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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 272, 'aut_gen_orders': [16, 2, 68], 'aut_gens': [[1, 4], [69, 44], [69, 268], [189, 4]], 'aut_group': '2176.21799', 'aut_hash': 21799, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2176, 'aut_permdeg': 68, 'aut_perms': [774102051495788953808281295946777790774569304326668062657026880066085919665235544924013619060923, 776939252927729442650880549990383859433721316085030820349665899818628211294819924114041405416383, 1444490691602843552836093663945796315434409713212586352901077956630504841122247974318944743424000], 'aut_phi_ratio': 17.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 34, 1, 1], [4, 2, 1, 1], [4, 17, 1, 2], [8, 34, 2, 2], [17, 4, 4, 1], [34, 4, 4, 1], [68, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times F_{17}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 272, 'autcentquo_group': '544.242', 'autcentquo_hash': 242, 'autcentquo_nilpotent': False, 'autcentquo_order': 544, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_{17}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 34, 1], [4, 2, 1], [4, 17, 2], [8, 34, 4], [17, 4, 4], [34, 4, 4], [68, 4, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '136.13', 'commutator_count': 1, 'commutator_label': '34.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '17.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 30, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 34, 1, 1], [4, 2, 1, 1], [4, 17, 2, 1], [8, 34, 2, 2], [17, 4, 4, 1], [34, 4, 4, 1], [68, 4, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 136, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 17], 'factors_of_order': [2, 17], 'faithful_reps': [[4, 0, 8]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '136.13', 'hash': 30, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 68, 'inner_gen_orders': [4, 34], 'inner_gens': [[1, 220], [57, 4]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 136, 'inner_split': False, 'inner_tex': 'C_{34}:C_4', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 2], [4, 16]], 'label': '272.30', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 2, 'linQ_dim': 20, 'linQ_dim_count': 2, 'linR_count': 12, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C17:OD16', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 11, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 26, 'number_divisions': 10, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 20, 'number_subgroups': 150, 'old_label': None, 'order': 272, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 35], [4, 36], [8, 136], [17, 16], [34, 16], [68, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 8], 'outer_gen_pows': [68, 2], 'outer_gens': [[69, 132], [1, 148]], 'outer_group': '16.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 10, 'outer_perms': [362880, 11825], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_8', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 1], [16, 2], [32, 1]], 'representations': {'PC': {'code': 2108308480403553988710553013452815, 'gens': [1, 3], 'pres': [5, -2, -2, -2, -2, -17, 10, 686, 3302, 997, 42, 3363, 2648, 58, 1604, 3209]}, 'GLZN': {'d': 2, 'p': 85, 'gens': [21744900, 614551, 11054283, 739909, 42374694]}, 'Perm': {'d': 25, 'gens': [27085530867981586123655, 13329, 55085788254874451536137, 24172, 702513255362746383360000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{17}:\\OD_{16}', 'transitive_degree': 136, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 109545966
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 30, 'group_order': 272, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 109545977
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 30, 'group_order': 272, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 136, 'size': 1}
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id: 109545985
{'aut_label': '2B', 'centralizer': '34.a1.a1', 'counter': 3, 'group_counter': 30, 'group_order': 272, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 222, 'size': 34}
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id: 109545986
{'aut_label': '4A', 'centralizer': '2.a1.a1', 'counter': 4, 'group_counter': 30, 'group_order': 272, 'label': '4A', 'order': 4, 'powers': [2, 4], 'representative': 68, 'size': 2}
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id: 109545987
{'aut_label': '4B1', 'centralizer': '17.a1.a1', 'counter': 5, 'group_counter': 30, 'group_order': 272, 'label': '4B1', 'order': 4, 'powers': [2, 5], 'representative': 106, 'size': 17}
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id: 109545988
{'aut_label': '4B-1', 'centralizer': '17.a1.a1', 'counter': 6, 'group_counter': 30, 'group_order': 272, 'label': '4B-1', 'order': 4, 'powers': [2, 6], 'representative': 242, 'size': 17}
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id: 109545989
{'aut_label': '8A1', 'centralizer': '34.b1.a1', 'counter': 7, 'group_counter': 30, 'group_order': 272, 'label': '8A1', 'order': 8, 'powers': [5, 7], 'representative': 127, 'size': 34}
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id: 109545990
{'aut_label': '8A-1', 'centralizer': '34.b1.a1', 'counter': 8, 'group_counter': 30, 'group_order': 272, 'label': '8A-1', 'order': 8, 'powers': [6, 8], 'representative': 117, 'size': 34}
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id: 109545991
