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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 352440, 'aut_gen_orders': [88, 3], 'aut_gens': [[21149073, 697225], [60632644, 9050486], [60025576, 38141073]], 'aut_group': '704880.b', 'aut_hash': 4134574405713480887, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 704880, 'aut_permdeg': 4005, 'aut_perms': 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'aut_phi_ratio': 8.34375, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 4005, 1, 1], [3, 7832, 1, 1], [4, 8010, 1, 1], [5, 7832, 1, 2], [9, 7832, 1, 3], [11, 8010, 1, 5], [15, 7832, 1, 4], [22, 8010, 1, 5], [44, 8010, 1, 10], [45, 7832, 1, 12], [89, 3960, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,89)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 352440, 'autcentquo_group': '704880.b', 'autcentquo_hash': 4134574405713480887, 'autcentquo_nilpotent': False, 'autcentquo_order': 704880, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,89)', 'cc_stats': [[1, 1, 1], [2, 4005, 1], [3, 7832, 1], [4, 8010, 1], [5, 7832, 2], [9, 7832, 3], [11, 8010, 5], [15, 7832, 4], [22, 8010, 5], [44, 8010, 10], [45, 7832, 12], [89, 3960, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '352440.a', 'commutator_count': 1, 'commutator_label': '352440.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['352440.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 4005, 1, 1], [3, 7832, 1, 1], [4, 8010, 1, 1], [5, 7832, 2, 1], [9, 7832, 3, 1], [11, 8010, 5, 1], [15, 7832, 4, 1], [22, 8010, 5, 1], [44, 8010, 10, 1], [45, 7832, 12, 1], [89, 3960, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 174146, 'exponent': 176220, 'exponents_of_order': [3, 2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11, 89], 'factors_of_order': [2, 3, 5, 11, 89], 'faithful_reps': [[45, 1, 2], [88, 1, 22], [89, 1, 1], [90, 1, 21]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '352440.a', 'hash': 8307062878014378175, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 176220, 'inner_gen_orders': [44, 3], 'inner_gens': [[21149073, 634658], [2328804, 697225]], 'inner_hash': 8307062878014378175, 'inner_nilpotent': False, 'inner_order': 352440, 'inner_split': True, 'inner_tex': '\\PSL(2,89)', 'inner_used': [1, 2], 'irrC_degree': 45, 'irrQ_degree': 88, 'irrQ_dim': 88, 'irrR_degree': 45, 'irrep_stats': [[1, 1], [45, 2], [88, 22], [89, 1], [90, 21]], 'label': '352440.a', 'linC_count': 2, 'linC_degree': 45, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 88, 'linQ_degree_count': 1, 'linQ_dim': 88, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 45, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,89)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 46, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 47, 'number_divisions': 12, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 31, 'number_subgroup_classes': 37, 'number_subgroups': 341323, 'old_label': None, 'order': 352440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 4005], [3, 7832], [4, 8010], [5, 15664], [9, 23496], [11, 40050], [15, 31328], [22, 40050], [44, 80100], [45, 93984], [89, 7920]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [55174927], 'outer_gens': [[48698450, 25558540]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 90, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [88, 1], [89, 1], [90, 2], [176, 1], [264, 1], [352, 1], [450, 2], [900, 1], [1056, 1]], 'representations': {'Lie': [{'d': 2, 'q': 89, 'gens': [21149073, 697225], 'family': 'PSL'}, {'d': 2, 'q': 89, 'family': 'PSU'}, {'d': 3, 'q': 89, 'family': 'Omega'}, {'d': 3, 'q': 89, 'family': 'POmega'}, {'d': 2, 'q': 89, 'family': 'PSigmaL'}], 'Perm': {'d': 90, 'gens': [157477727897833311123804616108855155343157916520143802629109545305530491730598630773013891981731357814328737009835556716066108308443372, 676874112369148305423907670513422161681583193418003806598076346614161082006458419246069497000544421202982279090608308913775651810820615589]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,89)', 'transitive_degree': 90, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
Hide schema
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id: 174553864
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 352440, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1, 1], 'representative': 704970, 'size': 1}
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id: 174553875
{'aut_label': '2A', 'centralizer': '4005.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 352440, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2, 2], 'representative': 34379406, 'size': 4005}
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id: 174553886
{'aut_label': '3A', 'centralizer': '7832.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 352440, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3, 3], 'representative': 32943572, 'size': 7832}
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id: 174553897
{'aut_label': '4A', 'centralizer': '8010.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 352440, 'label': '4A', 'order': 4, 'powers': [2, 4, 4, 4, 4], 'representative': 39097976, 'size': 8010}
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id: 174553906
{'aut_label': '5A1', 'centralizer': '7832.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 352440, 'label': '5A1', 'order': 5, 'powers': [6, 6, 1, 5, 5], 'representative': 54185982, 'size': 7832}
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id: 174553907
{'aut_label': '5A2', 'centralizer': '7832.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 352440, 'label': '5A2', 'order': 5, 'powers': [5, 5, 1, 6, 6], 'representative': 29933675, 'size': 7832}
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id: 174553908
{'aut_label': '9A1', 'centralizer': '7832.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 352440, 'label': '9A1', 'order': 9, 'powers': [8, 3, 9, 8, 7], 'representative': 52057581, 'size': 7832}
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id: 174553909
{'aut_label': '9A2', 'centralizer': '7832.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 352440, 'label': '9A2', 'order': 9, 'powers': [9, 3, 7, 9, 8], 'representative': 39166875, 'size': 7832}
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id: 174553910
{'aut_label': '9A4', 'centralizer': '7832.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 352440, 'label': '9A4', 'order': 9, 'powers': [7, 3, 8, 7, 9], 'representative': 27218423, 'size': 7832}
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id: 174553865
{'aut_label': '11A1', 'centralizer': '8010.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 352440, 'label': '11A1', 'order': 11, 'powers': [11, 12, 14, 1, 10], 'representative': 58696006, 'size': 8010}
