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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 42, 'aut_gen_orders': [6, 42, 7], 'aut_gens': [[1, 6, 42], [1, 6, 126], [253, 30, 42], [7, 6, 42]], 'aut_group': '1764.135', 'aut_hash': 135, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1764, 'aut_permdeg': 56, 'aut_perms': [530435412957233878936267264983710834004680553921556603786829870187508006156, 338320769452722140299704833003288006701386410818382842771126597286785470669, 12931604173989606014904735154326749151014761978757970414579959777965720620], 'aut_phi_ratio': 21.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 49, 1, 2], [6, 49, 1, 2], [7, 3, 2, 1], [7, 6, 1, 1], [7, 6, 6, 1], [14, 21, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_7^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1764.135', 'autcentquo_hash': 135, 'autcentquo_nilpotent': False, 'autcentquo_order': 1764, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_7^2', 'cc_stats': [[1, 1, 1], [2, 7, 1], [3, 49, 2], [6, 49, 2], [7, 3, 2], [7, 6, 7], [14, 21, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '294.12', 'commutator_count': 1, 'commutator_label': '49.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '7.1', '7.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 49, 2, 1], [6, 49, 2, 1], [7, 3, 2, 1], [7, 6, 1, 1], [7, 6, 2, 3], [14, 21, 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, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '294.12', 'hash': 12, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [6, 7, 7], 'inner_gens': [[1, 24, 126], [25, 6, 42], [211, 6, 42]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 294, 'inner_split': True, 'inner_tex': 'C_7:F_7', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 6], [3, 4], [6, 7]], 'label': '294.12', 'linC_count': 6, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 5, 'linQ_dim': 12, 'linQ_dim_count': 5, 'linR_count': 5, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C7: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': 17, 'number_divisions': 10, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 22, 'number_subgroups': 196, 'old_label': None, 'order': 294, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 7], [3, 98], [6, 98], [7, 48], [14, 42]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[1, 30, 42]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 3], [12, 3]], 'representations': {'PC': {'code': 5075672799945815, 'gens': [1, 3, 4], 'pres': [4, -2, -3, -7, -7, 8, 290, 78, 2019, 679]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [11652057, 21401649, 473244, 4590980]}, 'Perm': {'d': 14, 'gens': [47249833680, 1444303093, 13499863504, 37362125673]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7:F_7', 'transitive_degree': 14, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 109648118
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 12, 'group_order': 294, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 109648127
{'aut_label': '2A', 'centralizer': '7.a1.a1', 'counter': 2, 'group_counter': 12, 'group_order': 294, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 213, 'size': 7}
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id: 109648128
{'aut_label': '3A1', 'centralizer': '49.a1.a1', 'counter': 3, 'group_counter': 12, 'group_order': 294, 'label': '3A1', 'order': 3, 'powers': [4, 1, 3], 'representative': 62, 'size': 49}
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id: 109648129
{'aut_label': '3A-1', 'centralizer': '49.a1.a1', 'counter': 4, 'group_counter': 12, 'group_order': 294, 'label': '3A-1', 'order': 3, 'powers': [3, 1, 4], 'representative': 142, 'size': 49}
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id: 109648130
{'aut_label': '6A1', 'centralizer': '49.a1.a1', 'counter': 5, 'group_counter': 12, 'group_order': 294, 'label': '6A1', 'order': 6, 'powers': [3, 2, 5], 'representative': 97, 'size': 49}
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id: 109648131
{'aut_label': '6A-1', 'centralizer': '49.a1.a1', 'counter': 6, 'group_counter': 12, 'group_order': 294, 'label': '6A-1', 'order': 6, 'powers': [4, 2, 6], 'representative': 191, 'size': 49}
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id: 109648132
{'aut_label': '7A1', 'centralizer': '3.a1.a1', 'counter': 7, 'group_counter': 12, 'group_order': 294, 'label': '7A1', 'order': 7, 'powers': [7, 8, 1], 'representative': 30, 'size': 3}
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id: 109648133
{'aut_label': '7A1', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 12, 'group_order': 294, 'label': '7A-1', 'order': 7, 'powers': [8, 7, 1], 'representative': 12, 'size': 3}
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id: 109648134
{'aut_label': '7B', 'centralizer': '6.a1.a1', 'counter': 9, 'group_counter': 12, 'group_order': 294, 'label': '7B', 'order': 7, 'powers': [9, 9, 1], 'representative': 42, 'size': 6}
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id: 109648119
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 10, 'group_counter': 12, 'group_order': 294, 'label': '7C1', 'order': 7, 'powers': [10, 11, 1], 'representative': 48, 'size': 6}
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id: 109648120
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 11, 'group_counter': 12, 'group_order': 294, 'label': '7C-1', 'order': 7, 'powers': [11, 10, 1], 'representative': 144, 'size': 6}
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id: 109648121
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 12, 'group_counter': 12, 'group_order': 294, 'label': '7D1', 'order': 7, 'powers': [12, 13, 1], 'representative': 90, 'size': 6}
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id: 109648122
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 13, 'group_counter': 12, 'group_order': 294, 'label': '7D-1', 'order': 7, 'powers': [13, 12, 1], 'representative': 60, 'size': 6}
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id: 109648123
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 14, 'group_counter': 12, 'group_order': 294, 'label': '7E1', 'order': 7, 'powers': [14, 15, 1], 'representative': 54, 'size': 6}
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id: 109648124
{'aut_label': '7C1', 'centralizer': '6.a1.a1', 'counter': 15, 'group_counter': 12, 'group_order': 294, 'label': '7E-1', 'order': 7, 'powers': [15, 14, 1], 'representative': 102, 'size': 6}
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id: 109648125
