
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id: 61491660
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 21, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '126.7.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491661
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 21, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '126.7.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491639
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 21, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '126.7.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '126.7.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7.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': 7, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 61491641
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 14, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '126.7.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
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id: 61491642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '126.7.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.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': 14, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
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id: 61491643
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 21, 'characteristic': True, 'core_order': 7, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '126.7.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, '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: 61491644
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.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': 21, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 61491645
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.21.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.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': 21, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 61491646
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.21.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.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': 21, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 61491647
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.21.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.b1.c1', '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': 21, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 61491648
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': True, 'central_factor': False, 'centralizer_order': 126, 'characteristic': True, 'core_order': 3, 'counter': 19, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '126.7.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '42.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_7', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491650
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491651
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.42.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491652
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '126.7.42.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.c1', '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': 42, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 61491653
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '126.7.63.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '63.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': 63, '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: 61491654
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '126.7', 'ambient_counter': 7, 'ambient_order': 126, 'ambient_tex': 'C_3\\times F_7', 'central': True, 'central_factor': False, 'centralizer_order': 126, 'characteristic': True, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '126.7.126.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '126.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '126.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 126, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times F_7', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', '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: 61491645
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '21.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '7.a1.a1'], 'contains': ['42.b1.a1', '63.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '21T9', 'count': 7, 'diagramx': [5888, -1, 3984, -1, 9457, -1, 7830, -1], 'generators': [3, 2], 'label': '126.7.21.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.b1.a1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 61491638
{'ambient': '126.7', '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': '42.a1.a1', 'complements': ['126.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4697, 4528, 5030, 4606, 5920, 5916, 5356, 5284], 'generators': [3, 42, 18, 2], 'label': '126.7.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1', '3.b1.b1', '3.b1.a1', '3.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '42.1', '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': '42.1'}
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id: 61491639
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['21.a1.a1', '21.b1.b1', '21.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['18.a1.a1', '42.b1.c1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6944, 5761, 6483, 5996, 6362, 7706, 3922, 4905], 'generators': [8, 18], 'label': '126.7.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1', '3.b1.c1'], 'normal_contains': ['18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '126.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
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id: 61491640
{'ambient': '126.7', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.1', 'aut_weyl_index': 42, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '21.a1.a1', '21.b1.a1', '21.b1.b1', '21.b1.c1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1820, -1, 8431, -1, 7307, -1, 8046, -1], 'generators': [3, 2, 42], 'label': '126.7.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '42.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 61491641
{'ambient': '126.7', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['14.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.a1.a1', '63.a1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9281, 3406, 2217, 5228, 8010, 5413, 4962, 6540], 'generators': [3, 18], 'label': '126.7.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1', '3.b1.b1', '3.b1.a1', '3.b1.c1'], 'normal_contains': ['18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '126.7', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
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id: 61491642
{'ambient': '126.7', 'aut_centralizer_order': 6, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.1', 'aut_weyl_index': 42, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.b1.b1', '42.b1.c1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [719, -1, 7108, -1, 3166, -1, 5939, -1], 'generators': [2, 42], 'label': '126.7.14.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '42.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491643
{'ambient': '126.7', 'aut_centralizer_order': 42, 'aut_label': '18.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 42, 'centralizer': '6.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.a1.a1'], 'contains': ['126.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6787, 6123, 2397, 5415, 4955, 5357, 2995, 5723], 'generators': [18], 'label': '126.7.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.b1', '6.b1.a1', '6.b1.c1', '9.a1.a1'], 'normal_contains': ['126.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '126.7', 'quotient_action_image': '6.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 61491644
{'ambient': '126.7', 'aut_centralizer_order': 18, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 126, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '63.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1956, -1, 5763, -1, 4714, -1, 6916, -1], 'generators': [3, 42], 'label': '126.7.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '42.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491646