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id: 174553866
{'aut_label': '11A2', 'centralizer': '8010.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 352440, 'label': '11A2', 'order': 11, 'powers': [13, 14, 10, 1, 11], 'representative': 17776921, 'size': 8010}
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id: 174553867
{'aut_label': '11A3', 'centralizer': '8010.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 352440, 'label': '11A3', 'order': 11, 'powers': [14, 11, 13, 1, 12], 'representative': 32774429, 'size': 8010}
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id: 174553868
{'aut_label': '11A4', 'centralizer': '8010.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 352440, 'label': '11A4', 'order': 11, 'powers': [12, 10, 11, 1, 13], 'representative': 54035555, 'size': 8010}
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id: 174553869
{'aut_label': '11A5', 'centralizer': '8010.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 352440, 'label': '11A5', 'order': 11, 'powers': [10, 13, 12, 1, 14], 'representative': 30814000, 'size': 8010}
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id: 174553870
{'aut_label': '15A1', 'centralizer': '7832.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 352440, 'label': '15A1', 'order': 15, 'powers': [16, 5, 3, 17, 15], 'representative': 19402995, 'size': 7832}
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id: 174553871
{'aut_label': '15A2', 'centralizer': '7832.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 352440, 'label': '15A2', 'order': 15, 'powers': [17, 6, 3, 18, 16], 'representative': 61180583, 'size': 7832}
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id: 174553872
{'aut_label': '15A4', 'centralizer': '7832.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 352440, 'label': '15A4', 'order': 15, 'powers': [18, 5, 3, 15, 17], 'representative': 47902010, 'size': 7832}
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id: 174553873
{'aut_label': '15A7', 'centralizer': '7832.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 352440, 'label': '15A7', 'order': 15, 'powers': [15, 6, 3, 16, 18], 'representative': 14749270, 'size': 7832}
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id: 174553874
{'aut_label': '22A1', 'centralizer': '8010.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 352440, 'label': '22A1', 'order': 22, 'powers': [10, 20, 21, 2, 19], 'representative': 52084768, 'size': 8010}
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id: 174553876
{'aut_label': '22A3', 'centralizer': '8010.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 352440, 'label': '22A3', 'order': 22, 'powers': [12, 23, 22, 2, 20], 'representative': 49121948, 'size': 8010}
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id: 174553877
{'aut_label': '22A5', 'centralizer': '8010.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 352440, 'label': '22A5', 'order': 22, 'powers': [14, 22, 20, 2, 21], 'representative': 29577825, 'size': 8010}
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id: 174553878
{'aut_label': '22A7', 'centralizer': '8010.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 352440, 'label': '22A7', 'order': 22, 'powers': [13, 19, 23, 2, 22], 'representative': 27604135, 'size': 8010}
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id: 174553879
{'aut_label': '22A9', 'centralizer': '8010.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 352440, 'label': '22A9', 'order': 22, 'powers': [11, 21, 19, 2, 23], 'representative': 27503561, 'size': 8010}
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id: 174553880
{'aut_label': '44A1', 'centralizer': '8010.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 352440, 'label': '44A1', 'order': 44, 'powers': [19, 25, 26, 4, 24], 'representative': 9101060, 'size': 8010}
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id: 174553881
{'aut_label': '44A3', 'centralizer': '8010.a1.a1', 'counter': 25, 'group_counter': 1, 'group_order': 352440, 'label': '44A3', 'order': 44, 'powers': [20, 28, 30, 4, 25], 'representative': 57458110, 'size': 8010}
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id: 174553882
{'aut_label': '44A5', 'centralizer': '8010.a1.a1', 'counter': 26, 'group_counter': 1, 'group_order': 352440, 'label': '44A5', 'order': 44, 'powers': [21, 30, 32, 4, 26], 'representative': 20494417, 'size': 8010}
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id: 174553883
{'aut_label': '44A7', 'centralizer': '8010.a1.a1', 'counter': 27, 'group_counter': 1, 'group_order': 352440, 'label': '44A7', 'order': 44, 'powers': [22, 33, 28, 4, 27], 'representative': 3463110, 'size': 8010}
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id: 174553884
{'aut_label': '44A9', 'centralizer': '8010.a1.a1', 'counter': 28, 'group_counter': 1, 'group_order': 352440, 'label': '44A9', 'order': 44, 'powers': [23, 31, 24, 4, 28], 'representative': 59501550, 'size': 8010}
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id: 174553885
{'aut_label': '44A13', 'centralizer': '8010.a1.a1', 'counter': 29, 'group_counter': 1, 'group_order': 352440, 'label': '44A13', 'order': 44, 'powers': [23, 26, 33, 4, 29], 'representative': 48152370, 'size': 8010}
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id: 174553887
{'aut_label': '44A15', 'centralizer': '8010.a1.a1', 'counter': 30, 'group_counter': 1, 'group_order': 352440, 'label': '44A15', 'order': 44, 'powers': [22, 24, 29, 4, 30], 'representative': 2563192, 'size': 8010}
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id: 174553888
{'aut_label': '44A17', 'centralizer': '8010.a1.a1', 'counter': 31, 'group_counter': 1, 'group_order': 352440, 'label': '44A17', 'order': 44, 'powers': [21, 27, 25, 4, 31], 'representative': 60687349, 'size': 8010}
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id: 174553889
{'aut_label': '44A19', 'centralizer': '8010.a1.a1', 'counter': 32, 'group_counter': 1, 'group_order': 352440, 'label': '44A19', 'order': 44, 'powers': [20, 29, 27, 4, 32], 'representative': 48538735, 'size': 8010}
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id: 174553890
{'aut_label': '44A21', 'centralizer': '8010.a1.a1', 'counter': 33, 'group_counter': 1, 'group_order': 352440, 'label': '44A21', 'order': 44, 'powers': [19, 32, 31, 4, 33], 'representative': 23988353, 'size': 8010}
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id: 174553891
{'aut_label': '45A1', 'centralizer': '7832.a1.a1', 'counter': 34, 'group_counter': 1, 'group_order': 352440, 'label': '45A1', 'order': 45, 'powers': [35, 15, 7, 39, 34], 'representative': 8374250, 'size': 7832}
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id: 174553892