{'aut_label': '14A1', 'centralizer': '21.b1.a1', 'counter': 16, 'group_counter': 12, 'group_order': 294, 'label': '14A1', 'order': 14, 'powers': [7, 17, 2], 'representative': 249, 'size': 21}
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id: 109648126
{'aut_label': '14A1', 'centralizer': '21.b1.a1', 'counter': 17, 'group_counter': 12, 'group_order': 294, 'label': '14A-1', 'order': 14, 'powers': [8, 16, 2], 'representative': 219, 'size': 21}
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gps_qchar • Show schema
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id: 4354789
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.1a', '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], 'schur_index': 1}
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id: 4354791
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.1b', '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], 'schur_index': 1}
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id: 4354792
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
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id: 4354793
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
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id: 4354794
{'cdim': 3, 'counter': 5, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.3a', 'multiplicity': 2, 'nt': [7, 3], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 0, 0, -1, -1, -1, 6, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 4354795
{'cdim': 3, 'counter': 6, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.3b', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, -6, 0, 0, 0, 0, -1, -1, -1, 6, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
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id: 4354796
{'cdim': 6, 'counter': 7, 'faithful': False, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.6a', 'multiplicity': 1, 'nt': [7, 4], 'qdim': 6, 'qvalues': [6, 0, 0, 0, 0, 0, 6, 6, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
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id: 4354797
{'cdim': 6, 'counter': 8, 'faithful': True, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.6b', 'multiplicity': 2, 'nt': [14, 14], 'qdim': 12, 'qvalues': [12, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 5, 5, 0, 0], 'schur_index': 1}
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id: 4354798
{'cdim': 6, 'counter': 9, 'faithful': True, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.6c', 'multiplicity': 2, 'nt': [14, 14], 'qdim': 12, 'qvalues': [12, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 5, 5, -2, -2, 0, 0], 'schur_index': 1}
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id: 4354790
{'cdim': 6, 'counter': 10, 'faithful': True, 'group': '294.12', 'group_order': 294, 'image': None, 'label': '294.12.6d', 'multiplicity': 2, 'nt': [14, 14], 'qdim': 12, 'qvalues': [12, 0, 0, 0, 0, 0, -2, -2, 5, -2, 5, -2, -2, -2, -2, 0, 0], 'schur_index': 1}
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gps_char • Show schema
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id: 6555756
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 294, 'label': '294.12.1a', '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]]]}
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id: 6555765
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 147, 'label': '294.12.1b', '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]]]}
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id: 6555766
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 98, 'label': '294.12.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[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: 6555767
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 98, 'label': '294.12.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[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: 6555768
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 49, 'label': '294.12.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[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: 6555769
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 294, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 49, 'label': '294.12.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[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: 6555770
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 14, 'counter': 7, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 14, 'label': '294.12.3a1', 'nt': [7, 3], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[3, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
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id: 6555771
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 14, 'counter': 8, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 14, 'label': '294.12.3a2', 'nt': [7, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[3, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
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id: 6555772
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 14, 'counter': 9, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1.a1', 'kernel_order': 7, 'label': '294.12.3b1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[3, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
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id: 6555757
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 14, 'counter': 10, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1.a1', 'kernel_order': 7, 'label': '294.12.3b2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[3, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
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id: 6555758
{'center': '42.a1.a1', 'center_index': 42, 'center_order': 7, 'counter': 11, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '42.1', 'image_order': 42, 'indicator': 1, 'kernel': '42.a1.a1', 'kernel_order': 7, 'label': '294.12.6a', 'nt': [7, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
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id: 6555759
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6b1', 'nt': [14, 14], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[2, 1], [2, 2], [2, -3]], [[-1, 0]], [[-1, 0]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]]]}
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id: 6555760
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6b2', 'nt': [14, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-1, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[-1, 0]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]]]}
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id: 6555761
