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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '144.47', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 6, 3], 'aut_gens': [[1, 4, 16], [153, 6, 304], [297, 442, 382], [157, 438, 452]], 'aut_group': None, 'aut_hash': 2915816468698592651, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 36864, 'aut_permdeg': 38, 'aut_perms': [47666871835167676450325677320892968194718110, 469485100068283591292541512473469025745426261, 314243960475897588118936329128635196894945149], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [3, 1, 2, 1], [4, 2, 12, 1], [4, 4, 8, 1], [6, 1, 6, 1], [6, 1, 8, 1], [9, 1, 6, 1], [12, 2, 24, 1], [12, 4, 16, 1], [18, 1, 18, 1], [18, 1, 24, 1], [36, 2, 72, 1], [36, 4, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^8.C_2^2.C_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': None, 'autcent_hash': 1957374279625110835, 'autcent_nilpotent': True, 'autcent_order': 3072, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'A_4', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [4, 2, 12], [4, 4, 8], [6, 1, 14], [9, 1, 6], [12, 2, 24], [12, 4, 16], [18, 1, 42], [36, 2, 72], [36, 4, 48]], 'center_label': '72.18', 'center_order': 72, 'central_product': True, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 819, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['64.64', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 2, 2, 6], [4, 4, 2, 4], [6, 1, 2, 7], [9, 1, 6, 1], [12, 2, 4, 6], [12, 4, 4, 4], [18, 1, 6, 7], [36, 2, 12, 6], [36, 4, 12, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1638, 'exponent': 36, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '24.15', 'frattini_quotient': '24.15', 'hash': 819, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 292, 312], [289, 4, 16], [297, 4, 16]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 144], [2, 108]], 'label': '576.819', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:C36', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 252, 'number_divisions': 54, 'number_normal_subgroups': 123, 'number_subgroup_autclasses': 51, 'number_subgroup_classes': 207, 'number_subgroups': 315, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 56], [6, 14], [9, 6], [12, 112], [18, 42], [36, 336]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 12, 6], 'outer_gen_pows': [0, 0, 16], 'outer_gens': [[147, 434, 180], [149, 6, 210], [149, 292, 368]], 'outer_group': None, 'outer_hash': 6189875647093395715, 'outer_nilpotent': False, 'outer_order': 4608, 'outer_permdeg': 25, 'outer_perms': [3882352037610273771080760, 3883529811874799496332660, 620553016541827766880572], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^6.A_4.C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 10], [6, 8], [8, 6], [12, 4], [24, 6]], 'representations': {'PC': {'code': 15747833389076195978410344150275, 'gens': [1, 3, 5], 'pres': [8, -2, -2, -2, -2, 2, -2, -3, -3, 16, 7010, 66, 12484, 116, 141, 222]}, 'Perm': {'d': 29, 'gens': [305725951080615436199547667200, 643297706733012067538448595200, 43976142942049335890106259200, 357120, 88056384595200, 959835538826526612408238080000, 5109182273555539200, 80884]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 36], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:C_{36}', 'transitive_degree': 576, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 139469760
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 819, 'group_order': 576, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 139469871
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 819, 'group_order': 576, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 288, 'size': 1}
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id: 139469935
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 819, 'group_order': 576, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 8, 'size': 1}
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id: 139469946
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 819, 'group_order': 576, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 296, 'size': 1}
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id: 139469957
{'aut_label': '2D', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 819, 'group_order': 576, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 2, 'size': 1}
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id: 139469968
{'aut_label': '2D', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 819, 'group_order': 576, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 10, 'size': 1}
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id: 139469979
{'aut_label': '2D', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 819, 'group_order': 576, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 298, 'size': 1}
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id: 139469990
{'aut_label': '2D', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 819, 'group_order': 576, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 290, 'size': 1}
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id: 139470001
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 9, 'group_counter': 819, 'group_order': 576, 'label': '3A1', 'order': 3, 'powers': [10, 1], 'representative': 192, 'size': 1}
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id: 139469761
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 10, 'group_counter': 819, 'group_order': 576, 'label': '3A-1', 'order': 3, 'powers': [9, 1], 'representative': 384, 'size': 1}
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id: 139469772
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 11, 'group_counter': 819, 'group_order': 576, 'label': '4A1', 'order': 4, 'powers': [2, 12], 'representative': 144, 'size': 2}
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id: 139469783
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 12, 'group_counter': 819, 'group_order': 576, 'label': '4A-1', 'order': 4, 'powers': [2, 11], 'representative': 432, 'size': 2}
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id: 139469794
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 13, 'group_counter': 819, 'group_order': 576, 'label': '4B1', 'order': 4, 'powers': [3, 14], 'representative': 4, 'size': 2}
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id: 139469805
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 14, 'group_counter': 819, 'group_order': 576, 'label': '4B-1', 'order': 4, 'powers': [3, 13], 'representative': 12, 'size': 2}
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id: 139469816
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 15, 'group_counter': 819, 'group_order': 576, 'label': '4C1', 'order': 4, 'powers': [4, 16], 'representative': 148, 'size': 2}
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id: 139469827
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 16, 'group_counter': 819, 'group_order': 576, 'label': '4C-1', 'order': 4, 'powers': [4, 15], 'representative': 444, 'size': 2}
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id: 139469838
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 17, 'group_counter': 819, 'group_order': 576, 'label': '4D1', 'order': 4, 'powers': [2, 18], 'representative': 146, 'size': 2}
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id: 139469849
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 18, 'group_counter': 819, 'group_order': 576, 'label': '4D-1', 'order': 4, 'powers': [2, 17], 'representative': 434, 'size': 2}
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id: 139469860
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 19, 'group_counter': 819, 'group_order': 576, 'label': '4E1', 'order': 4, 'powers': [3, 20], 'representative': 6, 'size': 2}
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id: 139469872
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 20, 'group_counter': 819, 'group_order': 576, 'label': '4E-1', 'order': 4, 'powers': [3, 19], 'representative': 14, 'size': 2}
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id: 139469883
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 21, 'group_counter': 819, 'group_order': 576, 'label': '4F1', 'order': 4, 'powers': [4, 22], 'representative': 150, 'size': 2}
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id: 139469894
{'aut_label': '4A1', 'centralizer': '2.b1', 'counter': 22, 'group_counter': 819, 'group_order': 576, 'label': '4F-1', 'order': 4, 'powers': [4, 21], 'representative': 446, 'size': 2}
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id: 139469905
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 23, 'group_counter': 819, 'group_order': 576, 'label': '4G1', 'order': 4, 'powers': [5, 24], 'representative': 1, 'size': 4}
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id: 139469916
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 24, 'group_counter': 819, 'group_order': 576, 'label': '4G-1', 'order': 4, 'powers': [5, 23], 'representative': 3, 'size': 4}
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id: 139469927
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 25, 'group_counter': 819, 'group_order': 576, 'label': '4H1', 'order': 4, 'powers': [6, 26], 'representative': 145, 'size': 4}
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id: 139469931
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 26, 'group_counter': 819, 'group_order': 576, 'label': '4H-1', 'order': 4, 'powers': [6, 25], 'representative': 155, 'size': 4}
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id: 139469932
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 27, 'group_counter': 819, 'group_order': 576, 'label': '4I1', 'order': 4, 'powers': [7, 28], 'representative': 5, 'size': 4}
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id: 139469933
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 28, 'group_counter': 819, 'group_order': 576, 'label': '4I-1', 'order': 4, 'powers': [7, 27], 'representative': 303, 'size': 4}
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id: 139469934
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 29, 'group_counter': 819, 'group_order': 576, 'label': '4J1', 'order': 4, 'powers': [8, 30], 'representative': 149, 'size': 4}
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id: 139469936
{'aut_label': '4G1', 'centralizer': '4.b1', 'counter': 30, 'group_counter': 819, 'group_order': 576, 'label': '4J-1', 'order': 4, 'powers': [8, 29], 'representative': 439, 'size': 4}
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id: 139469937
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 31, 'group_counter': 819, 'group_order': 576, 'label': '6A1', 'order': 6, 'powers': [9, 2], 'representative': 96, 'size': 1}
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id: 139469938
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 32, 'group_counter': 819, 'group_order': 576, 'label': '6A-1', 'order': 6, 'powers': [10, 2], 'representative': 480, 'size': 1}
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id: 139469939
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 33, 'group_counter': 819, 'group_order': 576, 'label': '6B1', 'order': 6, 'powers': [9, 3], 'representative': 392, 'size': 1}
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id: 139469940
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 34, 'group_counter': 819, 'group_order': 576, 'label': '6B-1', 'order': 6, 'powers': [10, 3], 'representative': 200, 'size': 1}
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id: 139469941
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 35, 'group_counter': 819, 'group_order': 576, 'label': '6C1', 'order': 6, 'powers': [9, 4], 'representative': 104, 'size': 1}
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id: 139469942
{'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 36, 'group_counter': 819, 'group_order': 576, 'label': '6C-1', 'order': 6, 'powers': [10, 4], 'representative': 488, 'size': 1}
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id: 139469943
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 37, 'group_counter': 819, 'group_order': 576, 'label': '6D1', 'order': 6, 'powers': [9, 5], 'representative': 386, 'size': 1}
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id: 139469944
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 38, 'group_counter': 819, 'group_order': 576, 'label': '6D-1', 'order': 6, 'powers': [10, 5], 'representative': 194, 'size': 1}
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id: 139469945
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 39, 'group_counter': 819, 'group_order': 576, 'label': '6E1', 'order': 6, 'powers': [9, 6], 'representative': 394, 'size': 1}
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id: 139469947
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 40, 'group_counter': 819, 'group_order': 576, 'label': '6E-1', 'order': 6, 'powers': [10, 6], 'representative': 202, 'size': 1}
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id: 139469948
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 41, 'group_counter': 819, 'group_order': 576, 'label': '6F1', 'order': 6, 'powers': [9, 7], 'representative': 106, 'size': 1}
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id: 139469949
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 42, 'group_counter': 819, 'group_order': 576, 'label': '6F-1', 'order': 6, 'powers': [10, 7], 'representative': 490, 'size': 1}
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id: 139469950
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 43, 'group_counter': 819, 'group_order': 576, 'label': '6G1', 'order': 6, 'powers': [9, 8], 'representative': 98, 'size': 1}
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id: 139469951
{'aut_label': '6D1', 'centralizer': '1.a1', 'counter': 44, 'group_counter': 819, 'group_order': 576, 'label': '6G-1', 'order': 6, 'powers': [10, 8], 'representative': 482, 'size': 1}
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id: 139469952
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 45, 'group_counter': 819, 'group_order': 576, 'label': '9A1', 'order': 9, 'powers': [47, 9], 'representative': 64, 'size': 1}
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id: 139469953
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 46, 'group_counter': 819, 'group_order': 576, 'label': '9A-1', 'order': 9, 'powers': [48, 10], 'representative': 512, 'size': 1}
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id: 139469954
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 47, 'group_counter': 819, 'group_order': 576, 'label': '9A2', 'order': 9, 'powers': [49, 10], 'representative': 128, 'size': 1}
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id: 139469955
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 48, 'group_counter': 819, 'group_order': 576, 'label': '9A-2', 'order': 9, 'powers': [50, 9], 'representative': 448, 'size': 1}
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id: 139469956
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 49, 'group_counter': 819, 'group_order': 576, 'label': '9A4', 'order': 9, 'powers': [46, 9], 'representative': 256, 'size': 1}
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id: 139469958
{'aut_label': '9A1', 'centralizer': '1.a1', 'counter': 50, 'group_counter': 819, 'group_order': 576, 'label': '9A-4', 'order': 9, 'powers': [45, 10], 'representative': 320, 'size': 1}
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id: 139469959