{'aut_label': '45A2', 'centralizer': '7832.a1.a1', 'counter': 35, 'group_counter': 1, 'group_order': 352440, 'label': '45A2', 'order': 45, 'powers': [36, 16, 8, 45, 35], 'representative': 1398799, 'size': 7832}
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id: 174553893
{'aut_label': '45A4', 'centralizer': '7832.a1.a1', 'counter': 36, 'group_counter': 1, 'group_order': 352440, 'label': '45A4', 'order': 45, 'powers': [38, 17, 9, 34, 36], 'representative': 53081828, 'size': 7832}
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id: 174553894
{'aut_label': '45A7', 'centralizer': '7832.a1.a1', 'counter': 37, 'group_counter': 1, 'group_order': 352440, 'label': '45A7', 'order': 45, 'powers': [41, 18, 8, 40, 37], 'representative': 40582474, 'size': 7832}
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id: 174553895
{'aut_label': '45A8', 'centralizer': '7832.a1.a1', 'counter': 38, 'group_counter': 1, 'group_order': 352440, 'label': '45A8', 'order': 45, 'powers': [42, 18, 7, 35, 38], 'representative': 17778318, 'size': 7832}
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id: 174553896
{'aut_label': '45A11', 'centralizer': '7832.a1.a1', 'counter': 39, 'group_counter': 1, 'group_order': 352440, 'label': '45A11', 'order': 45, 'powers': [45, 17, 8, 41, 39], 'representative': 16453856, 'size': 7832}
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id: 174553898
{'aut_label': '45A13', 'centralizer': '7832.a1.a1', 'counter': 40, 'group_counter': 1, 'group_order': 352440, 'label': '45A13', 'order': 45, 'powers': [44, 16, 9, 38, 40], 'representative': 13567648, 'size': 7832}
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id: 174553899
{'aut_label': '45A14', 'centralizer': '7832.a1.a1', 'counter': 41, 'group_counter': 1, 'group_order': 352440, 'label': '45A14', 'order': 45, 'powers': [43, 15, 9, 44, 41], 'representative': 11083932, 'size': 7832}
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id: 174553900
{'aut_label': '45A16', 'centralizer': '7832.a1.a1', 'counter': 42, 'group_counter': 1, 'group_order': 352440, 'label': '45A16', 'order': 45, 'powers': [40, 15, 8, 36, 42], 'representative': 35672404, 'size': 7832}
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id: 174553901
{'aut_label': '45A17', 'centralizer': '7832.a1.a1', 'counter': 43, 'group_counter': 1, 'group_order': 352440, 'label': '45A17', 'order': 45, 'powers': [39, 16, 7, 37, 43], 'representative': 31908097, 'size': 7832}
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id: 174553902
{'aut_label': '45A19', 'centralizer': '7832.a1.a1', 'counter': 44, 'group_counter': 1, 'group_order': 352440, 'label': '45A19', 'order': 45, 'powers': [37, 17, 7, 42, 44], 'representative': 59481657, 'size': 7832}
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id: 174553903
{'aut_label': '45A22', 'centralizer': '7832.a1.a1', 'counter': 45, 'group_counter': 1, 'group_order': 352440, 'label': '45A22', 'order': 45, 'powers': [34, 18, 9, 43, 45], 'representative': 61792243, 'size': 7832}
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id: 174553904
{'aut_label': '89A1', 'centralizer': '3960.a1.a1', 'counter': 46, 'group_counter': 1, 'group_order': 352440, 'label': '89A1', 'order': 89, 'powers': [46, 47, 46, 46, 1], 'representative': 51811720, 'size': 3960}
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id: 174553905
{'aut_label': '89A1', 'centralizer': '3960.a1.a1', 'counter': 47, 'group_counter': 1, 'group_order': 352440, 'label': '89A3', 'order': 89, 'powers': [47, 46, 47, 47, 1], 'representative': 32799571, 'size': 3960}
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gps_qchar • Show schema
Hide schema
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id: 18083027
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 18083032
{'cdim': 88, 'counter': 3, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.88a', 'multiplicity': 1, 'nt': [3916, 0], 'qdim': 88, 'qvalues': [88, 0, -2, 0, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
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id: 18083037
{'cdim': 89, 'counter': 8, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.89a', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 89, 'qvalues': [89, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
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id: 18083031
{'cdim': 45, 'counter': 2, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.45a', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 90, 'qvalues': [90, 2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 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, 1, 1], 'schur_index': 1}
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id: 18083038
{'cdim': 90, 'counter': 9, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.90a', 'multiplicity': 1, 'nt': [360, 0], 'qdim': 90, 'qvalues': [90, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, -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, 1, 1], 'schur_index': 1}
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id: 18083033
{'cdim': 88, 'counter': 4, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.88b', 'multiplicity': 2, 'nt': [3916, 0], 'qdim': 176, 'qvalues': [176, 0, -4, 0, 1, 1, -4, -4, -4, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
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id: 18083034
{'cdim': 88, 'counter': 5, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.88c', 'multiplicity': 3, 'nt': [3916, 0], 'qdim': 264, 'qvalues': [264, 0, 3, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 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, -3, -3], 'schur_index': 1}
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id: 18083035
{'cdim': 88, 'counter': 6, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.88d', 'multiplicity': 4, 'nt': [3916, 0], 'qdim': 352, 'qvalues': [352, 0, -8, 0, 2, 2, 4, 4, 4, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4], 'schur_index': 1}
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id: 18083028
{'cdim': 90, 'counter': 10, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.90b', 'multiplicity': 5, 'nt': [990, 0], 'qdim': 450, 'qvalues': [450, 10, 0, 10, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5], 'schur_index': 1}
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id: 18083029
{'cdim': 90, 'counter': 11, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.90c', 'multiplicity': 5, 'nt': [1980, 0], 'qdim': 450, 'qvalues': [450, 10, 0, -10, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5], 'schur_index': 1}
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id: 18083030