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6c1', 'nt': [14, 14], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]]]}
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id: 6555762
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6c2', 'nt': [14, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]]]}
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id: 6555763
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6d1', 'nt': [14, 14], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
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id: 6555764
{'center': '294.a1.a1', 'center_index': 294, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 7, 'dim': 6, 'faithful': True, 'field': [2, -1, 1], 'group': '294.12', 'group_counter': 12, 'group_order': 294, 'image': None, 'image_isoclass': '294.12', 'image_order': 294, 'indicator': 0, 'kernel': '294.a1.a1', 'kernel_order': 1, 'label': '294.12.6d2', 'nt': [14, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0]], [[3, 0], [1, 1], [1, 2], [1, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 65066222
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 294, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '294.12.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '294.12', 'subgroup_hash': 12, 'subgroup_order': 294, 'subgroup_tex': 'C_7:F_7', 'supersolvable': True, 'sylow': 0}
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id: 65066233
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 147, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 21, 'label': '294.12.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': '147.4', 'subgroup_hash': 4, 'subgroup_order': 147, 'subgroup_tex': 'C_7^2:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066237
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': True, 'core_order': 98, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '294.12.3.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': '98.3', 'subgroup_hash': 3, 'subgroup_order': 98, 'subgroup_tex': 'C_7\\times D_7', 'supersolvable': True, 'sylow': 0}
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id: 65066238
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': True, 'core_order': 49, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 7, 'label': '294.12.6.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': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '49.2', 'subgroup_hash': 2, 'subgroup_order': 49, 'subgroup_tex': 'C_7^2', 'supersolvable': True, 'sylow': 7}
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id: 65066239
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 7, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
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id: 65066240
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 14, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.7.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.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': 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': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
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id: 65066241
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 7, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066242
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 7, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066243
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066223
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.14.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066224
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '294.12.14.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.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': 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': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
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id: 65066225
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': True, 'core_order': 14, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '294.12.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '21.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 21, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_3', '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: 65066226
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 7, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '294.12.21.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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 65066227
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 98, 'characteristic': True, 'core_order': 7, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '294.12.42.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
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id: 65066228
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': True, 'core_order': 7, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '294.12.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '42.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_6', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
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id: 65066229
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '294.12.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
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id: 65066230
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '294.12.42.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
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id: 65066231
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '294.12.42.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
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id: 65066232
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 6, 'label': '294.12.49.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '49.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': 49, '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: 65066234
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '294.12.98.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '98.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': 98, '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': 3}
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id: 65066235
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': False, 'central_factor': False, 'centralizer_order': 42, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '294.12.147.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '147.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': 147, '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: 65066236