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 51, 'group_counter': 819, 'group_order': 576, 'label': '12A1', 'order': 12, 'powers': [31, 11], 'representative': 48, 'size': 2}
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id: 139469960
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 52, 'group_counter': 819, 'group_order': 576, 'label': '12A-1', 'order': 12, 'powers': [32, 12], 'representative': 528, 'size': 2}
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id: 139469961
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 53, 'group_counter': 819, 'group_order': 576, 'label': '12A5', 'order': 12, 'powers': [32, 11], 'representative': 240, 'size': 2}
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id: 139469962
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 54, 'group_counter': 819, 'group_order': 576, 'label': '12A-5', 'order': 12, 'powers': [31, 12], 'representative': 336, 'size': 2}
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id: 139469963
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 55, 'group_counter': 819, 'group_order': 576, 'label': '12B1', 'order': 12, 'powers': [33, 13], 'representative': 204, 'size': 2}
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id: 139469964
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 56, 'group_counter': 819, 'group_order': 576, 'label': '12B-1', 'order': 12, 'powers': [34, 14], 'representative': 388, 'size': 2}
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id: 139469965
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 57, 'group_counter': 819, 'group_order': 576, 'label': '12B5', 'order': 12, 'powers': [34, 13], 'representative': 396, 'size': 2}
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id: 139469966
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 58, 'group_counter': 819, 'group_order': 576, 'label': '12B-5', 'order': 12, 'powers': [33, 14], 'representative': 196, 'size': 2}
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id: 139469967
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 59, 'group_counter': 819, 'group_order': 576, 'label': '12C1', 'order': 12, 'powers': [35, 15], 'representative': 60, 'size': 2}
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id: 139469969
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 60, 'group_counter': 819, 'group_order': 576, 'label': '12C-1', 'order': 12, 'powers': [36, 16], 'representative': 532, 'size': 2}
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id: 139469970
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 61, 'group_counter': 819, 'group_order': 576, 'label': '12C5', 'order': 12, 'powers': [36, 15], 'representative': 252, 'size': 2}
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id: 139469971
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 62, 'group_counter': 819, 'group_order': 576, 'label': '12C-5', 'order': 12, 'powers': [35, 16], 'representative': 340, 'size': 2}
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id: 139469972
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 63, 'group_counter': 819, 'group_order': 576, 'label': '12D1', 'order': 12, 'powers': [31, 17], 'representative': 50, 'size': 2}
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id: 139469973
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 64, 'group_counter': 819, 'group_order': 576, 'label': '12D-1', 'order': 12, 'powers': [32, 18], 'representative': 530, 'size': 2}
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id: 139469974
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 65, 'group_counter': 819, 'group_order': 576, 'label': '12D5', 'order': 12, 'powers': [32, 17], 'representative': 242, 'size': 2}
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id: 139469975
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 66, 'group_counter': 819, 'group_order': 576, 'label': '12D-5', 'order': 12, 'powers': [31, 18], 'representative': 338, 'size': 2}
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id: 139469976
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 67, 'group_counter': 819, 'group_order': 576, 'label': '12E1', 'order': 12, 'powers': [33, 19], 'representative': 206, 'size': 2}
-
id: 139469977
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 68, 'group_counter': 819, 'group_order': 576, 'label': '12E-1', 'order': 12, 'powers': [34, 20], 'representative': 390, 'size': 2}
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id: 139469978
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 69, 'group_counter': 819, 'group_order': 576, 'label': '12E5', 'order': 12, 'powers': [34, 19], 'representative': 398, 'size': 2}
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id: 139469980
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 70, 'group_counter': 819, 'group_order': 576, 'label': '12E-5', 'order': 12, 'powers': [33, 20], 'representative': 198, 'size': 2}
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id: 139469981
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 71, 'group_counter': 819, 'group_order': 576, 'label': '12F1', 'order': 12, 'powers': [35, 21], 'representative': 62, 'size': 2}
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id: 139469982
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 72, 'group_counter': 819, 'group_order': 576, 'label': '12F-1', 'order': 12, 'powers': [36, 22], 'representative': 534, 'size': 2}
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id: 139469983
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 73, 'group_counter': 819, 'group_order': 576, 'label': '12F5', 'order': 12, 'powers': [36, 21], 'representative': 254, 'size': 2}
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id: 139469984
{'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 74, 'group_counter': 819, 'group_order': 576, 'label': '12F-5', 'order': 12, 'powers': [35, 22], 'representative': 342, 'size': 2}
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id: 139469985
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 75, 'group_counter': 819, 'group_order': 576, 'label': '12G1', 'order': 12, 'powers': [37, 23], 'representative': 195, 'size': 4}
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id: 139469986
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 76, 'group_counter': 819, 'group_order': 576, 'label': '12G-1', 'order': 12, 'powers': [38, 24], 'representative': 385, 'size': 4}
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id: 139469987
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 77, 'group_counter': 819, 'group_order': 576, 'label': '12G5', 'order': 12, 'powers': [38, 23], 'representative': 387, 'size': 4}
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id: 139469988
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 78, 'group_counter': 819, 'group_order': 576, 'label': '12G-5', 'order': 12, 'powers': [37, 24], 'representative': 193, 'size': 4}
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id: 139469989
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 79, 'group_counter': 819, 'group_order': 576, 'label': '12H1', 'order': 12, 'powers': [39, 25], 'representative': 347, 'size': 4}
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id: 139469991
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 80, 'group_counter': 819, 'group_order': 576, 'label': '12H-1', 'order': 12, 'powers': [40, 26], 'representative': 529, 'size': 4}
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id: 139469992
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 81, 'group_counter': 819, 'group_order': 576, 'label': '12H5', 'order': 12, 'powers': [40, 25], 'representative': 539, 'size': 4}
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id: 139469993
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 82, 'group_counter': 819, 'group_order': 576, 'label': '12H-5', 'order': 12, 'powers': [39, 26], 'representative': 337, 'size': 4}
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id: 139469994
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 83, 'group_counter': 819, 'group_order': 576, 'label': '12I1', 'order': 12, 'powers': [41, 27], 'representative': 495, 'size': 4}
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id: 139469995
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 84, 'group_counter': 819, 'group_order': 576, 'label': '12I-1', 'order': 12, 'powers': [42, 28], 'representative': 389, 'size': 4}
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id: 139469996
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 85, 'group_counter': 819, 'group_order': 576, 'label': '12I5', 'order': 12, 'powers': [42, 27], 'representative': 111, 'size': 4}
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id: 139469997
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 86, 'group_counter': 819, 'group_order': 576, 'label': '12I-5', 'order': 12, 'powers': [41, 28], 'representative': 197, 'size': 4}
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id: 139469998
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 87, 'group_counter': 819, 'group_order': 576, 'label': '12J1', 'order': 12, 'powers': [43, 29], 'representative': 55, 'size': 4}
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id: 139469999
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 88, 'group_counter': 819, 'group_order': 576, 'label': '12J-1', 'order': 12, 'powers': [44, 30], 'representative': 533, 'size': 4}
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id: 139470000
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 89, 'group_counter': 819, 'group_order': 576, 'label': '12J5', 'order': 12, 'powers': [44, 29], 'representative': 247, 'size': 4}
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id: 139470002
{'aut_label': '12G1', 'centralizer': '4.b1', 'counter': 90, 'group_counter': 819, 'group_order': 576, 'label': '12J-5', 'order': 12, 'powers': [43, 30], 'representative': 341, 'size': 4}
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id: 139470003
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 91, 'group_counter': 819, 'group_order': 576, 'label': '18A1', 'order': 18, 'powers': [45, 31], 'representative': 32, 'size': 1}
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id: 139470004
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 92, 'group_counter': 819, 'group_order': 576, 'label': '18A-1', 'order': 18, 'powers': [46, 32], 'representative': 544, 'size': 1}
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id: 139470005
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 93, 'group_counter': 819, 'group_order': 576, 'label': '18A5', 'order': 18, 'powers': [50, 32], 'representative': 160, 'size': 1}
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id: 139470006
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 94, 'group_counter': 819, 'group_order': 576, 'label': '18A-5', 'order': 18, 'powers': [49, 31], 'representative': 416, 'size': 1}
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id: 139470007
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 95, 'group_counter': 819, 'group_order': 576, 'label': '18A7', 'order': 18, 'powers': [48, 31], 'representative': 224, 'size': 1}
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id: 139470008
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 96, 'group_counter': 819, 'group_order': 576, 'label': '18A-7', 'order': 18, 'powers': [47, 32], 'representative': 352, 'size': 1}
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id: 139470009
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 97, 'group_counter': 819, 'group_order': 576, 'label': '18B1', 'order': 18, 'powers': [49, 33], 'representative': 136, 'size': 1}
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id: 139470010
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 98, 'group_counter': 819, 'group_order': 576, 'label': '18B-1', 'order': 18, 'powers': [50, 34], 'representative': 456, 'size': 1}
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id: 139470011
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 99, 'group_counter': 819, 'group_order': 576, 'label': '18B5', 'order': 18, 'powers': [47, 34], 'representative': 72, 'size': 1}
-
id: 139469762
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 100, 'group_counter': 819, 'group_order': 576, 'label': '18B-5', 'order': 18, 'powers': [48, 33], 'representative': 520, 'size': 1}
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id: 139469763
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 101, 'group_counter': 819, 'group_order': 576, 'label': '18B7', 'order': 18, 'powers': [45, 33], 'representative': 328, 'size': 1}
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id: 139469764
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 102, 'group_counter': 819, 'group_order': 576, 'label': '18B-7', 'order': 18, 'powers': [46, 34], 'representative': 264, 'size': 1}
-
id: 139469765
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 103, 'group_counter': 819, 'group_order': 576, 'label': '18C1', 'order': 18, 'powers': [45, 35], 'representative': 40, 'size': 1}
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id: 139469766
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 104, 'group_counter': 819, 'group_order': 576, 'label': '18C-1', 'order': 18, 'powers': [46, 36], 'representative': 552, 'size': 1}
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id: 139469767
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 105, 'group_counter': 819, 'group_order': 576, 'label': '18C5', 'order': 18, 'powers': [50, 36], 'representative': 168, 'size': 1}
-
id: 139469768
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 106, 'group_counter': 819, 'group_order': 576, 'label': '18C-5', 'order': 18, 'powers': [49, 35], 'representative': 424, 'size': 1}
-
id: 139469769
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 107, 'group_counter': 819, 'group_order': 576, 'label': '18C7', 'order': 18, 'powers': [48, 35], 'representative': 232, 'size': 1}
-
id: 139469770
{'aut_label': '18A1', 'centralizer': '1.a1', 'counter': 108, 'group_counter': 819, 'group_order': 576, 'label': '18C-7', 'order': 18, 'powers': [47, 36], 'representative': 360, 'size': 1}
-
id: 139469771
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 109, 'group_counter': 819, 'group_order': 576, 'label': '18D1', 'order': 18, 'powers': [49, 37], 'representative': 130, 'size': 1}
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id: 139469773
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 110, 'group_counter': 819, 'group_order': 576, 'label': '18D-1', 'order': 18, 'powers': [50, 38], 'representative': 450, 'size': 1}
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id: 139469774
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 111, 'group_counter': 819, 'group_order': 576, 'label': '18D5', 'order': 18, 'powers': [47, 38], 'representative': 66, 'size': 1}
-
id: 139469775
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 112, 'group_counter': 819, 'group_order': 576, 'label': '18D-5', 'order': 18, 'powers': [48, 37], 'representative': 514, 'size': 1}
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id: 139469776
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 113, 'group_counter': 819, 'group_order': 576, 'label': '18D7', 'order': 18, 'powers': [45, 37], 'representative': 322, 'size': 1}
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id: 139469777
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 114, 'group_counter': 819, 'group_order': 576, 'label': '18D-7', 'order': 18, 'powers': [46, 38], 'representative': 258, 'size': 1}
