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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '16.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 12], 'aut_gens': [[1, 16], [1, 32], [15, 16], [35, 16]], 'aut_group': '48.35', 'aut_hash': 35, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 9, 'aut_perms': [1, 24, 131044], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [6, 2, 1, 1], [8, 1, 4, 1], [12, 2, 2, 1], [16, 3, 8, 1], [24, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 1, 2], [6, 2, 1], [8, 1, 4], [12, 2, 2], [16, 3, 8], [24, 2, 4]], 'center_label': '8.1', 'center_order': 8, 'central_product': False, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [6, 2, 1, 1], [8, 1, 4, 1], [12, 2, 2, 1], [16, 3, 8, 1], [24, 2, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 48, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 4]], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '6.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 32], [33, 16]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 16], [2, 8]], 'label': '48.1', 'linC_count': 4, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3:C16', '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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 24, 'number_divisions': 9, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 10, 'number_subgroups': 12, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [8, 4], [12, 4], [16, 24], [24, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[15, 16], [5, 16]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 137], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [16], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 2]], 'representations': {'PC': {'code': 61763227873, 'gens': [1, 5], 'pres': [5, -2, -2, -2, -2, -3, 10, 26, 42, 804]}, 'GLFp': {'d': 2, 'p': 17, 'gens': [74462, 64222]}, 'Perm': {'d': 19, 'gens': [6825021338425105, 14276338251085680, 21115580623822080, 27899279605229760, 3]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [16], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:C_{16}', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 110381531
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 48, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 110381542
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 48, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 8, 'size': 1}
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id: 110381548
{'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 48, 'label': '3A', 'order': 3, 'powers': [3, 1], 'representative': 32, 'size': 2}
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id: 110381549
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 48, 'label': '4A1', 'order': 4, 'powers': [2, 5], 'representative': 4, 'size': 1}
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id: 110381550
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 48, 'label': '4A-1', 'order': 4, 'powers': [2, 4], 'representative': 12, 'size': 1}
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id: 110381551
{'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 48, 'label': '6A', 'order': 6, 'powers': [3, 2], 'representative': 24, 'size': 2}
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id: 110381552
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 48, 'label': '8A1', 'order': 8, 'powers': [4, 9], 'representative': 2, 'size': 1}
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id: 110381553
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 48, 'label': '8A-1', 'order': 8, 'powers': [5, 10], 'representative': 14, 'size': 1}
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id: 110381554
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 48, 'label': '8A3', 'order': 8, 'powers': [5, 7], 'representative': 6, 'size': 1}
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id: 110381532
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 48, 'label': '8A-3', 'order': 8, 'powers': [4, 8], 'representative': 10, 'size': 1}
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id: 110381533
{'aut_label': '12A1', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 48, 'label': '12A1', 'order': 12, 'powers': [6, 5], 'representative': 36, 'size': 2}
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id: 110381534
{'aut_label': '12A1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 48, 'label': '12A-1', 'order': 12, 'powers': [6, 4], 'representative': 28, 'size': 2}
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id: 110381535
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 48, 'label': '16A1', 'order': 16, 'powers': [7, 15], 'representative': 1, 'size': 3}
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id: 110381536
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 48, 'label': '16A-1', 'order': 16, 'powers': [8, 16], 'representative': 15, 'size': 3}
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id: 110381537
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 48, 'label': '16A3', 'order': 16, 'powers': [9, 20], 'representative': 3, 'size': 3}
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id: 110381538
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 48, 'label': '16A-3', 'order': 16, 'powers': [10, 19], 'representative': 13, 'size': 3}
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id: 110381539
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 48, 'label': '16A5', 'order': 16, 'powers': [10, 14], 'representative': 5, 'size': 3}
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id: 110381540
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 48, 'label': '16A-5', 'order': 16, 'powers': [9, 13], 'representative': 11, 'size': 3}
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id: 110381541
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 48, 'label': '16A7', 'order': 16, 'powers': [8, 17], 'representative': 7, 'size': 3}
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id: 110381543
{'aut_label': '16A1', 'centralizer': '3.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 48, 'label': '16A-7', 'order': 16, 'powers': [7, 18], 'representative': 9, 'size': 3}
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id: 110381544
{'aut_label': '24A1', 'centralizer': '2.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 48, 'label': '24A1', 'order': 24, 'powers': [11, 9], 'representative': 18, 'size': 2}
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id: 110381545
{'aut_label': '24A1', 'centralizer': '2.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 48, 'label': '24A-1', 'order': 24, 'powers': [12, 10], 'representative': 30, 'size': 2}
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id: 110381546
{'aut_label': '24A1', 'centralizer': '2.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 48, 'label': '24A5', 'order': 24, 'powers': [11, 8], 'representative': 26, 'size': 2}
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id: 110381547
{'aut_label': '24A1', 'centralizer': '2.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 48, 'label': '24A-5', 'order': 24, 'powers': [12, 7], 'representative': 22, 'size': 2}
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gps_qchar • Show schema
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id: 4602527
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4602528
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4602529
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
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id: 4602532
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, -1, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
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id: 4602533
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.2b', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, 2, -1, 2, 2, -1, -2, -2, -2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 2}
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id: 4602530
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.1d', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4602534
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.2c', 'multiplicity': 2, 'nt': [24, 8], 'qdim': 4, 'qvalues': [4, 4, -2, -4, -4, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4602531
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.1e', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4602535
{'cdim': 2, 'counter': 9, 'faithful': True, 'group': '48.1', 'group_order': 48, 'image': None, 'label': '48.1.2d', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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gps_char • Show schema
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id: 7288990
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 48, 'label': '48.1.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 7289001
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 24, 'label': '48.1.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 7289007
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 12, 'label': '48.1.1c1', 'nt': [4, 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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 7289008
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 12, 'label': '48.1.1c2', 'nt': [4, 2], '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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 7289009
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 5, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 6, 'label': '48.1.1d1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]]]}
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id: 7289010
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 6, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 6, 'label': '48.1.1d2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]]]}
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id: 7289011
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 7, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 6, 'label': '48.1.1d3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]]]}
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id: 7289012
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 8, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 6, 'label': '48.1.1d4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]]]}
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id: 7289013
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 9, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e1', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[1, 5]], [[-1, 5]], [[1, 6]], [[-1, 2]], [[-1, 6]], [[1, 2]]]}