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '21.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1', '7.a1.a1'], 'contains': ['42.b1.b1', '63.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '21T9', 'count': 7, 'diagramx': [5888, -1, 7084, -1, 9457, -1, 8744, -1], 'generators': [21, 14], 'label': '126.7.21.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.b1.b1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491647
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '21.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1', '7.a1.a1'], 'contains': ['42.b1.c1', '63.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '21T9', 'count': 7, 'diagramx': [5888, -1, 9549, -1, 9457, -1, 9657, -1], 'generators': [75, 8], 'label': '126.7.21.b1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.b1.c1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491648
{'ambient': '126.7', 'aut_centralizer_order': 126, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 126, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['126.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1349, 8804, 4849, 8299, 3367, 3231, 4125, 7637], 'generators': [42], 'label': '126.7.42.a1.a1', 'mobius_quo': -1, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['126.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '42.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '42.1', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491649
{'ambient': '126.7', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '252.26', 'aut_weyl_index': 1, 'centralizer': '42.a1.a1', 'complements': ['63.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '14.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3551, 8225, 4417, 4606, 1497, 5916, 1637, 2911], 'generators': [2, 18, 42], 'label': '126.7.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.b1', '6.b1.a1', '6.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '42.1', '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': '42.1'}
-
id: 61491650
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.a1.a1', '21.b1.a1'], 'contains': ['126.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '42T17', 'count': 7, 'diagramx': [4653, -1, 3984, -1, 6402, -1, 5038, -1], 'generators': [2], 'label': '126.7.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491651
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '14.a1.a1', '21.b1.b1'], 'contains': ['126.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '42T17', 'count': 7, 'diagramx': [4653, -1, 7084, -1, 6402, -1, 5952, -1], 'generators': [14], 'label': '126.7.42.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.b1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491652
{'ambient': '126.7', 'aut_centralizer_order': 12, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '14.a1.a1', '21.b1.c1'], 'contains': ['126.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': '42T17', 'count': 7, 'diagramx': [4653, -1, 8310, -1, 6402, -1, 6866, -1], 'generators': [8], 'label': '126.7.42.b1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.c1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491653
{'ambient': '126.7', 'aut_centralizer_order': 36, 'aut_label': '63.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 252, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '21.a1.a1', '21.b1.a1', '21.b1.b1', '21.b1.c1'], 'contains': ['126.a1.a1'], 'core': '126.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5888, -1, 5739, -1, 7950, -1, 7805, -1], 'generators': [3], 'label': '126.7.63.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '63.a1.a1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '63.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491654
{'ambient': '126.7', 'aut_centralizer_order': None, 'aut_label': '126.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': ['18.a1.a1', '42.a1.a1', '42.b1.a1', '42.b1.b1', '42.b1.c1', '63.a1.a1'], 'contains': [], 'core': '126.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5281, 7500, 5186, 6971, 5678, 4294, 5495, 6441], 'generators': [], 'label': '126.7.126.a1.a1', 'mobius_quo': 1, 'mobius_sub': 21, 'normal_closure': '126.a1.a1', 'normal_contained_in': ['18.a1.a1', '42.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '126.a1.a1', 'projective_image': '126.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61491655
{'ambient': '126.7', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '84.7', 'aut_weyl_index': 3, 'centralizer': '42.a1.a1', 'complements': ['42.b1.a1', '42.b1.c1', '42.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '21.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5034, 4782, 715, 9274, 4553, 1664, 3566, 8814], 'generators': [3, 18, 42], 'label': '126.7.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '42.1', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
-
id: 61491656
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['42.a1.a1', '42.b1.c1', '42.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.a1.a1', '21.b1.a1'], 'core': '3.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8360, 978, 2638, 2842, 9397, 9245, 4899, 5284], 'generators': [3, 18, 2], 'label': '126.7.3.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.a1', 'projective_image': '126.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
-
id: 61491657
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['42.a1.a1', '42.b1.a1', '42.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '9.a1.a1', '21.b1.b1'], 'core': '3.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8360, 978, 5138, 561, 9397, 9245, 5812, 538], 'generators': [3, 18, 14], 'label': '126.7.3.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.b1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.b1', 'projective_image': '126.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
-
id: 61491658
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['42.a1.a1', '42.b1.b1', '42.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '9.a1.a1', '21.b1.c1'], 'core': '3.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8360, 978, 6472, 6307, 9397, 9245, 6726, 6720], 'generators': [3, 18, 8], 'label': '126.7.3.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.c1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.c1', 'projective_image': '126.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
-
id: 61491659
{'ambient': '126.7', 'aut_centralizer_order': 21, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 21, 'centralizer': '6.a1.a1', 'complements': ['21.b1.a1', '21.b1.c1', '21.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.a1.a1', '42.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3101, 9022, 451, 9439, 1457, 3175, 444, 8136], 'generators': [42, 18], 'label': '126.7.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['18.a1.a1', '42.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '42.1', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 61491660
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['21.a1.a1', '21.b1.c1', '21.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '42.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6944, 5761, 3359, 4087, 6362, 7706, 1586, 3071], 'generators': [2, 18], 'label': '126.7.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.b1.a1'], 'normal_contains': ['18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '126.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
-
id: 61491661
{'ambient': '126.7', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '42.1', 'aut_weyl_index': 6, 'centralizer': '42.a1.a1', 'complements': ['21.a1.a1', '21.b1.a1', '21.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['18.a1.a1', '42.b1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6944, 5761, 4464, 1390, 6362, 7706, 2754, 1236], 'generators': [14, 18], 'label': '126.7.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1', '3.b1.b1'], 'normal_contains': ['18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '126.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