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id: 139469778
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 115, 'group_counter': 819, 'group_order': 576, 'label': '18E1', 'order': 18, 'powers': [45, 39], 'representative': 330, 'size': 1}
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id: 139469779
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 116, 'group_counter': 819, 'group_order': 576, 'label': '18E-1', 'order': 18, 'powers': [46, 40], 'representative': 266, 'size': 1}
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id: 139469780
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 117, 'group_counter': 819, 'group_order': 576, 'label': '18E5', 'order': 18, 'powers': [50, 40], 'representative': 458, 'size': 1}
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id: 139469781
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 118, 'group_counter': 819, 'group_order': 576, 'label': '18E-5', 'order': 18, 'powers': [49, 39], 'representative': 138, 'size': 1}
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id: 139469782
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 119, 'group_counter': 819, 'group_order': 576, 'label': '18E7', 'order': 18, 'powers': [48, 39], 'representative': 522, 'size': 1}
-
id: 139469784
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 120, 'group_counter': 819, 'group_order': 576, 'label': '18E-7', 'order': 18, 'powers': [47, 40], 'representative': 74, 'size': 1}
-
id: 139469785
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 121, 'group_counter': 819, 'group_order': 576, 'label': '18F1', 'order': 18, 'powers': [49, 41], 'representative': 426, 'size': 1}
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id: 139469786
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 122, 'group_counter': 819, 'group_order': 576, 'label': '18F-1', 'order': 18, 'powers': [50, 42], 'representative': 170, 'size': 1}
-
id: 139469787
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 123, 'group_counter': 819, 'group_order': 576, 'label': '18F5', 'order': 18, 'powers': [47, 42], 'representative': 362, 'size': 1}
-
id: 139469788
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 124, 'group_counter': 819, 'group_order': 576, 'label': '18F-5', 'order': 18, 'powers': [48, 41], 'representative': 234, 'size': 1}
-
id: 139469789
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 125, 'group_counter': 819, 'group_order': 576, 'label': '18F7', 'order': 18, 'powers': [45, 41], 'representative': 42, 'size': 1}
-
id: 139469790
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 126, 'group_counter': 819, 'group_order': 576, 'label': '18F-7', 'order': 18, 'powers': [46, 42], 'representative': 554, 'size': 1}
-
id: 139469791
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 127, 'group_counter': 819, 'group_order': 576, 'label': '18G1', 'order': 18, 'powers': [45, 43], 'representative': 34, 'size': 1}
-
id: 139469792
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 128, 'group_counter': 819, 'group_order': 576, 'label': '18G-1', 'order': 18, 'powers': [46, 44], 'representative': 546, 'size': 1}
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id: 139469793
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 129, 'group_counter': 819, 'group_order': 576, 'label': '18G5', 'order': 18, 'powers': [50, 44], 'representative': 162, 'size': 1}
-
id: 139469795
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 130, 'group_counter': 819, 'group_order': 576, 'label': '18G-5', 'order': 18, 'powers': [49, 43], 'representative': 418, 'size': 1}
-
id: 139469796
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 131, 'group_counter': 819, 'group_order': 576, 'label': '18G7', 'order': 18, 'powers': [48, 43], 'representative': 226, 'size': 1}
-
id: 139469797
{'aut_label': '18D1', 'centralizer': '1.a1', 'counter': 132, 'group_counter': 819, 'group_order': 576, 'label': '18G-7', 'order': 18, 'powers': [47, 44], 'representative': 354, 'size': 1}
-
id: 139469798
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 133, 'group_counter': 819, 'group_order': 576, 'label': '36A1', 'order': 36, 'powers': [91, 51], 'representative': 16, 'size': 2}
-
id: 139469799
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 134, 'group_counter': 819, 'group_order': 576, 'label': '36A-1', 'order': 36, 'powers': [92, 52], 'representative': 280, 'size': 2}
-
id: 139469800
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 135, 'group_counter': 819, 'group_order': 576, 'label': '36A5', 'order': 36, 'powers': [93, 53], 'representative': 80, 'size': 2}
-
id: 139469801
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 136, 'group_counter': 819, 'group_order': 576, 'label': '36A-5', 'order': 36, 'powers': [94, 54], 'representative': 216, 'size': 2}
-
id: 139469802
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 137, 'group_counter': 819, 'group_order': 576, 'label': '36A7', 'order': 36, 'powers': [95, 54], 'representative': 112, 'size': 2}
-
id: 139469803
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 138, 'group_counter': 819, 'group_order': 576, 'label': '36A-7', 'order': 36, 'powers': [96, 53], 'representative': 464, 'size': 2}
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id: 139469804
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 139, 'group_counter': 819, 'group_order': 576, 'label': '36A11', 'order': 36, 'powers': [96, 52], 'representative': 176, 'size': 2}
-
id: 139469806
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 140, 'group_counter': 819, 'group_order': 576, 'label': '36A-11', 'order': 36, 'powers': [95, 51], 'representative': 400, 'size': 2}
-
id: 139469807
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 141, 'group_counter': 819, 'group_order': 576, 'label': '36A13', 'order': 36, 'powers': [94, 51], 'representative': 208, 'size': 2}
-
id: 139469808
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 142, 'group_counter': 819, 'group_order': 576, 'label': '36A-13', 'order': 36, 'powers': [93, 52], 'representative': 88, 'size': 2}
-
id: 139469809
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 143, 'group_counter': 819, 'group_order': 576, 'label': '36A17', 'order': 36, 'powers': [92, 53], 'representative': 272, 'size': 2}
-
id: 139469810
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 144, 'group_counter': 819, 'group_order': 576, 'label': '36A-17', 'order': 36, 'powers': [91, 54], 'representative': 24, 'size': 2}
-
id: 139469811
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 145, 'group_counter': 819, 'group_order': 576, 'label': '36B1', 'order': 36, 'powers': [97, 55], 'representative': 68, 'size': 2}
-
id: 139469812
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 146, 'group_counter': 819, 'group_order': 576, 'label': '36B-1', 'order': 36, 'powers': [98, 56], 'representative': 236, 'size': 2}
-
id: 139469813
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 147, 'group_counter': 819, 'group_order': 576, 'label': '36B5', 'order': 36, 'powers': [99, 57], 'representative': 36, 'size': 2}
-
id: 139469814
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 148, 'group_counter': 819, 'group_order': 576, 'label': '36B-5', 'order': 36, 'powers': [100, 58], 'representative': 268, 'size': 2}
-
id: 139469815
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 149, 'group_counter': 819, 'group_order': 576, 'label': '36B7', 'order': 36, 'powers': [101, 58], 'representative': 460, 'size': 2}
-
id: 139469817
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 150, 'group_counter': 819, 'group_order': 576, 'label': '36B-7', 'order': 36, 'powers': [102, 57], 'representative': 132, 'size': 2}
-
id: 139469818
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 151, 'group_counter': 819, 'group_order': 576, 'label': '36B11', 'order': 36, 'powers': [102, 56], 'representative': 140, 'size': 2}
-
id: 139469819
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 152, 'group_counter': 819, 'group_order': 576, 'label': '36B-11', 'order': 36, 'powers': [101, 55], 'representative': 452, 'size': 2}
-
id: 139469820
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 153, 'group_counter': 819, 'group_order': 576, 'label': '36B13', 'order': 36, 'powers': [100, 55], 'representative': 260, 'size': 2}
-
id: 139469821
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 154, 'group_counter': 819, 'group_order': 576, 'label': '36B-13', 'order': 36, 'powers': [99, 56], 'representative': 44, 'size': 2}
-
id: 139469822
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 155, 'group_counter': 819, 'group_order': 576, 'label': '36B17', 'order': 36, 'powers': [98, 57], 'representative': 228, 'size': 2}
-
id: 139469823
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 156, 'group_counter': 819, 'group_order': 576, 'label': '36B-17', 'order': 36, 'powers': [97, 58], 'representative': 76, 'size': 2}
-
id: 139469824
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 157, 'group_counter': 819, 'group_order': 576, 'label': '36C1', 'order': 36, 'powers': [103, 59], 'representative': 20, 'size': 2}
-
id: 139469825
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 158, 'group_counter': 819, 'group_order': 576, 'label': '36C-1', 'order': 36, 'powers': [104, 60], 'representative': 564, 'size': 2}
-
id: 139469826
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 159, 'group_counter': 819, 'group_order': 576, 'label': '36C5', 'order': 36, 'powers': [105, 61], 'representative': 84, 'size': 2}
-
id: 139469828
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 160, 'group_counter': 819, 'group_order': 576, 'label': '36C-5', 'order': 36, 'powers': [106, 62], 'representative': 500, 'size': 2}
-
id: 139469829
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 161, 'group_counter': 819, 'group_order': 576, 'label': '36C7', 'order': 36, 'powers': [107, 62], 'representative': 116, 'size': 2}
-
id: 139469830
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 162, 'group_counter': 819, 'group_order': 576, 'label': '36C-7', 'order': 36, 'powers': [108, 61], 'representative': 468, 'size': 2}
-
id: 139469831
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 163, 'group_counter': 819, 'group_order': 576, 'label': '36C11', 'order': 36, 'powers': [108, 60], 'representative': 180, 'size': 2}
-
id: 139469832
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 164, 'group_counter': 819, 'group_order': 576, 'label': '36C-11', 'order': 36, 'powers': [107, 59], 'representative': 404, 'size': 2}
-
id: 139469833
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 165, 'group_counter': 819, 'group_order': 576, 'label': '36C13', 'order': 36, 'powers': [106, 59], 'representative': 212, 'size': 2}
-
id: 139469834
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 166, 'group_counter': 819, 'group_order': 576, 'label': '36C-13', 'order': 36, 'powers': [105, 60], 'representative': 372, 'size': 2}
-
id: 139469835
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 167, 'group_counter': 819, 'group_order': 576, 'label': '36C17', 'order': 36, 'powers': [104, 61], 'representative': 276, 'size': 2}
-
id: 139469836
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 168, 'group_counter': 819, 'group_order': 576, 'label': '36C-17', 'order': 36, 'powers': [103, 62], 'representative': 308, 'size': 2}
-
id: 139469837
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 169, 'group_counter': 819, 'group_order': 576, 'label': '36D1', 'order': 36, 'powers': [91, 63], 'representative': 18, 'size': 2}
-
id: 139469839
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 170, 'group_counter': 819, 'group_order': 576, 'label': '36D-1', 'order': 36, 'powers': [92, 64], 'representative': 282, 'size': 2}
-
id: 139469840
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 171, 'group_counter': 819, 'group_order': 576, 'label': '36D5', 'order': 36, 'powers': [93, 65], 'representative': 82, 'size': 2}
-
id: 139469841
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 172, 'group_counter': 819, 'group_order': 576, 'label': '36D-5', 'order': 36, 'powers': [94, 66], 'representative': 218, 'size': 2}
-
id: 139469842
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 173, 'group_counter': 819, 'group_order': 576, 'label': '36D7', 'order': 36, 'powers': [95, 66], 'representative': 114, 'size': 2}
-
id: 139469843
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 174, 'group_counter': 819, 'group_order': 576, 'label': '36D-7', 'order': 36, 'powers': [96, 65], 'representative': 466, 'size': 2}
-
id: 139469844
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 175, 'group_counter': 819, 'group_order': 576, 'label': '36D11', 'order': 36, 'powers': [96, 64], 'representative': 178, 'size': 2}
-
id: 139469845
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 176, 'group_counter': 819, 'group_order': 576, 'label': '36D-11', 'order': 36, 'powers': [95, 63], 'representative': 402, 'size': 2}
-
id: 139469846
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 177, 'group_counter': 819, 'group_order': 576, 'label': '36D13', 'order': 36, 'powers': [94, 63], 'representative': 210, 'size': 2}
-
id: 139469847
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 178, 'group_counter': 819, 'group_order': 576, 'label': '36D-13', 'order': 36, 'powers': [93, 64], 'representative': 90, 'size': 2}
-
id: 139469848
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 179, 'group_counter': 819, 'group_order': 576, 'label': '36D17', 'order': 36, 'powers': [92, 65], 'representative': 274, 'size': 2}
-
id: 139469850
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 180, 'group_counter': 819, 'group_order': 576, 'label': '36D-17', 'order': 36, 'powers': [91, 66], 'representative': 26, 'size': 2}
-
id: 139469851
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 181, 'group_counter': 819, 'group_order': 576, 'label': '36E1', 'order': 36, 'powers': [97, 67], 'representative': 70, 'size': 2}
-
id: 139469852
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 182, 'group_counter': 819, 'group_order': 576, 'label': '36E-1', 'order': 36, 'powers': [98, 68], 'representative': 238, 'size': 2}
-
id: 139469853
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 183, 'group_counter': 819, 'group_order': 576, 'label': '36E5', 'order': 36, 'powers': [99, 69], 'representative': 38, 'size': 2}
-
id: 139469854
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 184, 'group_counter': 819, 'group_order': 576, 'label': '36E-5', 'order': 36, 'powers': [100, 70], 'representative': 270, 'size': 2}
-
id: 139469855
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 185, 'group_counter': 819, 'group_order': 576, 'label': '36E7', 'order': 36, 'powers': [101, 70], 'representative': 462, 'size': 2}
-
id: 139469856
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 186, 'group_counter': 819, 'group_order': 576, 'label': '36E-7', 'order': 36, 'powers': [102, 69], 'representative': 134, 'size': 2}
-
id: 139469857
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 187, 'group_counter': 819, 'group_order': 576, 'label': '36E11', 'order': 36, 'powers': [102, 68], 'representative': 142, 'size': 2}
-
id: 139469858
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 188, 'group_counter': 819, 'group_order': 576, 'label': '36E-11', 'order': 36, 'powers': [101, 67], 'representative': 454, 'size': 2}
-
id: 139469859