{'aut_label': '8A1', 'centralizer': '34.b1.b1', 'counter': 9, 'group_counter': 30, 'group_order': 272, 'label': '8B1', 'order': 8, 'powers': [5, 9], 'representative': 251, 'size': 34}
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id: 109545967
{'aut_label': '8A-1', 'centralizer': '34.b1.b1', 'counter': 10, 'group_counter': 30, 'group_order': 272, 'label': '8B-1', 'order': 8, 'powers': [6, 10], 'representative': 97, 'size': 34}
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id: 109545968
{'aut_label': '17A1', 'centralizer': '4.b1.a1', 'counter': 11, 'group_counter': 30, 'group_order': 272, 'label': '17A1', 'order': 17, 'powers': [12, 1], 'representative': 16, 'size': 4}
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id: 109545969
{'aut_label': '17A1', 'centralizer': '4.b1.a1', 'counter': 12, 'group_counter': 30, 'group_order': 272, 'label': '17A2', 'order': 17, 'powers': [11, 1], 'representative': 32, 'size': 4}
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id: 109545970
{'aut_label': '17A1', 'centralizer': '4.b1.a1', 'counter': 13, 'group_counter': 30, 'group_order': 272, 'label': '17A3', 'order': 17, 'powers': [14, 1], 'representative': 48, 'size': 4}
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id: 109545971
{'aut_label': '17A1', 'centralizer': '4.b1.a1', 'counter': 14, 'group_counter': 30, 'group_order': 272, 'label': '17A6', 'order': 17, 'powers': [13, 1], 'representative': 96, 'size': 4}
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id: 109545972
{'aut_label': '34A1', 'centralizer': '4.b1.a1', 'counter': 15, 'group_counter': 30, 'group_order': 272, 'label': '34A1', 'order': 34, 'powers': [11, 2], 'representative': 8, 'size': 4}
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id: 109545973
{'aut_label': '34A1', 'centralizer': '4.b1.a1', 'counter': 16, 'group_counter': 30, 'group_order': 272, 'label': '34A3', 'order': 34, 'powers': [13, 2], 'representative': 24, 'size': 4}
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id: 109545974
{'aut_label': '34A1', 'centralizer': '4.b1.a1', 'counter': 17, 'group_counter': 30, 'group_order': 272, 'label': '34A7', 'order': 34, 'powers': [14, 2], 'representative': 56, 'size': 4}
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id: 109545975
{'aut_label': '34A1', 'centralizer': '4.b1.a1', 'counter': 18, 'group_counter': 30, 'group_order': 272, 'label': '34A9', 'order': 34, 'powers': [12, 2], 'representative': 72, 'size': 4}
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id: 109545976
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 19, 'group_counter': 30, 'group_order': 272, 'label': '68A1', 'order': 68, 'powers': [15, 4], 'representative': 4, 'size': 4}
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id: 109545978
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 20, 'group_counter': 30, 'group_order': 272, 'label': '68A-1', 'order': 68, 'powers': [15, 4], 'representative': 52, 'size': 4}
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id: 109545979
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 21, 'group_counter': 30, 'group_order': 272, 'label': '68A3', 'order': 68, 'powers': [16, 4], 'representative': 20, 'size': 4}
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id: 109545980
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 22, 'group_counter': 30, 'group_order': 272, 'label': '68A-3', 'order': 68, 'powers': [16, 4], 'representative': 148, 'size': 4}
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id: 109545981
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 23, 'group_counter': 30, 'group_order': 272, 'label': '68A7', 'order': 68, 'powers': [17, 4], 'representative': 180, 'size': 4}
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id: 109545982
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 24, 'group_counter': 30, 'group_order': 272, 'label': '68A-7', 'order': 68, 'powers': [17, 4], 'representative': 164, 'size': 4}
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id: 109545983
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 25, 'group_counter': 30, 'group_order': 272, 'label': '68A9', 'order': 68, 'powers': [18, 4], 'representative': 36, 'size': 4}
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id: 109545984
{'aut_label': '68A1', 'centralizer': '4.b1.a1', 'counter': 26, 'group_counter': 30, 'group_order': 272, 'label': '68A-9', 'order': 68, 'powers': [18, 4], 'representative': 196, 'size': 4}
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gps_qchar • Show schema
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id: 4318311
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1a', '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, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4318313
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1b', '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, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 4318314
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 4318315
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4318316
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
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id: 4318317
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
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id: 4318318
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.2a', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4318319
{'cdim': 4, 'counter': 8, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.4a', 'multiplicity': 4, 'nt': [17, 3], 'qdim': 16, 'qvalues': [16, 16, 0, 16, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 4318320
