-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 32, 'aut_gen_orders': [2, 8, 32], 'aut_gens': [[1, 2], [31, 62], [21, 6], [51, 34]], 'aut_group': '512.58302', 'aut_hash': 7772715459544409331, 'aut_nilpotency_class': 5, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 32, 'aut_perms': [209110625063666949217196394943844509, 166831302240608821283181734550591682, 192584446486825221723391051205525821], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 16, 2, 1], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_{32}:C_8', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 16, 'autcentquo_group': '128.913', 'autcentquo_hash': 913, 'autcentquo_nilpotent': True, 'autcentquo_order': 128, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{16}:C_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 2, 1], [4, 16, 2], [8, 2, 2], [16, 2, 4], [32, 2, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '32.18', 'commutator_count': 1, 'commutator_label': '16.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 54, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 16, 1, 2], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 32, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[2, -1, 8]], 'familial': True, 'frattini_label': '16.1', 'frattini_quotient': '4.2', 'hash': 54, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 16, 'inner_gen_orders': [2, 16], 'inner_gens': [[1, 62], [5, 2]], 'inner_hash': 18, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'D_{16}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 15]], 'label': '64.54', 'linC_count': 8, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 32, 'linQ_dim_count': 1, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'Q64', 'ngens': 2, 'nilpotency_class': 5, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 19, 'number_divisions': 8, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 11, 'number_subgroup_classes': 15, 'number_subgroups': 37, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 1], [4, 34], [8, 4], [16, 8], [32, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 8], 'outer_gen_pows': [2, 0], 'outer_gens': [[3, 2], [1, 10]], 'outer_group': '16.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 10, 'outer_perms': [362880, 6057], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_8', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 64, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 1], [8, 1], [16, 1]], 'representations': {'PC': {'code': 309504273051162771967, 'gens': [1, 2], 'pres': [6, -2, 2, -2, -2, -2, -2, 192, 745, 31, 1082, 50, 1347, 69, 1444, 88]}, 'Lie': [{'d': 2, 'q': 31, 'gens': [896293, 653851, 893760, 405374], 'family': 'CSOMinus'}], 'GLFp': {'d': 2, 'p': 31, 'gens': [893666, 687030]}, 'Perm': {'d': 64, 'gens': [66450134624445933678799560050331607746391532584685435254529204790382042061733888000000000, 34216625329393954566794504615428400130324458319121250657957939996263067413000027270329600, 24175131827739636274127375045840733860693888662420563914564207161518320707982436785337600, 12087040917006882684584735480871444149038188995887599735100184001816510068360415118652856, 6010765313484612917937180565556780809330360821355660294198753718800751569568892186006982, 1983116034341975454789449189498620955194254460449807567074683265838922666583379392681647]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_{64}', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
-
gps_conj_classes • Show schema
Hide schema
-
id: 110757690
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 54, 'group_order': 64, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
-
id: 110757701
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 54, 'group_order': 64, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
-
id: 110757702
{'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 54, 'group_order': 64, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 16, 'size': 2}
-
id: 110757703
{'aut_label': '4B', 'centralizer': '16.b1.a1', 'counter': 4, 'group_counter': 54, 'group_order': 64, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 39, 'size': 16}
-
id: 110757704
{'aut_label': '4B', 'centralizer': '16.b1.b1', 'counter': 5, 'group_counter': 54, 'group_order': 64, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 17, 'size': 16}
-
id: 110757705
{'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 54, 'group_order': 64, 'label': '8A1', 'order': 8, 'powers': [3], 'representative': 8, 'size': 2}
-
id: 110757706
{'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 7, 'group_counter': 54, 'group_order': 64, 'label': '8A3', 'order': 8, 'powers': [3], 'representative': 24, 'size': 2}
-
id: 110757707
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 54, 'group_order': 64, 'label': '16A1', 'order': 16, 'powers': [6], 'representative': 4, 'size': 2}
-
id: 110757708
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 54, 'group_order': 64, 'label': '16A3', 'order': 16, 'powers': [7], 'representative': 12, 'size': 2}
-
id: 110757691
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 54, 'group_order': 64, 'label': '16A5', 'order': 16, 'powers': [7], 'representative': 20, 'size': 2}
-
id: 110757692
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 54, 'group_order': 64, 'label': '16A7', 'order': 16, 'powers': [6], 'representative': 28, 'size': 2}
-
id: 110757693
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 54, 'group_order': 64, 'label': '32A1', 'order': 32, 'powers': [8], 'representative': 2, 'size': 2}
-
id: 110757694
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 54, 'group_order': 64, 'label': '32A3', 'order': 32, 'powers': [9], 'representative': 6, 'size': 2}
-
id: 110757695
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 54, 'group_order': 64, 'label': '32A5', 'order': 32, 'powers': [10], 'representative': 10, 'size': 2}
-
id: 110757696
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 54, 'group_order': 64, 'label': '32A7', 'order': 32, 'powers': [11], 'representative': 50, 'size': 2}
-
id: 110757697
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 54, 'group_order': 64, 'label': '32A9', 'order': 32, 'powers': [11], 'representative': 18, 'size': 2}
-
id: 110757698
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 54, 'group_order': 64, 'label': '32A11', 'order': 32, 'powers': [10], 'representative': 42, 'size': 2}
-
id: 110757699
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 54, 'group_order': 64, 'label': '32A13', 'order': 32, 'powers': [9], 'representative': 26, 'size': 2}
-
id: 110757700