{'cdim': 90, 'counter': 12, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.90d', 'multiplicity': 10, 'nt': [3960, 0], 'qdim': 900, 'qvalues': [900, -20, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 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, 10, 10], 'schur_index': 1}
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id: 18083036
{'cdim': 88, 'counter': 7, 'faithful': True, 'group': '352440.a', 'group_order': 352440, 'image': None, 'label': '352440.a.88e', 'multiplicity': 12, 'nt': [3916, 0], 'qdim': 1056, 'qvalues': [1056, 0, 12, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, -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, -12, -12], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 39159512
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 352440, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 352440, 'label': '352440.a.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159523
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 2, 'cyclotomic_n': 89, 'dim': 45, 'faithful': True, 'field': [-22, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.45a1', 'nt': [180, 0], 'q_character': None, 'values': [[[45, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 3], [1, 6], [1, 7], [1, 12], [1, 13], [1, 14], [1, 15], [1, 19], [1, 23], [1, 24], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 35], [1, 37], [1, 38], [1, 41], [1, 43], [1, -43], [1, -41], [1, -38], [1, -37], [1, -35], [1, -33], [1, -31], [1, -30], [1, -29], [1, -28], [1, -27], [1, -26], [1, -24], [1, -23], [1, -19], [1, -15], [1, -14], [1, -13], [1, -12], [1, -7], [1, -6], [1, -3]], [[-1, 3], [-1, 6], [-1, 7], [-1, 12], [-1, 13], [-1, 14], [-1, 15], [-1, 19], [-1, 23], [-1, 24], [-1, 26], [-1, 27], [-1, 28], [-1, 29], [-1, 30], [-1, 31], [-1, 33], [-1, 35], [-1, 37], [-1, 38], [-1, 41], [-1, 43], [-1, -43], [-1, -41], [-1, -38], [-1, -37], [-1, -35], [-1, -33], [-1, -31], [-1, -30], [-1, -29], [-1, -28], [-1, -27], [-1, -26], [-1, -24], [-1, -23], [-1, -19], [-1, -15], [-1, -14], [-1, -13], [-1, -12], [-1, -7], [-1, -6], [-1, -3]]]}
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id: 39159534
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 89, 'dim': 45, 'faithful': True, 'field': [-22, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.45a2', 'nt': [180, 0], 'q_character': None, 'values': [[[45, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 6], [-1, 7], [-1, 12], [-1, 13], [-1, 14], [-1, 15], [-1, 19], [-1, 23], [-1, 24], [-1, 26], [-1, 27], [-1, 28], [-1, 29], [-1, 30], [-1, 31], [-1, 33], [-1, 35], [-1, 37], [-1, 38], [-1, 41], [-1, 43], [-1, -43], [-1, -41], [-1, -38], [-1, -37], [-1, -35], [-1, -33], [-1, -31], [-1, -30], [-1, -29], [-1, -28], [-1, -27], [-1, -26], [-1, -24], [-1, -23], [-1, -19], [-1, -15], [-1, -14], [-1, -13], [-1, -12], [-1, -7], [-1, -6], [-1, -3]], [[1, 0], [1, 3], [1, 6], [1, 7], [1, 12], [1, 13], [1, 14], [1, 15], [1, 19], [1, 23], [1, 24], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 35], [1, 37], [1, 38], [1, 41], [1, 43], [1, -43], [1, -41], [1, -38], [1, -37], [1, -35], [1, -33], [1, -31], [1, -30], [1, -29], [1, -28], [1, -27], [1, -26], [1, -24], [1, -23], [1, -19], [1, -15], [1, -14], [1, -13], [1, -12], [1, -7], [1, -6], [1, -3]]]}
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id: 39159545
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 1, 'dim': 88, 'faithful': True, 'field': [0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88a', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 39159554
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 5, 'dim': 88, 'faithful': True, 'field': [-1, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88b1', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
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id: 39159555
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 5, 'dim': 88, 'faithful': True, 'field': [-1, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88b2', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -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]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
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id: 39159556
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 9, 'dim': 88, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88c1', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
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id: 39159557
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 9, 'dim': 88, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88c2', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
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id: 39159558
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 9, 'dim': 88, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88c3', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 0]], [[-1, 0]]]}
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id: 39159513
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 15, 'dim': 88, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88d1', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -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]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 0]], [[-1, 0]]]}
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id: 39159514
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 15, 'dim': 88, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88d2', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -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]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
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id: 39159515
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 15, 'dim': 88, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88d3', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 0]], [[-1, 0]]]}
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id: 39159516
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 15, 'dim': 88, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88d4', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
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id: 39159517
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e1', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 14], [-1, -14]], [[-1, 19], [-1, -19]], [[-1, 22], [-1, -22]], [[-1, 2], [-1, -2]], [[-1, 16], [-1, -16]], [[-1, 8], [-1, -8]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 17], [-1, -17]], [[-1, 4], [-1, -4]], [[-1, 0]], [[-1, 0]]]}
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id: 39159527
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e10', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[-1, 19], [-1, -19]], [[-1, 14], [-1, -14]], [[-1, 22], [-1, -22]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 16], [-1, -16]], [[-1, 17], [-1, -17]], [[-1, 0]], [[-1, 0]]]}