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id: 7288991
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 10, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e2', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 4]], [[-1, 4]], [[1, 5]], [[-1, 5]], [[1, 7]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[-1, 3]], [[1, 3]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 6]]]}
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id: 7288992
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 11, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e3', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 6]], [[-1, 2]], [[-1, 6]], [[1, 2]]]}
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id: 7288993
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 12, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e4', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 5]], [[1, 5]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 7]], [[1, 3]], [[-1, 3]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 6]]]}
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id: 7288994
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 13, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e5', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 7]], [[-1, 7]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 6]], [[1, 2]], [[1, 6]], [[-1, 2]]]}
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id: 7288995
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 14, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e6', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 3]], [[1, 7]], [[-1, 7]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[1, 6]]]}
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id: 7288996
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 15, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e7', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[-1, 7]], [[1, 7]], [[1, 5]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 6]], [[1, 2]], [[1, 6]], [[-1, 2]]]}
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id: 7288997
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 16, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3, 'label': '48.1.1e8', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 3]], [[-1, 7]], [[1, 7]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[1, 6]]]}
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id: 7288998
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 8, 'label': '48.1.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 7288999
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 4, 'label': '48.1.2b', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 7289000
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 2, 'label': '48.1.2c1', 'nt': [24, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
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id: 7289002
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 2, 'label': '48.1.2c2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
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id: 7289003
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': True, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '48.1', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 1, 'label': '48.1.2d1', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[1, 0]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]]]}
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id: 7289004
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': True, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '48.1', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 1, 'label': '48.1.2d2', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[1, 0]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[2, 1]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
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id: 7289005
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 23, 'cyclotomic_n': 8, 'dim': 2, 'faithful': True, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '48.1', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 1, 'label': '48.1.2d3', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[1, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]]]}
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id: 7289006
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 8, 'dim': 2, 'faithful': True, 'field': [1, 0, 0, 0, 1], 'group': '48.1', 'group_counter': 1, 'group_order': 48, 'image': None, 'image_isoclass': '48.1', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 1, 'label': '48.1.2d4', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[1, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 66929197
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '48.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.1', 'subgroup_hash': 1, 'subgroup_order': 48, 'subgroup_tex': 'C_3:C_{16}', 'supersolvable': True, 'sylow': 0}
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id: 66929199
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 2, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
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id: 66929200
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 3, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '48.1.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.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': 3, '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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 2}
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id: 66929201
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 12, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 66929202
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 8, 'counter': 5, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.6.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': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0'], 'split': False, '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: 66929203
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 6, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.8.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': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C3'], 'split': False, '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: 66929204
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 4, 'counter': 7, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 66929205
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 3, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '48.1.16.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': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': True, '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: 66929206
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 2, 'counter': 9, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.1.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, '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: 66929198
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.1', 'ambient_counter': 1, 'ambient_order': 48, 'ambient_tex': 'C_3:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 1, 'counter': 10, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '48.1.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '48.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', '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: 66929197
{'ambient': '48.1', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.a1.a1', 'complements': ['48.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8088, 6950, 2938, 7487, 5000, 5282, 5000, 4718], 'generators': [1, 16, 2, 4, 8], 'label': '48.1.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 66929198
{'ambient': '48.1', 'aut_centralizer_order': None, 'aut_label': '48.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', '24.a1.a1'], 'contains': [], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2236, 3354, 7588, 2763, 4494, 5000, 4494, 5000], 'generators': [], 'label': '48.1.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66929199
{'ambient': '48.1', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 6, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6340, 6950, 4299, 7487, 2215, 5282, 2215, 4718], 'generators': [2, 16, 4, 8], 'label': '48.1.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '6.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 66929200
{'ambient': '48.1', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 6, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8902, -1, 1534, -1, 7785, -1, 7785, -1], 'generators': [1], 'label': '48.1.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66929201
{'ambient': '48.1', 'aut_centralizer_order': 12, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3781, 4512, 7062, 5477, 2215, 2465, 2215, 7535], 'generators': [4, 16, 8], 'label': '48.1.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '12.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 66929202
{'ambient': '48.1', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 12, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6990, 8354, 2632, 8643, 7279, 8099, 7279, 1901], 'generators': [2], 'label': '48.1.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '6.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66929203
{'ambient': '48.1', 'aut_centralizer_order': 24, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2520, 1646, 7456, 3115, 2215, 2465, 2215, 7535], 'generators': [8, 16], 'label': '48.1.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 66929204
{'ambient': '48.1', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5568, 8354, 3641, 6883, 6772, 7535, 6772, 2465], 'generators': [4], 'label': '48.1.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 66929205
{'ambient': '48.1', 'aut_centralizer_order': 24, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1098, 1646, 8466, 1357, 2215, 2465, 2215, 7535], 'generators': [16], 'label': '48.1.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 66929206
{'ambient': '48.1', 'aut_centralizer_order': 48, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 48, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['48.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3332, 5000, 6052, 4120, 6772, 7535, 6772, 2465], 'generators': [8], 'label': '48.1.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.1', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