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '294.12', 'ambient_counter': 12, 'ambient_order': 294, 'ambient_tex': 'C_7:F_7', 'central': True, 'central_factor': False, 'centralizer_order': 294, 'characteristic': True, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '294.12.294.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '294.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '294.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 294, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:F_7', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 65066222
{'ambient': '294.12', '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': '294.a1.a1', 'complements': ['294.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '7.a1.a1', '7.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3873, 5024, 7354, 5088, 5734, 4720, 6627, 4720], 'generators': [3, 6, 42, 2], 'label': '294.12.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '294.12', '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': '294.12'}
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id: 65066223
{'ambient': '294.12', 'aut_centralizer_order': 1, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '294.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['42.c1.b1', '98.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '14T14', 'count': 14, 'diagramx': [9303, -1, 3478, -1, 647, -1, 1706, -1], 'generators': [2, 90], 'label': '294.12.14.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.b1', 'old_label': '14.c1.b1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
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id: 65066224
{'ambient': '294.12', 'aut_centralizer_order': 1, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '294.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['42.c1.c1', '98.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '14T14', 'count': 14, 'diagramx': [9303, -1, 433, -1, 647, -1, 489, -1], 'generators': [2, 132], 'label': '294.12.14.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.c1', 'old_label': '14.c1.c1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.c1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
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id: 65066225
{'ambient': '294.12', 'aut_centralizer_order': 42, 'aut_label': '21.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '42.a1.a1', 'complements': ['14.a1.a1', '14.c1.a1', '14.c1.b1', '14.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.b1.a1'], 'contains': ['42.b1.a1', '147.a1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [438, 2806, 6850, 7704, 9528, 7435, 8690, 7435], 'generators': [3, 42], 'label': '294.12.21.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '21.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['42.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '294.12', 'quotient_action_image': '3.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
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id: 65066226
{'ambient': '294.12', 'aut_centralizer_order': 42, 'aut_label': '21.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '21.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '147.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4425, -1, 9567, -1, 8129, -1, 7632, -1], 'generators': [3, 6], 'label': '294.12.21.b1.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.b1.a1', 'projective_image': '294.12', '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': '3.1'}
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id: 65066227
{'ambient': '294.12', 'aut_centralizer_order': 294, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '3.a1.a1', 'complements': ['7.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.a1.a1', '21.b1.a1'], 'contains': ['294.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6337, 7194, 8923, 2296, 4038, 4116, 5489, 4116], 'generators': [6], 'label': '294.12.42.a1.a1', 'mobius_quo': -1, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['294.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '294.12', 'quotient_action_image': '3.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 65066228
{'ambient': '294.12', 'aut_centralizer_order': 294, 'aut_label': '42.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '6.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['294.a1.a1'], 'core': '42.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [891, 3798, 5562, 6483, 5297, 7220, 6442, 7220], 'generators': [42], 'label': '294.12.42.b1.a1', 'mobius_quo': -1, 'mobius_sub': -7, 'normal_closure': '42.b1.a1', 'normal_contained_in': ['6.a1.a1', '21.a1.a1'], 'normal_contains': ['294.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '294.12', 'quotient_action_image': '6.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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id: 65066229
{'ambient': '294.12', 'aut_centralizer_order': 49, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.c1.a1'], 'contains': ['294.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '42T61', 'count': 2, 'diagramx': [9562, -1, 1956, -1, 1521, -1, 3585, -1], 'generators': [48], 'label': '294.12.42.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 65066230
{'ambient': '294.12', 'aut_centralizer_order': 49, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.c1.b1'], 'contains': ['294.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '42T61', 'count': 2, 'diagramx': [9562, -1, 4719, -1, 1521, -1, 2632, -1], 'generators': [90], 'label': '294.12.42.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '42.c1.b1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 65066231
{'ambient': '294.12', 'aut_centralizer_order': 49, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 294, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.c1.c1'], 'contains': ['294.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '42T61', 'count': 2, 'diagramx': [9562, -1, 468, -1, 1521, -1, 1680, -1], 'generators': [132], 'label': '294.12.42.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '42.c1.c1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 65066232
{'ambient': '294.12', 'aut_centralizer_order': 36, 'aut_label': '49.a1', 'aut_quo_index': None, 'aut_stab_index': 49, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1764, 'centralizer': '49.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '7.b1.a1'], 'contains': ['98.a1.a1', '147.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': None, 'count': 49, 'diagramx': [2674, -1, 6206, -1, 6731, -1, 9643, -1], 'generators': [3, 2], 'label': '294.12.49.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '49.a1.a1', 'old_label': '49.a1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '49.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65066233