{'cdim': 4, 'counter': 9, 'faithful': False, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.4b', 'multiplicity': 4, 'nt': [34, 5], 'qdim': 16, 'qvalues': [16, 16, 0, -16, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4318312
{'cdim': 4, 'counter': 10, 'faithful': True, 'group': '272.30', 'group_order': 272, 'image': None, 'label': '272.30.4c', 'multiplicity': 8, 'nt': [136, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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gps_char • Show schema
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id: 6453604
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 272, 'label': '272.30.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 6453615
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 136, 'label': '272.30.1b', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 6453623
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 136, 'label': '272.30.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 6453624
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 136, 'label': '272.30.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 6453625
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 68, 'label': '272.30.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 6453626
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 68, 'label': '272.30.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 6453627
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 68, 'label': '272.30.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 6453628
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 272, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 68, 'label': '272.30.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 6453629
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 68, 'counter': 9, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 17, 'label': '272.30.2a1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 6453605
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 68, 'counter': 10, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 17, 'label': '272.30.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 6453606
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 11, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '68.3', 'image_order': 68, 'indicator': 1, 'kernel': '68.a1.a1', 'kernel_order': 4, 'label': '272.30.4a1', 'nt': [17, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 3], [1, 5], [1, -5], [1, -3]]]}
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id: 6453607
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 12, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '68.3', 'image_order': 68, 'indicator': 1, 'kernel': '68.a1.a1', 'kernel_order': 4, 'label': '272.30.4a2', 'nt': [17, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 1], [1, 4], [1, -4], [1, -1]]]}
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id: 6453608
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 13, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '68.3', 'image_order': 68, 'indicator': 1, 'kernel': '68.a1.a1', 'kernel_order': 4, 'label': '272.30.4a3', 'nt': [17, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 6], [1, 7], [1, -7], [1, -6]]]}
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id: 6453609
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 14, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '68.3', 'image_order': 68, 'indicator': 1, 'kernel': '68.a1.a1', 'kernel_order': 4, 'label': '272.30.4a4', 'nt': [17, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 2], [1, 8], [1, -8], [1, -2]]]}
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id: 6453610
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 15, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '136.13', 'image_order': 136, 'indicator': 1, 'kernel': '136.a1.a1', 'kernel_order': 2, 'label': '272.30.4b1', 'nt': [34, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]]]}
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id: 6453611
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 16, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '136.13', 'image_order': 136, 'indicator': 1, 'kernel': '136.a1.a1', 'kernel_order': 2, 'label': '272.30.4b2', 'nt': [34, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]]]}
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id: 6453612
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 17, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '136.13', 'image_order': 136, 'indicator': 1, 'kernel': '136.a1.a1', 'kernel_order': 2, 'label': '272.30.4b3', 'nt': [34, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]]]}
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id: 6453613
{'center': '68.a1.a1', 'center_index': 68, 'center_order': 4, 'counter': 18, 'cyclotomic_n': 17, 'dim': 4, 'faithful': False, 'field': [1, 1, -6, -1, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '136.13', 'image_order': 136, 'indicator': 1, 'kernel': '136.a1.a1', 'kernel_order': 2, 'label': '272.30.4b4', 'nt': [34, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 2], [1, 8], [1, -8], [1, -2]], [[1, 6], [1, 7], [1, -7], [1, -6]], [[1, 3], [1, 5], [1, -5], [1, -3]], [[1, 1], [1, 4], [1, -4], [1, -1]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]], [[-1, 1], [-1, 4], [-1, -4], [-1, -1]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 6], [-1, 7], [-1, -7], [-1, -6]], [[-1, 3], [-1, 5], [-1, -5], [-1, -3]], [[-1, 2], [-1, 8], [-1, -8], [-1, -2]]]}