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 54, 'group_order': 64, 'label': '32A15', 'order': 32, 'powers': [8], 'representative': 34, 'size': 2}
-
gps_qchar • Show schema
Hide schema
-
id: 4732969
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.1a', '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], 'schur_index': 1}
-
id: 4732970
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.1b', '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], 'schur_index': 1}
-
id: 4732971
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.1c', '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], 'schur_index': 1}
-
id: 4732972
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.1d', '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], 'schur_index': 1}
-
id: 4732973
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4732974
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.2b', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4732975
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.2c', 'multiplicity': 4, 'nt': [16, 56], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4732976
{'cdim': 2, 'counter': 8, 'faithful': True, 'group': '64.54', 'group_order': 64, 'image': None, 'label': '64.54.2d', 'multiplicity': 8, 'nt': [64, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
-
gps_char • Show schema
Hide schema
-
id: 7665149
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 64, 'label': '64.54.1a', '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]]]}
-
id: 7665160
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 32, 'label': '64.54.1b', '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]]]}
-
id: 7665161
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 32, 'label': '64.54.1c', '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]]]}
-
id: 7665162
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 32, 'label': '64.54.1d', '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]]]}
-
id: 7665163
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 16, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 8, 'label': '64.54.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]]]}
-
id: 7665164
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 8, 'counter': 6, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 4, 'label': '64.54.2b1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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], [1, -1]], [[-1, 1], [-1, -1]]]}
-
id: 7665165
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 8, 'counter': 7, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 4, 'label': '64.54.2b2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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], [-1, -1]], [[1, 1], [1, -1]]]}
-
id: 7665166
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 4, 'counter': 8, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 2, 'label': '64.54.2c1', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
-
id: 7665167
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 4, 'counter': 9, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 2, 'label': '64.54.2c2', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
-
id: 7665150
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 4, 'counter': 10, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 2, 'label': '64.54.2c3', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
-
id: 7665151
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 4, 'counter': 11, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 2, 'label': '64.54.2c4', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
-
id: 7665152
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 12, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d1', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
-
id: 7665153
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 13, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d2', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
-
id: 7665154
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d3', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]]]}
-
id: 7665155
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d4', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]]]}
-
id: 7665156
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d5', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]]]}
-
id: 7665157
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 17, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d6', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]]]}
-
id: 7665158
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 18, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d7', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
-
id: 7665159
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 2, 'counter': 19, 'cyclotomic_n': 32, 'dim': 2, 'faithful': True, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '64.54', 'group_counter': 54, 'group_order': 64, 'image': None, 'image_isoclass': '64.54', 'image_order': 64, 'indicator': -1, 'kernel': '64.a1.a1', 'kernel_order': 1, 'label': '64.54.2d8', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
-
gps_subgroup_search • Show schema
Hide schema
-
id: 67936679
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 64, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '64.54.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.54', 'subgroup_hash': 54, 'subgroup_order': 64, 'subgroup_tex': 'Q_{64}', 'supersolvable': True, 'sylow': 2}
-
id: 67936686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.54.2.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
-
id: 67936687
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.54.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
-
id: 67936688
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.54.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.1', 'subgroup_hash': 1, 'subgroup_order': 32, 'subgroup_tex': 'C_{32}', 'supersolvable': True, 'sylow': 0}
-
id: 67936689
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 5, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.54.4.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': '4.2', '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': ['D', 'Phi', 'U1', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 67936690
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.54.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 67936691
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.54.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 67936692