{'ambient': '294.12', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1764.135', 'aut_weyl_index': 1, 'centralizer': '294.a1.a1', 'complements': ['147.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '14.a1.a1', '14.b1.a1', '14.c1.a1', '14.c1.b1', '14.c1.c1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6143, 6816, 4555, 2761, 2255, 2047, 3968, 2047], 'generators': [2, 42, 6], 'label': '294.12.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '294.12', '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': '294.12'}
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id: 65066234
{'ambient': '294.12', 'aut_centralizer_order': 36, 'aut_label': '98.a1', 'aut_quo_index': None, 'aut_stab_index': 49, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1764, 'centralizer': '49.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.c1.b1', '14.c1.c1', '49.a1.a1'], 'contains': ['294.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': None, 'count': 49, 'diagramx': [4458, -1, 3982, -1, 2780, -1, 4537, -1], 'generators': [2], 'label': '294.12.98.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '49.a1.a1', 'old_label': '98.a1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '98.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65066235
{'ambient': '294.12', 'aut_centralizer_order': 252, 'aut_label': '147.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1764, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1.a1', '21.b1.a1', '49.a1.a1'], 'contains': ['294.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1313, -1, 6535, -1, 7430, -1, 8161, -1], 'generators': [3], 'label': '294.12.147.a1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '147.a1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '147.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65066236
{'ambient': '294.12', 'aut_centralizer_order': None, 'aut_label': '294.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': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.c1.c1', '98.a1.a1', '147.a1.a1'], 'contains': [], 'core': '294.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3565, 5496, 5117, 4389, 4038, 5668, 4537, 5668], 'generators': [], 'label': '294.12.294.a1.a1', 'mobius_quo': 1, 'mobius_sub': 49, 'normal_closure': '294.a1.a1', 'normal_contained_in': ['42.a1.a1', '42.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '294.a1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '294.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65066237
{'ambient': '294.12', 'aut_centralizer_order': 7, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '252.28', 'aut_weyl_index': 7, 'centralizer': '42.a1.a1', 'complements': ['98.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '21.a1.a1', '21.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2755, 2806, 8127, 7704, 8619, 7435, 5622, 7435], 'generators': [3, 42, 6], 'label': '294.12.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '21.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '294.12', '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'}
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id: 65066238
{'ambient': '294.12', 'aut_centralizer_order': 49, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '36.14', 'aut_weyl_index': 49, 'centralizer': '6.a1.a1', 'complements': ['49.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.c1.c1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6143, 6297, 5316, 3401, 3776, 4116, 2857, 4116], 'generators': [6, 42], 'label': '294.12.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['42.a1.a1', '42.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '294.12', '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'}
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id: 65066239
{'ambient': '294.12', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '147.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '21.b1.a1', '49.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5219, -1, 9181, -1, 4703, -1, 7632, -1], 'generators': [3, 6, 2], 'label': '294.12.7.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': '294.12', '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': '21.1'}
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id: 65066240
{'ambient': '294.12', 'aut_centralizer_order': 6, 'aut_label': '7.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '294.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.b1.a1', '21.a1.a1', '49.a1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1184, -1, 6429, -1, 6783, -1, 9206, -1], 'generators': [3, 42, 2], 'label': '294.12.7.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.b1.a1', 'old_label': '7.b1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
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id: 65066241
{'ambient': '294.12', 'aut_centralizer_order': 6, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '147.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '98.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7115, -1, 8302, -1, 2255, -1, 5225, -1], 'generators': [2, 6], 'label': '294.12.14.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': '294.12', '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': '21.1'}
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id: 65066242
{'ambient': '294.12', 'aut_centralizer_order': 6, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '294.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.b1.a1'], 'contains': ['42.b1.a1', '98.a1.a1'], 'core': '42.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3161, -1, 4555, -1, 5297, -1, 6442, -1], 'generators': [2, 42], 'label': '294.12.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.b1.a1', 'old_label': '14.b1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
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id: 65066243
{'ambient': '294.12', 'aut_centralizer_order': 1, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 42, 'centralizer': '294.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['42.c1.a1', '98.a1.a1'], 'core': '294.a1.a1', 'coset_action_label': '14T14', 'count': 14, 'diagramx': [9303, -1, 1956, -1, 647, -1, 4008, -1], 'generators': [2, 48], 'label': '294.12.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '14.c1.a1', 'projective_image': '294.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