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id: 6453614
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 19, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c1', 'nt': [136, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[1, 3], [1, 5], [1, 29], [1, 31]]]}
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id: 6453616
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c2', 'nt': [136, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]]]}
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id: 6453617
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c3', 'nt': [136, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]]]}
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id: 6453618
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c4', 'nt': [136, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]]]}
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id: 6453619
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c5', 'nt': [136, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[1, 7], [-1, 11], [-1, 23], [1, 27]]]}
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id: 6453620
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c6', 'nt': [136, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[-1, 7], [1, 11], [1, 23], [-1, 27]]]}
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id: 6453621
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c7', 'nt': [136, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[1, 9], [1, 15], [1, 19], [1, 25]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]]]}
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id: 6453622
{'center': '136.a1.a1', 'center_index': 136, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 68, 'dim': 4, 'faithful': True, 'field': [17, 0, 85, 0, 68, 0, 17, 0, 1], 'group': '272.30', 'group_counter': 30, 'group_order': 272, 'image': None, 'image_isoclass': '272.30', 'image_order': 272, 'indicator': 0, 'kernel': '272.a1.a1', 'kernel_order': 1, 'label': '272.30.4c8', 'nt': [136, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, 16], [-1, 18], [-1, 30]], [[-1, 0], [-1, 4], [1, 6], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18], [-1, 20], [1, 22], [-1, 24], [-1, 28], [1, 30]], [[1, 12], [-1, 14], [1, 20], [-1, 22]], [[-1, 6], [-1, 10], [1, 24], [1, 28]], [[1, 0], [1, 4], [-1, 6], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 22], [1, 24], [1, 28], [-1, 30]], [[1, 6], [1, 10], [-1, 24], [-1, 28]], [[-1, 12], [1, 14], [-1, 20], [1, 22]], [[-1, 4], [-1, 16], [1, 18], [1, 30]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [-1, 19], [2, 21], [-1, 23], [1, 25], [-1, 27], [1, 29], [-1, 31]], [[-1, 7], [1, 11], [1, 23], [-1, 27]], [[-1, 9], [-1, 15], [-1, 19], [-1, 25]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [1, 19], [-2, 21], [1, 23], [-1, 25], [1, 27], [-1, 29], [1, 31]], [[-1, 3], [-1, 5], [-1, 29], [-1, 31]], [[1, 7], [-1, 11], [-1, 23], [1, 27]], [[1, 3], [1, 5], [1, 29], [1, 31]], [[1, 9], [1, 15], [1, 19], [1, 25]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 64822214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 272, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 34, 'label': '272.30.1.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': '272.30', 'subgroup_hash': 30, 'subgroup_order': 272, 'subgroup_tex': 'C_{17}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
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id: 64822225
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 136, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '272.30.2.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '136.5', 'subgroup_hash': 5, 'subgroup_order': 136, 'subgroup_tex': 'C_4\\times D_{17}', 'supersolvable': True, 'sylow': 0}
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id: 64822227
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 136, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '272.30.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '136.3', 'subgroup_hash': 3, 'subgroup_order': 136, 'subgroup_tex': 'C_{17}:C_8', 'supersolvable': True, 'sylow': 0}
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id: 64822228
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 136, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '272.30.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '136.3', 'subgroup_hash': 3, 'subgroup_order': 136, 'subgroup_tex': 'C_{17}:C_8', 'supersolvable': True, 'sylow': 0}
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id: 64822229
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 68, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '272.30.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '68.4', 'subgroup_hash': 4, 'subgroup_order': 68, 'subgroup_tex': 'D_{34}', 'supersolvable': True, 'sylow': 0}
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id: 64822230
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 68, 'characteristic': True, 'core_order': 68, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '272.30.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '68.2', 'subgroup_hash': 2, 'subgroup_order': 68, 'subgroup_tex': 'C_{68}', 'supersolvable': True, 'sylow': 0}
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id: 64822231