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 189, 'group_counter': 819, 'group_order': 576, 'label': '36E13', 'order': 36, 'powers': [100, 67], 'representative': 262, 'size': 2}
-
id: 139469861
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 190, 'group_counter': 819, 'group_order': 576, 'label': '36E-13', 'order': 36, 'powers': [99, 68], 'representative': 46, 'size': 2}
-
id: 139469862
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 191, 'group_counter': 819, 'group_order': 576, 'label': '36E17', 'order': 36, 'powers': [98, 69], 'representative': 230, 'size': 2}
-
id: 139469863
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 192, 'group_counter': 819, 'group_order': 576, 'label': '36E-17', 'order': 36, 'powers': [97, 70], 'representative': 78, 'size': 2}
-
id: 139469864
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 193, 'group_counter': 819, 'group_order': 576, 'label': '36F1', 'order': 36, 'powers': [103, 71], 'representative': 22, 'size': 2}
-
id: 139469865
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 194, 'group_counter': 819, 'group_order': 576, 'label': '36F-1', 'order': 36, 'powers': [104, 72], 'representative': 566, 'size': 2}
-
id: 139469866
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 195, 'group_counter': 819, 'group_order': 576, 'label': '36F5', 'order': 36, 'powers': [105, 73], 'representative': 86, 'size': 2}
-
id: 139469867
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 196, 'group_counter': 819, 'group_order': 576, 'label': '36F-5', 'order': 36, 'powers': [106, 74], 'representative': 502, 'size': 2}
-
id: 139469868
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 197, 'group_counter': 819, 'group_order': 576, 'label': '36F7', 'order': 36, 'powers': [107, 74], 'representative': 118, 'size': 2}
-
id: 139469869
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 198, 'group_counter': 819, 'group_order': 576, 'label': '36F-7', 'order': 36, 'powers': [108, 73], 'representative': 470, 'size': 2}
-
id: 139469870
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 199, 'group_counter': 819, 'group_order': 576, 'label': '36F11', 'order': 36, 'powers': [108, 72], 'representative': 182, 'size': 2}
-
id: 139469873
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 200, 'group_counter': 819, 'group_order': 576, 'label': '36F-11', 'order': 36, 'powers': [107, 71], 'representative': 406, 'size': 2}
-
id: 139469874
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 201, 'group_counter': 819, 'group_order': 576, 'label': '36F13', 'order': 36, 'powers': [106, 71], 'representative': 214, 'size': 2}
-
id: 139469875
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 202, 'group_counter': 819, 'group_order': 576, 'label': '36F-13', 'order': 36, 'powers': [105, 72], 'representative': 374, 'size': 2}
-
id: 139469876
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 203, 'group_counter': 819, 'group_order': 576, 'label': '36F17', 'order': 36, 'powers': [104, 73], 'representative': 278, 'size': 2}
-
id: 139469877
{'aut_label': '36A1', 'centralizer': '2.b1', 'counter': 204, 'group_counter': 819, 'group_order': 576, 'label': '36F-17', 'order': 36, 'powers': [103, 74], 'representative': 310, 'size': 2}
-
id: 139469878
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 205, 'group_counter': 819, 'group_order': 576, 'label': '36G1', 'order': 36, 'powers': [109, 75], 'representative': 65, 'size': 4}
-
id: 139469879
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 206, 'group_counter': 819, 'group_order': 576, 'label': '36G-1', 'order': 36, 'powers': [110, 76], 'representative': 227, 'size': 4}
-
id: 139469880
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 207, 'group_counter': 819, 'group_order': 576, 'label': '36G5', 'order': 36, 'powers': [111, 77], 'representative': 33, 'size': 4}
-
id: 139469881
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 208, 'group_counter': 819, 'group_order': 576, 'label': '36G-5', 'order': 36, 'powers': [112, 78], 'representative': 259, 'size': 4}
-
id: 139469882
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 209, 'group_counter': 819, 'group_order': 576, 'label': '36G7', 'order': 36, 'powers': [113, 78], 'representative': 451, 'size': 4}
-
id: 139469884
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 210, 'group_counter': 819, 'group_order': 576, 'label': '36G-7', 'order': 36, 'powers': [114, 77], 'representative': 129, 'size': 4}
-
id: 139469885
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 211, 'group_counter': 819, 'group_order': 576, 'label': '36G11', 'order': 36, 'powers': [114, 76], 'representative': 131, 'size': 4}
-
id: 139469886
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 212, 'group_counter': 819, 'group_order': 576, 'label': '36G-11', 'order': 36, 'powers': [113, 75], 'representative': 449, 'size': 4}
-
id: 139469887
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 213, 'group_counter': 819, 'group_order': 576, 'label': '36G13', 'order': 36, 'powers': [112, 75], 'representative': 257, 'size': 4}
-
id: 139469888
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 214, 'group_counter': 819, 'group_order': 576, 'label': '36G-13', 'order': 36, 'powers': [111, 76], 'representative': 35, 'size': 4}
-
id: 139469889
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 215, 'group_counter': 819, 'group_order': 576, 'label': '36G17', 'order': 36, 'powers': [110, 77], 'representative': 225, 'size': 4}
-
id: 139469890
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 216, 'group_counter': 819, 'group_order': 576, 'label': '36G-17', 'order': 36, 'powers': [109, 78], 'representative': 67, 'size': 4}
-
id: 139469891
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 217, 'group_counter': 819, 'group_order': 576, 'label': '36H1', 'order': 36, 'powers': [115, 79], 'representative': 17, 'size': 4}
-
id: 139469892
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 218, 'group_counter': 819, 'group_order': 576, 'label': '36H-1', 'order': 36, 'powers': [116, 80], 'representative': 275, 'size': 4}
-
id: 139469893
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 219, 'group_counter': 819, 'group_order': 576, 'label': '36H5', 'order': 36, 'powers': [117, 81], 'representative': 81, 'size': 4}
-
id: 139469895
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 220, 'group_counter': 819, 'group_order': 576, 'label': '36H-5', 'order': 36, 'powers': [118, 82], 'representative': 211, 'size': 4}
-
id: 139469896
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 221, 'group_counter': 819, 'group_order': 576, 'label': '36H7', 'order': 36, 'powers': [119, 82], 'representative': 403, 'size': 4}
-
id: 139469897
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 222, 'group_counter': 819, 'group_order': 576, 'label': '36H-7', 'order': 36, 'powers': [120, 81], 'representative': 465, 'size': 4}
-
id: 139469898
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 223, 'group_counter': 819, 'group_order': 576, 'label': '36H11', 'order': 36, 'powers': [120, 80], 'representative': 467, 'size': 4}
-
id: 139469899
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 224, 'group_counter': 819, 'group_order': 576, 'label': '36H-11', 'order': 36, 'powers': [119, 79], 'representative': 401, 'size': 4}
-
id: 139469900
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 225, 'group_counter': 819, 'group_order': 576, 'label': '36H13', 'order': 36, 'powers': [118, 79], 'representative': 209, 'size': 4}
-
id: 139469901
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 226, 'group_counter': 819, 'group_order': 576, 'label': '36H-13', 'order': 36, 'powers': [117, 80], 'representative': 83, 'size': 4}
-
id: 139469902
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 227, 'group_counter': 819, 'group_order': 576, 'label': '36H17', 'order': 36, 'powers': [116, 81], 'representative': 273, 'size': 4}
-
id: 139469903
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 228, 'group_counter': 819, 'group_order': 576, 'label': '36H-17', 'order': 36, 'powers': [115, 82], 'representative': 19, 'size': 4}
-
id: 139469904
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 229, 'group_counter': 819, 'group_order': 576, 'label': '36I1', 'order': 36, 'powers': [121, 83], 'representative': 69, 'size': 4}
-
id: 139469906
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 230, 'group_counter': 819, 'group_order': 576, 'label': '36I-1', 'order': 36, 'powers': [122, 84], 'representative': 231, 'size': 4}
-
id: 139469907
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 231, 'group_counter': 819, 'group_order': 576, 'label': '36I5', 'order': 36, 'powers': [123, 85], 'representative': 37, 'size': 4}
-
id: 139469908
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 232, 'group_counter': 819, 'group_order': 576, 'label': '36I-5', 'order': 36, 'powers': [124, 86], 'representative': 263, 'size': 4}
-
id: 139469909
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 233, 'group_counter': 819, 'group_order': 576, 'label': '36I7', 'order': 36, 'powers': [125, 86], 'representative': 455, 'size': 4}
-
id: 139469910
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 234, 'group_counter': 819, 'group_order': 576, 'label': '36I-7', 'order': 36, 'powers': [126, 85], 'representative': 133, 'size': 4}
-
id: 139469911
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 235, 'group_counter': 819, 'group_order': 576, 'label': '36I11', 'order': 36, 'powers': [126, 84], 'representative': 135, 'size': 4}
-
id: 139469912
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 236, 'group_counter': 819, 'group_order': 576, 'label': '36I-11', 'order': 36, 'powers': [125, 83], 'representative': 453, 'size': 4}
-
id: 139469913
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 237, 'group_counter': 819, 'group_order': 576, 'label': '36I13', 'order': 36, 'powers': [124, 83], 'representative': 261, 'size': 4}
-
id: 139469914
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 238, 'group_counter': 819, 'group_order': 576, 'label': '36I-13', 'order': 36, 'powers': [123, 84], 'representative': 39, 'size': 4}
-
id: 139469915
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 239, 'group_counter': 819, 'group_order': 576, 'label': '36I17', 'order': 36, 'powers': [122, 85], 'representative': 229, 'size': 4}
-
id: 139469917
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 240, 'group_counter': 819, 'group_order': 576, 'label': '36I-17', 'order': 36, 'powers': [121, 86], 'representative': 71, 'size': 4}
-
id: 139469918
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 241, 'group_counter': 819, 'group_order': 576, 'label': '36J1', 'order': 36, 'powers': [127, 87], 'representative': 21, 'size': 4}
-
id: 139469919
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 242, 'group_counter': 819, 'group_order': 576, 'label': '36J-1', 'order': 36, 'powers': [128, 88], 'representative': 279, 'size': 4}
-
id: 139469920
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 243, 'group_counter': 819, 'group_order': 576, 'label': '36J5', 'order': 36, 'powers': [129, 89], 'representative': 85, 'size': 4}
-
id: 139469921
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 244, 'group_counter': 819, 'group_order': 576, 'label': '36J-5', 'order': 36, 'powers': [130, 90], 'representative': 215, 'size': 4}
-
id: 139469922
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 245, 'group_counter': 819, 'group_order': 576, 'label': '36J7', 'order': 36, 'powers': [131, 90], 'representative': 407, 'size': 4}
-
id: 139469923
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 246, 'group_counter': 819, 'group_order': 576, 'label': '36J-7', 'order': 36, 'powers': [132, 89], 'representative': 469, 'size': 4}
-
id: 139469924
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 247, 'group_counter': 819, 'group_order': 576, 'label': '36J11', 'order': 36, 'powers': [132, 88], 'representative': 471, 'size': 4}
-
id: 139469925
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 248, 'group_counter': 819, 'group_order': 576, 'label': '36J-11', 'order': 36, 'powers': [131, 87], 'representative': 405, 'size': 4}
-
id: 139469926
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 249, 'group_counter': 819, 'group_order': 576, 'label': '36J13', 'order': 36, 'powers': [130, 87], 'representative': 213, 'size': 4}
-
id: 139469928
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 250, 'group_counter': 819, 'group_order': 576, 'label': '36J-13', 'order': 36, 'powers': [129, 88], 'representative': 87, 'size': 4}
-
id: 139469929
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 251, 'group_counter': 819, 'group_order': 576, 'label': '36J17', 'order': 36, 'powers': [128, 89], 'representative': 277, 'size': 4}
-
id: 139469930
{'aut_label': '36G1', 'centralizer': '4.b1', 'counter': 252, 'group_counter': 819, 'group_order': 576, 'label': '36J-17', 'order': 36, 'powers': [127, 90], 'representative': 23, 'size': 4}
-
gps_qchar • Show schema
Hide schema
-
id: 12710976
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id: 12710987
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id: 12710998
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id: 12711020
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id: 12711026
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id: 12711027
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id: 12711028
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id: 12711029
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id: 12710977
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id: 12710978
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id: 12710979
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710980
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1m', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710981
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -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, -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, 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, 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, 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, 1, 1], 'schur_index': 1}
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id: 12710982
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -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, -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, 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, 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, -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, -1, -1], 'schur_index': 1}
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id: 12710983
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -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, -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, -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, -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, 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, 1, 1], 'schur_index': 1}
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id: 12710984
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1q', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -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, -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, -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, -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, -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, -1, -1], 'schur_index': 1}
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id: 12710985