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.54.8.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': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'L2', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 67936693
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.54.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 67936680
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.54.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 67936681
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 11, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.54.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': ['U3', 'L3', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 67936682
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.54.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, '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}
-
id: 67936683
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.54.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, '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}
-
id: 67936684
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.54.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.18', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{16}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U4', 'L4', 'C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 67936685
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.54', 'ambient_counter': 54, 'ambient_order': 64, 'ambient_tex': 'Q_{64}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 1, 'counter': 15, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '64.54.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '64.54', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{64}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U5', 'L5', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
-
gps_subgroup_data • Show schema
Hide schema
-
id: 67936679
{'ambient': '64.54', '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': '32.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5032, 4968, 5000, 5000, 4953, 4984, 5000, 5000], 'generators': [1, 2], 'label': '64.54.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.18', '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': '32.18'}
-
id: 67936680
{'ambient': '64.54', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.a1', '16.b1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7799, -1, 7891, -1, 7774, -1, 7892, -1], 'generators': [1, 48], 'label': '64.54.8.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.b1.b1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 67936681
{'ambient': '64.54', 'aut_centralizer_order': 256, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['32.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3270, 5030, 5000, 5000, 3260, 4984, 5000, 5000], 'generators': [48], 'label': '64.54.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.18', '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'}
-
id: 67936682
{'ambient': '64.54', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7799, -1, 2109, -1, 7774, -1, 2108, -1], 'generators': [3], 'label': '64.54.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 67936683
{'ambient': '64.54', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '16.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7799, -1, 7891, -1, 7774, -1, 7892, -1], 'generators': [1], 'label': '64.54.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 67936684
{'ambient': '64.54', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['64.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5534, 5030, 5000, 5000, 5517, 4984, 5000, 5000], 'generators': [32], 'label': '64.54.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.18', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.18', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 67936685
{'ambient': '64.54', 'aut_centralizer_order': None, 'aut_label': '64.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': ['32.a1.a1'], 'contains': [], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5534, 5030, 5000, 5000, 5517, 4984, 5000, 5000], 'generators': [], 'label': '64.54.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 67936686
{'ambient': '64.54', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.913', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7799, 2219, 1425, 1425, 7774, 2226, 1426, 1426], 'generators': [3, 60], 'label': '64.54.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.18', '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': '32.18'}
-
id: 67936687
{'ambient': '64.54', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.913', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7799, 2219, 8575, 8575, 7774, 2226, 8574, 8574], 'generators': [1, 60], 'label': '64.54.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
-
id: 67936688
{'ambient': '64.54', 'aut_centralizer_order': 32, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.5', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2201, 7781, 5000, 5000, 2194, 7806, 5000, 5000], 'generators': [2], 'label': '64.54.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.18', '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': '2.1'}
-
id: 67936689
{'ambient': '64.54', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2201, 5030, 5000, 5000, 2194, 4984, 5000, 5000], 'generators': [60], 'label': '64.54.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.18', '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'}
-
id: 67936690
{'ambient': '64.54', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7799, -1, 1425, -1, 7774, -1, 1426, -1], 'generators': [3, 8], 'label': '64.54.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
-
id: 67936691
{'ambient': '64.54', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '8.b1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7799, -1, 8575, -1, 7774, -1, 8574, -1], 'generators': [1, 8], 'label': '64.54.4.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.b1.b1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
-
id: 67936692
{'ambient': '64.54', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3270, 5030, 5000, 5000, 3260, 4984, 5000, 5000], 'generators': [8], 'label': '64.54.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.18', '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'}
-
id: 67936693
{'ambient': '64.54', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '16.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7799, -1, 2109, -1, 7774, -1, 2108, -1], 'generators': [3, 48], 'label': '64.54.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.18', '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': '8.3'}