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id: 39159528
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e11', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -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]], [[-1, 2], [-1, -2]], [[-1, 22], [-1, -22]], [[-1, 16], [-1, -16]], [[-1, 19], [-1, -19]], [[-1, 17], [-1, -17]], [[-1, 14], [-1, -14]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 8], [-1, -8]], [[-1, 13], [-1, -13]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 0]], [[-1, 0]]]}
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id: 39159529
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e12', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 7], [-1, -7]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 16], [-1, -16]], [[-1, 19], [-1, -19]], [[-1, 17], [-1, -17]], [[-1, 22], [-1, -22]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
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id: 39159518
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e2', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 11], [-1, -11]], [[-1, 17], [-1, -17]], [[-1, 22], [-1, -22]], [[-1, 2], [-1, -2]], [[-1, 16], [-1, -16]], [[-1, 19], [-1, -19]], [[-1, 8], [-1, -8]], [[-1, 14], [-1, -14]], [[-1, 0]], [[-1, 0]]]}
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id: 39159519
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e3', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[-1, 8], [-1, -8]], [[-1, 13], [-1, -13]], [[-1, 14], [-1, -14]], [[-1, 7], [-1, -7]], [[-1, 17], [-1, -17]], [[-1, 22], [-1, -22]], [[-1, 4], [-1, -4]], [[-1, 16], [-1, -16]], [[-1, 2], [-1, -2]], [[-1, 19], [-1, -19]], [[-1, 0]], [[-1, 0]]]}
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id: 39159520
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e4', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 19], [-1, -19]], [[-1, 16], [-1, -16]], [[-1, 17], [-1, -17]], [[-1, 22], [-1, -22]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, -8]], [[-1, 13], [-1, -13]], [[-1, 14], [-1, -14]], [[-1, 11], [-1, -11]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
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id: 39159521
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e5', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 17], [-1, -17]], [[-1, 1], [-1, -1]], [[-1, 22], [-1, -22]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, -8]], [[-1, 19], [-1, -19]], [[-1, 14], [-1, -14]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 0]], [[-1, 0]]]}
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id: 39159522
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e6', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 11], [-1, -11]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, -8]], [[-1, 19], [-1, -19]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 17], [-1, -17]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 22], [-1, -22]], [[-1, 16], [-1, -16]], [[-1, 0]], [[-1, 0]]]}
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id: 39159524
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e7', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -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]], [[-1, 13], [-1, -13]], [[-1, 8], [-1, -8]], [[-1, 14], [-1, -14]], [[-1, 11], [-1, -11]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 16], [-1, -16]], [[-1, 7], [-1, -7]], [[-1, 17], [-1, -17]], [[-1, 19], [-1, -19]], [[-1, 22], [-1, -22]], [[-1, 0]], [[-1, 0]]]}
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id: 39159525
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e8', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 22], [-1, -22]], [[-1, 17], [-1, -17]], [[-1, 4], [-1, -4]], [[-1, 16], [-1, -16]], [[-1, 7], [-1, -7]], [[-1, 19], [-1, -19]], [[-1, 14], [-1, -14]], [[-1, 11], [-1, -11]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, -8]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 0]], [[-1, 0]]]}
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id: 39159526
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 45, 'dim': 88, 'faithful': True, 'field': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.88e9', 'nt': [3916, 0], 'q_character': None, 'values': [[[88, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 9], [-1, -9]], [[-1, 10], [-1, -10]], [[-1, 20], [-1, -20]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 21], [-1, -21]], [[-1, 3], [-1, -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]], [[-1, 17], [-1, -17]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 13], [-1, -13]], [[-1, 16], [-1, -16]], [[-1, 19], [-1, -19]], [[-1, 14], [-1, -14]], [[-1, 22], [-1, -22]], [[-1, 2], [-1, -2]], [[-1, 11], [-1, -11]], [[-1, 8], [-1, -8]], [[-1, 0]], [[-1, 0]]]}
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id: 39159530
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 1, 'dim': 89, 'faithful': True, 'field': [0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.89a', 'nt': [90, 0], 'q_character': None, 'values': [[[89, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
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id: 39159531
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 1, 'dim': 90, 'faithful': True, 'field': [0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90a', 'nt': [360, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159532
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90b1', 'nt': [990, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159533
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90b2', 'nt': [990, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159535
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90b3', 'nt': [990, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159536
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90b4', 'nt': [990, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159537
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90b5', 'nt': [990, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159538
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90c1', 'nt': [1980, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159539
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90c2', 'nt': [1980, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159540
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90c3', 'nt': [1980, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159541
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90c4', 'nt': [1980, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159542