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1r', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -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, -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, 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, 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, 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, 1, 1], 'schur_index': 1}
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id: 12710986
{'cdim': 1, 'counter': 19, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1s', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, -2, -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, -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, 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, 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, -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, -1, -1], 'schur_index': 1}
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id: 12710988
{'cdim': 1, 'counter': 20, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1t', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -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, -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, -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, -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, 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, 1, 1], 'schur_index': 1}
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id: 12710989
{'cdim': 1, 'counter': 21, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1u', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, 4, -4, -4, 4, 4, -4, -4, 4, -4, 4, 4, -4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710990
{'cdim': 1, 'counter': 22, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1v', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, 4, -4, -4, 4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710991
{'cdim': 1, 'counter': 23, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1w', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, -4, -4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -4, -4, 4, -4, -4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710992
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id: 12711006
{'cdim': 2, 'counter': 37, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.2a', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, 4, -4, 4, -4, -4, -4, 4, -4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, -4, 4, -4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, 4, -4, -4, -4, 4, 4, 4, 4, -4, 4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 12711007
{'cdim': 2, 'counter': 38, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.2b', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, 4, -4, 4, 4, -4, -4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 4, 4, 4, -4, 4, -4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 12711008
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id: 12711010
{'cdim': 2, 'counter': 40, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.2d', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, 4, -4, 4, -4, -4, -4, 4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 12711011
{'cdim': 2, 'counter': 41, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, -4, -4, 4, -4, 4, 4, -4, 4, 4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, -4, 4, 4, 4, -4, -4, 4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, -4, 4, 4, 4, 4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 12711012
{'cdim': 2, 'counter': 42, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.2f', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, 4, -4, 4, 4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, -4, 4, -4, -4, -4, -4, -4, -4, -4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, -4, 4, -4, -4, -4, 4, -4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 12710993
{'cdim': 1, 'counter': 25, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1y', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -3, -3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710994
{'cdim': 1, 'counter': 26, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1z', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -6, -6, -6, -6, 6, 6, 6, 6, -6, -6, -6, -6, -6, 6, -6, 6, -6, 6, -6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -3, 3, 3, 3, -3, 3, -3, -3, -3, 3, 3, 3, -3, 3, 3, -3, 3, -3, 3, 3, -3, -3, -3, -3, 3, -3, -3, 3, 3, 3, 3, 3, 3, -3, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710995
{'cdim': 1, 'counter': 27, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1aa', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -6, -6, -6, -6, 6, 6, 6, 6, -6, -6, -6, -6, 6, -6, 6, -6, 6, -6, 6, -6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -3, 3, 3, 3, -3, 3, -3, -3, -3, 3, 3, 3, -3, 3, 3, -3, 3, -3, 3, 3, 3, 3, 3, 3, -3, 3, 3, -3, -3, -3, -3, -3, -3, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710996
{'cdim': 1, 'counter': 28, 'faithful': False, 'group': '576.819', 'group_order': 576, 'image': None, 'label': '576.819.1ab', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -6, 6, -6, -6, -6, -6, -6, -6, 6, 6, -6, 6, -6, -6, -6, -6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, 3, 3, -3, 3, -3, 3, 3, 3, 3, 3, 3, 3, -3, -3, -3, 3, 3, -3, 3, -3, 3, 3, 3, -3, -3, 3, 3, -3, -3, -3, 3, -3, 3, 3, -3, 3, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12710997
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id: 12710999
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id: 12711000
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id: 12711001
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id: 12711013
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id: 12711014
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id: 12711015
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id: 12711016
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id: 12711017
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id: 12711018
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id: 12711002
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id: 12711003
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id: 12711024
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id: 12711025
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gps_char • Show schema
Hide schema
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id: 29301041
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id: 29301042
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id: 29301043
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id: 29301044
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id: 29301045
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id: 29301046
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id: 29301047
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id: 29301048
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id: 29301050
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id: 29301051
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id: 29301052
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id: 29301053
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id: 29301054
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id: 29301055
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id: 29301056
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id: 29301057
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id: 29301058
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id: 29301059
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id: 29301061
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id: 29301062
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id: 29301063
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id: 29301064
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id: 29301065
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id: 29301066
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id: 29301067
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id: 29301068
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id: 29301069
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id: 29301070
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id: 29301072
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id: 29301073
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id: 29301074
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id: 29301075
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id: 29301076
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id: 29301077
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id: 29301078
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id: 29301079
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id: 29300838
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id: 29300839
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id: 29300840
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id: 29301080
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id: 29301081
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id: 29300832
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id: 29300833
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id: 29300834
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id: 29300835
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id: 29300836
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id: 29300837
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id: 29300841
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id: 29300851
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id: 29300852
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id: 29300854
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id: 29300843
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id: 29300844
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id: 29300845
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id: 29300846
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id: 29300847
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id: 29300848
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id: 29300849
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id: 29300850
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id: 29300855
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id: 29300865
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id: 29300866
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id: 29300867
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id: 29300856
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id: 29300857
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id: 29300858
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id: 29300859
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id: 29300860
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id: 29300861
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id: 29300862
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id: 29300863
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id: 29300868
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id: 29300878
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id: 29300879
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id: 29300880
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id: 29300869
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id: 29300870
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id: 29300871
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id: 29300872
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id: 29300873
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id: 29300874
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id: 29300876
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id: 29300877
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id: 29300941
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id: 29301005
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id: 29301016
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id: 29301027
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id: 29301038
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id: 29301049
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id: 29301060
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id: 29301071
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id: 29300831
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id: 29300842
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id: 29300853
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id: 29300864
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id: 29300875
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id: 29300886
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id: 29300897
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id: 29300908
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id: 29300919
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id: 29300930
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id: 29300942
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id: 29300953
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id: 29300964
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id: 29300975
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id: 29300986
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id: 29300997
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id: 29301001
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id: 29301002
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id: 29301003
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id: 29301004
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id: 29301006
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id: 29301007
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id: 29301008
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id: 29301009
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id: 29301010
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id: 29301011
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id: 29301012
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id: 29301013
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id: 29301014
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id: 29301015
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id: 29301017
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id: 29301018
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id: 29301019
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id: 29301020
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id: 29301021
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id: 29301022
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id: 29301023
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id: 29301024
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id: 29301025
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id: 29301026
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id: 29301028
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id: 29301029
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id: 29301030
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id: 29301031
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id: 29301032
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id: 29301033
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id: 29301034
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id: 29301035