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 68, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '272.30.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '68.1', 'subgroup_hash': 1, 'subgroup_order': 68, 'subgroup_tex': 'C_{17}:C_4', 'supersolvable': True, 'sylow': 0}
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id: 64822232
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 68, 'characteristic': True, 'core_order': 34, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '272.30.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '34.2', 'subgroup_hash': 2, 'subgroup_order': 34, 'subgroup_tex': 'C_{34}', 'supersolvable': True, 'sylow': 0}
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id: 64822233
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 17, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '272.30.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, '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': '34.1', 'subgroup_hash': 1, 'subgroup_order': 34, 'subgroup_tex': 'D_{17}', 'supersolvable': True, 'sylow': 0}
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id: 64822215
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 68, 'characteristic': True, 'core_order': 17, 'counter': 10, 'cyclic': True, 'direct': False, 'hall': 17, 'label': '272.30.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '17.1', 'subgroup_hash': 1, 'subgroup_order': 17, 'subgroup_tex': 'C_{17}', 'supersolvable': True, 'sylow': 17}
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id: 64822216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '272.30.17.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '17.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': 17, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 2}
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id: 64822217
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '272.30.34.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '34.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': 34, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 64822218
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '272.30.34.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '34.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': 34, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
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id: 64822219
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '272.30.34.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '34.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': 34, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
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id: 64822220
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 136, 'characteristic': True, 'core_order': 4, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '272.30.68.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '68.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '68.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 68, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{17}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 64822221
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '272.30.68.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '68.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': 68, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 64822222
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '272.30.68.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '68.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': 68, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 64822223
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 272, 'characteristic': True, 'core_order': 2, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '272.30.136.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '136.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '136.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 136, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{34}:C_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 64822224
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '272.30.136.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '136.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': 136, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 64822226
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '272.30', 'ambient_counter': 30, 'ambient_order': 272, 'ambient_tex': 'C_{17}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 272, 'characteristic': True, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '272.30.272.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '272.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '272.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 272, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{17}:\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C5'], '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: 64822214
{'ambient': '272.30', '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': '136.a1.a1', 'complements': ['272.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '17.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7756, 3882, 8307, 4104, 6328, 4084, 5818, 4264], 'generators': [136, 16, 2, 68, 1], 'label': '272.30.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '136.13'}
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id: 64822215