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 11, 'dim': 90, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90c5', 'nt': [1980, 0], 'q_character': None, 'values': [[[90, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159543
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d1', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159553
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 47, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d10', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 8], [-1, -8]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159544
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d2', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 39159546
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d3', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159547
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d4', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159548
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d5', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 7], [-1, -7]], [[-1, 9], [-1, -9]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159549
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d6', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 9], [1, -9]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159550
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d7', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159551
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d8', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[1, 7], [1, -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]], [[1, 0]], [[1, 0]]]}
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id: 39159552
{'center': '352440.a1.a1', 'center_index': 352440, 'center_order': 1, 'counter': 46, 'cyclotomic_n': 44, 'dim': 90, 'faithful': True, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'group': '352440.a', 'group_counter': 1, 'group_order': 352440, 'image': None, 'image_isoclass': '352440.a', 'image_order': 352440, 'indicator': 1, 'kernel': '352440.a1.a1', 'kernel_order': 1, 'label': '352440.a.90d9', 'nt': [3960, 0], 'q_character': None, 'values': [[[90, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 8], [-1, -8]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[-1, 9], [-1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 269273611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 352440, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 29370, 'label': '352440.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '352440.a', 'subgroup_hash': 8307062878014378175, 'subgroup_order': 352440, 'subgroup_tex': '\\PSL(2,89)', 'supersolvable': False, 'sylow': 0}
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id: 269273622
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.90.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, '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': '3916.b', 'subgroup_hash': 3, 'subgroup_order': 3916, 'subgroup_tex': 'C_{89}:C_{44}', 'supersolvable': True, 'sylow': 0}
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id: 269273633
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, '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': '1958.1', 'subgroup_hash': 1, 'subgroup_order': 1958, 'subgroup_tex': 'C_{89}:C_{22}', 'supersolvable': True, 'sylow': 0}
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id: 269273642
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 979, 'label': '352440.a.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, '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': '979.1', 'subgroup_hash': 1, 'subgroup_order': 979, 'subgroup_tex': 'C_{89}:C_{11}', 'supersolvable': True, 'sylow': 0}
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id: 269273643
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.990.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '990.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 990, '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': '356.3', 'subgroup_hash': 3, 'subgroup_order': 356, 'subgroup_tex': 'C_{89}:C_4', 'supersolvable': True, 'sylow': 0}
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id: 269273644
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.1980.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1980.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1980, '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': '178.1', 'subgroup_hash': 1, 'subgroup_order': 178, 'subgroup_tex': 'D_{89}', 'supersolvable': True, 'sylow': 0}
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id: 269273645
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.3916.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3916.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3916, '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': '90.3', 'subgroup_hash': 3, 'subgroup_order': 90, 'subgroup_tex': 'D_{45}', 'supersolvable': True, 'sylow': 0}
-
id: 269273646
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 89, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': True, 'direct': None, 'hall': 89, 'label': '352440.a.3960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3960.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '89.1', 'subgroup_hash': 1, 'subgroup_order': 89, 'subgroup_tex': 'C_{89}', 'supersolvable': True, 'sylow': 89}
-
id: 269273647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 22, 'label': '352440.a.4005.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4005.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4005, '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': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
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id: 269273612
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.5874.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5874.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5874, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
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id: 269273613
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.5874.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5874.a1.a2', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5874, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
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id: 269273614
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '352440.a.7832.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7832.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7832, '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': '45.1', 'subgroup_hash': 1, 'subgroup_order': 45, 'subgroup_tex': 'C_{45}', 'supersolvable': True, 'sylow': 0}
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id: 269273615