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id: 29301036
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id: 29301037
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id: 29301039
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id: 29300881
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id: 29300882
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id: 29300883
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id: 29300884
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id: 29300885
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id: 29300887
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id: 29300888
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id: 29300889
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id: 29300890
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id: 29300891
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id: 29300892
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id: 29300893
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id: 29300894
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id: 29300895
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id: 29300896
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id: 29300898
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id: 29300899
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id: 29300900
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id: 29300901
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id: 29300902
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id: 29300903
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id: 29300904
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id: 29300905
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id: 29300906
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id: 29300907
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id: 29300909
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id: 29300910
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id: 29300911
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id: 29300912
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id: 29300913
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id: 29300914
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id: 29300915
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id: 29300916
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id: 29300917
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id: 29300918
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id: 29300920
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id: 29300921
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id: 29300931
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id: 29300932
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id: 29300933
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id: 29300922
{'center': '4.a1', 'center_index': 4, 'center_order': 144, 'counter': 182, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '576.819', 'group_counter': 819, 'group_order': 576, 'image': None, 'image_isoclass': '144.50', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 4, 'label': '576.819.2m2', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9]], [[2, 9]], [[0, 0]], [[-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 12]], [[2, 6]], [[2, 12]], [[-2, 12]], [[-2, 6]], [[-2, 12]], [[2, 12]], [[2, 6]], [[-2, 12]], [[2, 6]], [[-2, 6]], [[2, 6]], [[-2, 12]], [[-2, 2]], [[-2, 14]], [[2, 8]], [[2, 4]], [[2, 16]], [[-2, 10]], [[2, 15]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 15]], [[-2, 3]], [[-2, 15]], [[0, 0]], [[0, 0]], [[-2, 15]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 14]], [[-2, 8]], [[2, 10]], [[2, 2]], [[2, 14]], [[-2, 8]], [[2, 10]], [[2, 16]], [[2, 4]], [[-2, 4]], [[-2, 10]], [[-2, 16]], [[2, 8]], [[-2, 10]], [[-2, 4]], [[-2, 4]], [[-2, 16]], [[2, 10]], [[-2, 8]], [[2, 10]], [[2, 2]], [[2, 14]], [[-2, 16]], [[-2, 14]], [[2, 4]], [[-2, 2]], [[-2, 8]], [[2, 2]], [[2, 14]], [[-2, 14]], [[-2, 10]], [[2, 8]], [[2, 16]], [[-2, 4]], [[2, 8]], [[2, 16]], [[-2, 2]], [[2, 4]], [[-2, 14]], [[-2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 13]], [[0, 0]], [[0, 0]], [[2, 5]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 11]], [[0, 0]], [[2, 17]], [[-2, 11]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 17]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 13]], [[2, 7]], [[-2, 17]], [[-2, 13]], [[0, 0]], [[2, 13]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[0, 0]], [[2, 17]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 29300923
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id: 29300924
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id: 29300925
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id: 29300926
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id: 29300927
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id: 29300928
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id: 29300929
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id: 29300934
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id: 29300945
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id: 29300946
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id: 29300947
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id: 29300935
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id: 29300936
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id: 29300937
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id: 29300938
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id: 29300939
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id: 29300940
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id: 29300943
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id: 29300944
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id: 29300948
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id: 29300958
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id: 29300959
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id: 29300960
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id: 29300949
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id: 29300950
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id: 29300951
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id: 29300952
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id: 29300954
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id: 29300955
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id: 29300956
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id: 29300957
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id: 29300961
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id: 29300971
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id: 29300972
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id: 29300973
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id: 29300962
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id: 29300963
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id: 29300965
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id: 29300966
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id: 29300967
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id: 29300968
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id: 29300969
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id: 29300970
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id: 29300974
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id: 29300984
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id: 29300985
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id: 29300987
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id: 29300976
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id: 29300977
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id: 29300978
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id: 29300979
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id: 29300980
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id: 29300981
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id: 29300982
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id: 29300983
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id: 29300988
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id: 29300998
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id: 29300999
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id: 29301000
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id: 29300989
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id: 29300990
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id: 29300991
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id: 29300992
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id: 29300993
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id: 29300994
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id: 29300995
{'center': '4.a1', 'center_index': 4, 'center_order': 144, 'counter': 248, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '576.819', 'group_counter': 819, 'group_order': 576, 'image': None, 'image_isoclass': '144.50', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 4, 'label': '576.819.2r8', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[-2, 9]], [[0, 0]], [[2, 9]], [[2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 6]], [[-2, 12]], [[2, 12]], [[-2, 6]], [[2, 12]], [[2, 6]], [[2, 6]], [[2, 6]], [[2, 12]], [[-2, 2]], [[-2, 14]], [[2, 8]], [[2, 4]], [[2, 16]], [[-2, 10]], [[0, 0]], [[2, 15]], [[-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 15]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 14]], [[2, 8]], [[-2, 10]], [[2, 2]], [[-2, 14]], [[-2, 8]], [[2, 10]], [[-2, 16]], [[-2, 4]], [[-2, 4]], [[2, 10]], [[-2, 16]], [[2, 8]], [[-2, 10]], [[-2, 4]], [[2, 4]], [[2, 16]], [[-2, 10]], [[-2, 8]], [[2, 10]], [[2, 2]], [[-2, 14]], [[-2, 16]], [[2, 14]], [[-2, 4]], [[2, 2]], [[2, 8]], [[-2, 2]], [[2, 14]], [[-2, 14]], [[2, 10]], [[-2, 8]], [[-2, 16]], [[2, 4]], [[-2, 8]], [[2, 16]], [[-2, 2]], [[2, 4]], [[2, 14]], [[2, 16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 17]], [[0, 0]], [[-2, 7]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[-2, 13]], [[0, 0]], [[0, 0]], [[-2, 17]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 13]], [[2, 1]], [[0, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 17]], [[0, 0]], [[-2, 7]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[-2, 13]], [[0, 0]], [[-2, 17]], [[0, 0]], [[2, 13]], [[2, 1]], [[0, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[0, 0]], [[-2, 1]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 29300996
{'center': '4.a1', 'center_index': 4, 'center_order': 144, 'counter': 249, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '576.819', 'group_counter': 819, 'group_order': 576, 'image': None, 'image_isoclass': '144.50', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 4, 'label': '576.819.2r9', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 9]], [[0, 0]], [[-2, 9]], [[-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 12]], [[2, 6]], [[2, 6]], [[2, 12]], [[2, 6]], [[-2, 6]], [[2, 12]], [[-2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 12]], [[-2, 6]], [[-2, 10]], [[2, 16]], [[2, 4]], [[-2, 2]], [[2, 8]], [[-2, 14]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 15]], [[2, 15]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 10]], [[-2, 10]], [[-2, 16]], [[2, 4]], [[-2, 14]], [[2, 10]], [[2, 16]], [[-2, 4]], [[2, 14]], [[-2, 8]], [[2, 2]], [[2, 2]], [[2, 14]], [[-2, 8]], [[2, 4]], [[-2, 14]], [[2, 2]], [[-2, 2]], [[2, 8]], [[-2, 14]], [[-2, 4]], [[2, 14]], [[2, 10]], [[2, 16]], [[-2, 8]], [[-2, 16]], [[2, 2]], [[2, 10]], [[2, 4]], [[-2, 10]], [[-2, 16]], [[2, 16]], [[2, 14]], [[-2, 4]], [[-2, 8]], [[-2, 2]], [[-2, 4]], [[2, 8]], [[-2, 10]], [[-2, 2]], [[-2, 16]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 13]], [[0, 0]], [[-2, 17]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 17]], [[-2, 11]], [[0, 0]], [[0, 0]], [[2, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 7]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 5]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 13]], [[0, 0]], [[-2, 17]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 17]], [[-2, 11]], [[0, 0]], [[2, 13]], [[0, 0]], [[2, 11]], [[-2, 5]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 5]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 110221644
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 576, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '576.819.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '576.819', 'subgroup_hash': 819, 'subgroup_order': 576, 'subgroup_tex': 'C_4^2:C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 288, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': '288.45', 'subgroup_hash': 45, 'subgroup_order': 288, 'subgroup_tex': 'C_{18}.C_4^2', 'supersolvable': True, 'sylow': 0}
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id: 110221666
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 288, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': '288.164', 'subgroup_hash': 164, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_4\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 192, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '192.816', 'subgroup_hash': 816, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.47', 'subgroup_hash': 47, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 144, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.47', 'subgroup_hash': 47, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 144, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.20', 'subgroup_hash': 20, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221693
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 96, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.45', 'subgroup_hash': 45, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_4^2', 'supersolvable': True, 'sylow': 0}
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id: 110221694
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 96, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.161', 'subgroup_hash': 161, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221645
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.18', 'subgroup_hash': 18, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
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id: 110221646
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221647
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 36, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, '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': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
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id: 110221648
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 36, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, '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': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
-
id: 110221649
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '576.819.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.64', 'subgroup_hash': 64, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 2}
-
id: 110221650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 48, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 48, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 110221652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 48, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 36, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