{'ambient': '272.30', 'aut_centralizer_order': 136, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.1', 'aut_weyl_index': 136, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1'], 'contains': ['272.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [692, 4616, 654, 5920, 1856, 5967, 1617, 6981], 'generators': [16], 'label': '272.30.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['272.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '272.30', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
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id: 64822216
{'ambient': '272.30', 'aut_centralizer_order': 16, 'aut_label': '17.a1', 'aut_quo_index': None, 'aut_stab_index': 17, 'aut_weyl_group': '8.3', 'aut_weyl_index': 272, 'centralizer': '68.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['34.a1.a1', '34.b1.a1', '34.b1.b1'], 'core': '68.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [9328, -1, 8863, -1, 8585, -1, 8856, -1], 'generators': [1, 68], 'label': '272.30.17.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '17.a1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 64822217
{'ambient': '272.30', 'aut_centralizer_order': 64, 'aut_label': '34.a1', 'aut_quo_index': None, 'aut_stab_index': 17, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1088, 'centralizer': '34.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '17.a1.a1'], 'contains': ['68.a1.a1', '68.b1.a1', '68.c1.a1'], 'core': '68.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [5653, -1, 5386, -1, 7313, -1, 6372, -1], 'generators': [2, 68], 'label': '272.30.34.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '34.a1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '34.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 64822218
{'ambient': '272.30', 'aut_centralizer_order': 32, 'aut_label': '34.b1', 'aut_quo_index': None, 'aut_stab_index': 34, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1088, 'centralizer': '34.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '17.a1.a1'], 'contains': ['68.c1.a1'], 'core': '136.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [8343, -1, 9222, -1, 9446, -1, 9517, -1], 'generators': [5], 'label': '272.30.34.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '34.b1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '34.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 64822219
{'ambient': '272.30', 'aut_centralizer_order': 32, 'aut_label': '34.b1', 'aut_quo_index': None, 'aut_stab_index': 34, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1088, 'centralizer': '34.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '17.a1.a1'], 'contains': ['68.c1.a1'], 'core': '136.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [8343, -1, 7932, -1, 9446, -1, 8231, -1], 'generators': [1], 'label': '272.30.34.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '34.b1.b1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '34.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 64822220
{'ambient': '272.30', 'aut_centralizer_order': 1088, 'aut_label': '68.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1088, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '34.a1.a1'], 'contains': ['136.a1.a1'], 'core': '68.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4119, 8386, 3970, 8777, 5877, 8723, 5121, 9044], 'generators': [68], 'label': '272.30.68.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '68.a1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['136.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '68.a1.a1', 'projective_image': '136.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '34.1', 'quotient_action_kernel_order': 34, 'quotient_fusion': None, 'short_label': '68.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 64822221
{'ambient': '272.30', 'aut_centralizer_order': 64, 'aut_label': '68.b1', 'aut_quo_index': None, 'aut_stab_index': 17, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1088, 'centralizer': '34.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '34.a1.a1'], 'contains': ['136.a1.a1', '136.b1.a1'], 'core': '136.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [1922, -1, 1909, -1, 4297, -1, 3744, -1], 'generators': [134, 136], 'label': '272.30.68.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '68.b1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '68.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 64822222
{'ambient': '272.30', 'aut_centralizer_order': 128, 'aut_label': '68.c1', 'aut_quo_index': None, 'aut_stab_index': 17, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2176, 'centralizer': '17.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '34.a1.a1', '34.b1.a1', '34.b1.b1'], 'contains': ['136.a1.a1'], 'core': '136.a1.a1', 'coset_action_label': None, 'count': 17, 'diagramx': [6486, -1, 6946, -1, 7354, -1, 6408, -1], 'generators': [2], 'label': '272.30.68.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '17.a1.a1', 'old_label': '68.c1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '68.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 64822223
{'ambient': '272.30', 'aut_centralizer_order': 2176, 'aut_label': '136.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2176, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '68.a1.a1', '68.b1.a1', '68.c1.a1'], 'contains': ['272.a1.a1'], 'core': '136.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3097, 6630, 2984, 7446, 4974, 8656, 4334, 8994], 'generators': [136], 'label': '272.30.136.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '136.a1.a1', 'normal_contained_in': ['8.a1.a1', '68.a1.a1'], 'normal_contains': ['272.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '136.a1.a1', 'projective_image': '136.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '136.13', 'quotient_action_kernel_order': 136, 'quotient_fusion': None, 'short_label': '136.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 64822224