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.8010.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8010.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8010, '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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
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id: 269273616
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.8010.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8010.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8010, '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 269273617
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.8010.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8010.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8010, '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 269273618
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.11748.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11748.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11748, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 269273619
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.14685.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14685.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14685, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 269273620
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.14685.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14685.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14685, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 269273621
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.16020.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16020.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16020, '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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 269273623
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.16020.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16020.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16020, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
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id: 269273624
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.16020.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16020.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16020, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
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id: 269273625
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.19580.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '19580.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19580, '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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
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id: 269273626
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.23496.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23496.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23496, '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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 269273627
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.29370.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '29370.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 29370, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 269273628
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.29370.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '29370.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 29370, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 269273629
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '352440.a.32040.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32040.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32040, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
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id: 269273630
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.35244.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '35244.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 35244, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
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id: 269273631
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '352440.a.39160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '39160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 39160, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 3}
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id: 269273632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '352440.a.44055.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44055.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44055, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
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id: 269273634
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.58740.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '58740.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 58740, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 269273635
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '352440.a.70488.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '70488.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70488, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
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id: 269273636
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.88110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88110, '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: 269273637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.88110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88110.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 269273638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352440.a.88110.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88110.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 269273639
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.117480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '117480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 117480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 269273640
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352440.a.176220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176220.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 176220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 269273641