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id: 110221654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 36, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
-
id: 110221656
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 18, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
-
id: 110221657
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
-
id: 110221658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 110221659
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
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id: 110221660
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 110221661
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 24, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221662
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 12, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, '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': 24, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 110221663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, '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': 24, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221664
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
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id: 110221665
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.33', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 33, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
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id: 110221667
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110221668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110221669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
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id: 110221670
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 12, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 110221671
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 12, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.44', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 110221672
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, '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': 48, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221673
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, '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': 48, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110221674
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 9, 'counter': 37, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '576.819.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.64', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 64, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 3}
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id: 110221675
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.18', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 110221676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 110221678
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 110221679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.819.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 110221680
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], '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: 110221681
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.173', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 173, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], '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: 110221682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 110221683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.819.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.47', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{36}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 110221684
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 110221685
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.819.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 110221686
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 3, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.816', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 816, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_{12}', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 110221687
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.167', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 167, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_{18}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 110221689
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.819.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.176', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 176, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_{18}', '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: 110221690
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.819', 'ambient_counter': 819, 'ambient_order': 576, 'ambient_tex': 'C_4^2:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 1, 'counter': 51, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '576.819.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '576.819', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 819, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_{36}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C8'], '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: 110221679
{'ambient': '576.819', 'aut_centralizer_order': 384, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 9216, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.d1', '36.b1'], 'contains': ['144.a1', '144.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3883, -1, 7494, -1], 'generators': [1, 288], 'label': '576.819.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.d1', 'projective_image': '144.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221644
{'ambient': '576.819', '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': '8.a1', 'complements': ['576.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6773, 6688, 3197, 4235], 'generators': [1, 2, 8, 4, 64, 192, 288, 144], 'label': '576.819.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 110221645
{'ambient': '576.819', 'aut_centralizer_order': 512, 'aut_label': '8.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '72.47', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1'], 'contains': ['16.a1', '16.b1', '24.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3828, 1947, 6551, 750], 'generators': [2, 192, 296, 288, 64], 'label': '576.819.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1'], 'normal_contains': ['16.a1', '16.b1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '8.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221646
{'ambient': '576.819', 'aut_centralizer_order': 256, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1536, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.c1'], 'contains': ['16.b1', '16.c1', '24.b1'], 'core': '8.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5277, 4266, 2502, 2285], 'generators': [296, 192, 144, 64, 288], 'label': '576.819.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.c1'], 'normal_contains': ['16.b1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221647
{'ambient': '576.819', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.45', 'aut_weyl_index': 768, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1'], 'contains': ['16.a1', '16.c1', '24.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2640, -1, 5441, -1], 'generators': [2, 192, 144, 64, 288], 'label': '576.819.8.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.c1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221648
{'ambient': '576.819', 'aut_centralizer_order': 64, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1536, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.b1'], 'contains': ['16.a1', '16.d1', '24.d1'], 'core': '16.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1527, -1, 8903, -1], 'generators': [1, 192, 288, 64, 2], 'label': '576.819.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.d1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221649
{'ambient': '576.819', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6144.en', 'aut_weyl_index': 6, 'centralizer': '8.a1', 'complements': ['64.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1'], 'core': '9.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9710, 9713, 2961, 9008], 'generators': [1, 4, 144], 'label': '576.819.9.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': ['3.a1'], 'normal_contains': ['18.a1', '18.b1'], 'normalizer': '1.a1', 'old_label': '9.a1', 'projective_image': '72.18', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 110221650
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '12.a1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 576, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '6.a1', '6.b1'], 'contains': ['24.a1', '24.b1', '24.c1', '36.a1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6724, 5906, 3612, 5443], 'generators': [2, 288, 296, 144, 192], 'label': '576.819.12.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1', '6.b1'], 'normal_contains': ['24.a1', '24.b1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221651
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '48.49', 'aut_weyl_index': 768, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.a1', '24.d1', '36.b1'], 'core': '12.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5208, 3813, 7724, 3820], 'generators': [1, 2, 296, 288, 192], 'label': '576.819.12.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '24.15', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 110221652
{'ambient': '576.819', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '96.228', 'aut_weyl_index': 384, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.b1'], 'contains': ['24.b1', '36.c1'], 'core': '12.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [8172, 7904, 462, 6978], 'generators': [4, 288, 144, 192, 8], 'label': '576.819.12.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': ['4.c1', '6.b1'], 'normal_contains': ['24.b1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '48.44', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221653
{'ambient': '576.819', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 3072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.c1', '8.d1'], 'contains': ['32.a1', '32.b1', '48.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [495, 683, 7934, 873], 'generators': [2, 288, 64, 192], 'label': '576.819.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['32.a1', '32.b1', '48.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221654
{'ambient': '576.819', 'aut_centralizer_order': 2048, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '18.5', 'aut_weyl_index': 2048, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1'], 'contains': ['32.a1', '48.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3719, 2220, 4893, 2311], 'generators': [296, 288, 64, 192], 'label': '576.819.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221655
{'ambient': '576.819', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '768.29598', 'aut_weyl_index': 48, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5304, 4680, 4842, 2356], 'generators': [1, 288, 296, 144, 192, 64, 2], 'label': '576.819.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 110221656
{'ambient': '576.819', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 3072, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '8.c1'], 'contains': ['32.a1', '48.c1'], 'core': '32.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2599, -1, 3051, -1], 'generators': [144, 64, 288, 192], 'label': '576.819.16.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.c1', 'projective_image': '32.24', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221657
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.5', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1'], 'contains': ['32.b1', '48.d1'], 'core': '32.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1356, -1, 9777, -1], 'generators': [1, 64, 2, 192], 'label': '576.819.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.d1', 'projective_image': '32.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221658
{'ambient': '576.819', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 288, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.a1', '36.b1'], 'core': '18.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7906, 7781, 4562, 8196], 'generators': [1, 144], 'label': '576.819.18.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1', '9.a1'], 'normal_contains': ['36.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '72.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 110221659
{'ambient': '576.819', 'aut_centralizer_order': 48, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1083694', 'aut_weyl_index': 48, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.a1', '36.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9497, 9421, 1482, 9387], 'generators': [2, 4, 144], 'label': '576.819.18.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': ['6.b1', '9.a1'], 'normal_contains': ['36.a1', '36.c1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '72.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221660
{'ambient': '576.819', 'aut_centralizer_order': 1536, 'aut_label': '24.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '24.13', 'aut_weyl_index': 1536, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.b1'], 'contains': ['48.a1', '48.b1', '72.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5078, 3578, 5913, 3785], 'generators': [2, 296, 288, 192], 'label': '576.819.24.a1', 'mobius_quo': 8, 'mobius_sub': 8, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1'], 'normal_contains': ['48.a1', '48.b1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '24.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.15', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221661
{'ambient': '576.819', 'aut_centralizer_order': 768, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '12.a1', '12.c1'], 'contains': ['48.b1', '48.c1', '72.b1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6437, 5641, 1246, 5196], 'generators': [296, 144, 192, 288], 'label': '576.819.24.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': ['8.b1', '12.a1', '12.c1'], 'normal_contains': ['48.b1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '48.44', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221662
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '12.a1'], 'contains': ['48.a1', '48.c1', '72.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3719, -1, 3854, -1], 'generators': [2, 144, 192, 288], 'label': '576.819.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.c1', 'projective_image': '48.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221663
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4608, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.d1', '12.b1'], 'contains': ['48.a1', '48.d1', '72.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2340, -1, 8974, -1], 'generators': [1, 288, 192, 2], 'label': '576.819.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.d1', 'projective_image': '48.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221664