{'ambient': '272.30', 'aut_centralizer_order': 64, 'aut_label': '136.b1', 'aut_quo_index': None, 'aut_stab_index': 34, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2176, 'centralizer': '34.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '68.b1.a1'], 'contains': ['272.a1.a1'], 'core': '272.a1.a1', 'coset_action_label': None, 'count': 34, 'diagramx': [1733, -1, 1425, -1, 3498, -1, 3047, -1], 'generators': [134], 'label': '272.30.136.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '34.a1.a1', 'old_label': '136.b1.a1', 'projective_image': '272.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '136.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 64822225
{'ambient': '272.30', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '544.242', 'aut_weyl_index': 4, 'centralizer': '68.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '34.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5028, 6150, 4687, 7542, 3415, 6471, 2225, 7837], 'generators': [2, 68, 16, 136], 'label': '272.30.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '68.3'}
-
id: 64822226
{'ambient': '272.30', 'aut_centralizer_order': None, 'aut_label': '272.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': ['16.a1.a1', '136.a1.a1', '136.b1.a1'], 'contains': [], 'core': '272.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1733, 5703, 1425, 6743, 3498, 7311, 3047, 7987], 'generators': [], 'label': '272.30.272.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '272.a1.a1', 'normal_contained_in': ['16.a1.a1', '136.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '272.a1.a1', 'projective_image': '272.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '272.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 64822227
{'ambient': '272.30', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '544.242', 'aut_weyl_index': 4, 'centralizer': '136.a1.a1', 'complements': ['136.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '34.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7756, 1614, 9364, 4104, 6328, 1697, 6890, 4264], 'generators': [5, 226, 16, 136], 'label': '272.30.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '136.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '136.13'}
-
id: 64822228
{'ambient': '272.30', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '544.242', 'aut_weyl_index': 4, 'centralizer': '136.a1.a1', 'complements': ['136.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '34.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7756, 1614, 7232, 1223, 6328, 1697, 4763, 1270], 'generators': [1, 2, 16, 136], 'label': '272.30.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '136.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '136.13'}
-
id: 64822229
{'ambient': '272.30', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '544.242', 'aut_weyl_index': 4, 'centralizer': '68.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '68.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1999, 5543, 1963, 6622, 728, 5832, 635, 6881], 'generators': [134, 136, 16], 'label': '272.30.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '68.3'}
-
id: 64822230
{'ambient': '272.30', 'aut_centralizer_order': 68, 'aut_label': '4.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.16', 'aut_weyl_index': 68, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '68.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3835, 8386, 3665, 8777, 2554, 8824, 2225, 9120], 'generators': [68, 16, 136], 'label': '272.30.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '68.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '136.13', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 64822231
{'ambient': '272.30', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '272.50', 'aut_weyl_index': 8, 'centralizer': '68.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '68.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6525, 2221, 6211, 4104, 4687, 2336, 4084, 4264], 'generators': [2, 136, 16], 'label': '272.30.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '136.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '68.3'}
-
id: 64822232
{'ambient': '272.30', 'aut_centralizer_order': 136, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.1', 'aut_weyl_index': 136, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '136.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3078, 5543, 2913, 6622, 2554, 5967, 2225, 6981], 'generators': [136, 16], 'label': '272.30.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '136.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '136.13', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 64822233
{'ambient': '272.30', 'aut_centralizer_order': 4, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '272.50', 'aut_weyl_index': 8, 'centralizer': '68.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '136.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [672, -1, 636, -1, 728, -1, 635, -1], 'generators': [134, 16], 'label': '272.30.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '272.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '34.1'}