{'ambient': '576.819', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '16.b1', '16.c1'], 'contains': ['64.a1', '96.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1561, 1268, 5913, 1976], 'generators': [288, 64, 192], 'label': '576.819.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['64.a1', '96.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '32.24', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.24', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221665
{'ambient': '576.819', 'aut_centralizer_order': 1536, 'aut_label': '32.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.d1'], 'contains': ['64.a1', '96.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [297, 439, 8208, 1200], 'generators': [2, 64, 192], 'label': '576.819.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1', '96.b1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.33', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.33', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221666
{'ambient': '576.819', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6773, 6688, 1744, 4235], 'generators': [2, 288, 8, 4, 192, 144, 64], 'label': '576.819.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221667
{'ambient': '576.819', 'aut_centralizer_order': 384, 'aut_label': '36.a1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 1152, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['12.a1', '18.a1', '18.b1'], 'contains': ['72.a1', '72.b1', '72.c1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7954, 7160, 2266, 7993], 'generators': [2, 296, 144], 'label': '576.819.36.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '18.a1', '18.b1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '72.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221668
{'ambient': '576.819', 'aut_centralizer_order': 384, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.13', 'aut_weyl_index': 1536, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '18.a1'], 'contains': ['72.a1', '72.d1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6615, 5312, 6914, 6608], 'generators': [1, 296, 288], 'label': '576.819.36.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': ['12.b1', '18.a1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '72.18', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 110221669
{'ambient': '576.819', 'aut_centralizer_order': 192, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.49', 'aut_weyl_index': 768, 'centralizer': '2.b1', 'complements': ['16.d1'], 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '18.b1'], 'contains': ['72.b1'], 'core': '36.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [8828, 8498, 462, 9052], 'generators': [4, 144], 'label': '576.819.36.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': ['12.c1', '18.b1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '144.47', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221670
{'ambient': '576.819', 'aut_centralizer_order': 1536, 'aut_label': '48.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '24.a1', '24.c1', '24.d1'], 'contains': ['96.a1', '96.b1', '144.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1916, 2295, 6627, 2964], 'generators': [2, 288, 192], 'label': '576.819.48.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1'], 'normal_contains': ['96.a1', '96.b1', '144.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '48.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.47', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221671
{'ambient': '576.819', 'aut_centralizer_order': 6144, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.a1', '24.b1'], 'contains': ['96.a1', '144.b1'], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4833, 3578, 4677, 4164], 'generators': [296, 288, 192], 'label': '576.819.48.b1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.b1', '24.a1', '24.b1'], 'normal_contains': ['96.a1', '144.b1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '48.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.44', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221672
{'ambient': '576.819', 'aut_centralizer_order': 768, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 9216, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.c1', '24.b1', '24.c1'], 'contains': ['96.a1', '144.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3719, -1, 3095, -1], 'generators': [144, 192, 288], 'label': '576.819.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.c1', 'projective_image': '96.164', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221673
{'ambient': '576.819', 'aut_centralizer_order': 576, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 9216, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '24.d1'], 'contains': ['96.b1', '144.d1'], 'core': '96.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1151, -1, 8891, -1], 'generators': [1, 192, 2], 'label': '576.819.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '48.d1', 'projective_image': '96.173', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221674
{'ambient': '576.819', 'aut_centralizer_order': 6144, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1'], 'contains': ['192.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [290, 287, 6372, 1835], 'generators': [64], 'label': '576.819.64.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': ['192.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.64', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.64', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221675
{'ambient': '576.819', 'aut_centralizer_order': 3072, 'aut_label': '72.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '12.3', 'aut_weyl_index': 3072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.a1', '36.b1'], 'contains': ['144.a1', '144.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6076, 4398, 5371, 5126], 'generators': [2, 296, 288], 'label': '576.819.72.a1', 'mobius_quo': -8, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '36.a1', '36.b1'], 'normal_contains': ['144.a1', '144.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '72.18', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.18', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221676
{'ambient': '576.819', 'aut_centralizer_order': 1536, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 9216, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['24.b1', '36.a1', '36.c1'], 'contains': ['144.b1', '144.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7284, 6641, 2266, 7005], 'generators': [296, 144], 'label': '576.819.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['24.b1', '36.a1', '36.c1'], 'normal_contains': ['144.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '144.47', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.5', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221677
{'ambient': '576.819', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12288.bmz', 'aut_weyl_index': 3, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '9.a1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8685, 9195, 3197, 6785], 'generators': [1, 8, 2, 4, 288, 144, 192], 'label': '576.819.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.b1', '9.a1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '24.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 110221678
{'ambient': '576.819', 'aut_centralizer_order': 384, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.c1', '36.a1'], 'contains': ['144.a1', '144.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5072, -1, 3809, -1], 'generators': [2, 144], 'label': '576.819.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.c1', 'projective_image': '144.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221680
{'ambient': '576.819', 'aut_centralizer_order': 6144, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1'], 'contains': ['192.a1', '288.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2135, 2295, 5390, 3105], 'generators': [288, 192], 'label': '576.819.96.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1', '48.b1'], 'normal_contains': ['192.a1', '288.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '96.164', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.164', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221681
{'ambient': '576.819', 'aut_centralizer_order': 4608, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['32.b1', '48.a1', '48.d1'], 'contains': ['192.a1', '288.b1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1356, 1362, 6831, 2470], 'generators': [2, 192], 'label': '576.819.96.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': ['32.b1', '48.a1'], 'normal_contains': ['192.a1', '288.b1'], 'normalizer': '1.a1', 'old_label': '96.b1', 'projective_image': '96.173', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.173', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221682
{'ambient': '576.819', 'aut_centralizer_order': 3072, 'aut_label': '144.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '72.a1', '72.c1', '72.d1'], 'contains': ['288.a1', '288.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3699, 3143, 5881, 3785], 'generators': [2, 288], 'label': '576.819.144.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['48.a1', '72.a1'], 'normal_contains': ['288.a1', '288.b1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '144.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.50', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221683
{'ambient': '576.819', 'aut_centralizer_order': 12288, 'aut_label': '144.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '72.a1', '72.b1'], 'contains': ['288.a1'], 'core': '144.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5830, 4284, 4785, 4888], 'generators': [296, 288], 'label': '576.819.144.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': ['48.b1', '72.a1', '72.b1'], 'normal_contains': ['288.a1'], 'normalizer': '1.a1', 'old_label': '144.b1', 'projective_image': '144.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.47', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221684
{'ambient': '576.819', 'aut_centralizer_order': 1536, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.c1', '72.b1', '72.c1'], 'contains': ['288.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4689, -1, 3452, -1], 'generators': [144], 'label': '576.819.144.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '144.c1', 'projective_image': '288.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110221685
{'ambient': '576.819', 'aut_centralizer_order': 1152, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.d1', '72.d1'], 'contains': ['288.b1'], 'core': '288.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [2408, -1, 7494, -1], 'generators': [1], 'label': '576.819.144.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '144.d1', 'projective_image': '288.176', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221686
{'ambient': '576.819', 'aut_centralizer_order': 18432, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.a1', '96.b1'], 'contains': ['576.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1417, 1248, 6372, 2488], 'generators': [192], 'label': '576.819.192.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': ['64.a1', '96.a1', '96.b1'], 'normal_contains': ['576.a1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '192.816', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.816', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221687
{'ambient': '576.819', 'aut_centralizer_order': 12288, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 36864, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['96.a1', '144.a1', '144.b1', '144.c1'], 'contains': ['576.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3699, 2964, 5390, 3776], 'generators': [288], 'label': '576.819.288.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.a1', 'normal_contained_in': ['96.a1', '144.a1', '144.b1'], 'normal_contains': ['576.a1'], 'normalizer': '1.a1', 'old_label': '288.a1', 'projective_image': '288.167', 'quotient_action_image': '1.1', 'quotient_action_kernel': '288.167', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221688
{'ambient': '576.819', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '192.1410', 'aut_weyl_index': 192, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.c1', '12.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5283, 4680, 4007, 2356], 'generators': [2, 192, 288, 296, 144, 64], 'label': '576.819.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110221689
{'ambient': '576.819', 'aut_centralizer_order': 9216, 'aut_label': '288.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 36864, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['96.b1', '144.a1', '144.d1'], 'contains': ['576.a1'], 'core': '288.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2408, 2088, 6831, 3132], 'generators': [2], 'label': '576.819.288.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.b1', 'normal_contained_in': ['96.b1', '144.a1'], 'normal_contains': ['576.a1'], 'normalizer': '1.a1', 'old_label': '288.b1', 'projective_image': '288.176', 'quotient_action_image': '1.1', 'quotient_action_kernel': '288.176', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221690
{'ambient': '576.819', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '288.a1', '288.b1'], 'contains': [], 'core': '576.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2408, 2088, 6372, 3132], 'generators': [], 'label': '576.819.576.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '576.a1', 'normal_contained_in': ['192.a1', '288.a1', '288.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '576.a1', 'projective_image': '576.819', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110221691
{'ambient': '576.819', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '144.193', 'aut_weyl_index': 256, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.d1', '12.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3972, 2946, 7137, 732], 'generators': [1, 192, 2, 296, 288, 64], 'label': '576.819.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 110221692
{'ambient': '576.819', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '288.1041', 'aut_weyl_index': 128, 'centralizer': '2.b1', 'complements': ['144.d1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1'], 'contains': ['8.b1', '12.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6773, 6679, 462, 3891], 'generators': [4, 192, 288, 144, 64, 8], 'label': '576.819.4.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110221693
{'ambient': '576.819', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 144, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.b1', '18.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6971, 6244, 5193, 5443], 'generators': [1, 288, 296, 144, 192, 2], 'label': '576.819.6.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.a1', '12.b1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '24.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 110221694
{'ambient': '576.819', 'aut_centralizer_order': 24, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408529567', 'aut_weyl_index': 24, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.c1', '18.b1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8685, 8610, 1744, 7323], 'generators': [2, 288, 8, 4, 144, 192], 'label': '576.819.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.a1', '12.c1', '18.b1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}