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352440.a', 'ambient_counter': 1, 'ambient_order': 352440, 'ambient_tex': '\\PSL(2,89)', 'central': True, 'central_factor': False, 'centralizer_order': 352440, 'characteristic': True, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '352440.a.352440.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '352440.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '352440.a', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8307062878014378175, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352440, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,89)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C1'], '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: 269273642
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1'], 'contains': ['3960.a1.a1', '32040.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [752, -1, 473, -1, 760, -1, 587, -1], 'generators': [923016, 31707850], 'label': '352440.a.360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3916.b'}
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id: 269273643
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '990.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1'], 'contains': ['1980.a1.a1', '88110.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2667, -1, 1973, -1, 2109, -1, 1629, -1], 'generators': [54330176, 39256510, 923016], 'label': '352440.a.990.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '990.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '990.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3916.b'}
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id: 269273644
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '1980.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '990.a1.a1'], 'contains': ['3960.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2181, -1, 946, -1, 2024, -1, 1563, -1], 'generators': [39256510, 923016], 'label': '352440.a.1980.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1980.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1980.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3916.b'}
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id: 269273611
{'ambient': '352440.a', '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': '352440.a1.a1', 'complements': ['352440.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['90.a1.a1', '3916.a1.a1', '4005.a1.a1', '5874.a1.a1', '5874.a1.a2', '14685.a1.a1', '14685.a1.a2'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5555, 5000, 5616, 5000, 5814, 5000, 5823, 5000], 'generators': [58314587, 47133443], 'label': '352440.a.1.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['352440.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '352440.a'}
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id: 269273612
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '5874.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['29370.a1.a1', '35244.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 5874, 'diagramx': [6426, -1, 6570, -1, 6702, -1, 7403, -1], 'generators': [36930676, 394358], 'label': '352440.a.5874.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5874.a1.a1', 'old_label': '5874.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5874.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
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id: 269273613
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '5874.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['29370.a1.a2', '35244.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 5874, 'diagramx': [6426, -1, 7389, -1, 6702, -1, 6666, -1], 'generators': [3102358, 394358], 'label': '352440.a.5874.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5874.a1.a2', 'old_label': '5874.a1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5874.a1.a2', 'subgroup_fusion': None, 'weyl_group': '60.5'}
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id: 269273614
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '7832.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7832.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3916.a1.a1'], 'contains': ['23496.a1.a1', '39160.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [9001, -1, 9433, -1, 9625, -1, 9711, -1], 'generators': [22014087, 55017185, 19819213], 'label': '352440.a.7832.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '7832.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7832.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 269273615
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '8010.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8010.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '4005.a1.a1'], 'contains': ['16020.a1.a1', '88110.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [3107, -1, 2396, -1, 3223, -1, 2490, -1], 'generators': [28270118, 54330176, 31707850], 'label': '352440.a.8010.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '8010.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8010.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 269273616
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '8010.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4005.a1.a1'], 'contains': ['16020.a1.a1', '16020.b1.a1', '88110.b1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [3923, -1, 3214, -1, 4176, -1, 3226, -1], 'generators': [30479675, 7881213, 24610602], 'label': '352440.a.8010.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '8010.b1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8010.b1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
-
id: 269273617
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '8010.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4005.a1.a1'], 'contains': ['16020.a1.a1', '16020.b1.a2', '88110.b1.a2'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [3923, -1, 3881, -1, 4176, -1, 3962, -1], 'generators': [48257334, 30479675, 7881213], 'label': '352440.a.8010.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '8010.b1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8010.b1.a2', 'subgroup_fusion': None, 'weyl_group': '44.3'}
-
id: 269273618
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '11748.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3916.a1.a1'], 'contains': ['23496.a1.a1', '35244.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 11748, 'diagramx': [7609, -1, 8802, -1, 7902, -1, 8974, -1], 'generators': [22014087, 39161458, 19819213], 'label': '352440.a.11748.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11748.a1.a1', 'old_label': '11748.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11748.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
-
id: 269273619
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '14685.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['29370.a1.a2', '44055.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [5555, -1, 5086, -1, 5814, -1, 5227, -1], 'generators': [31412506, 394358], 'label': '352440.a.14685.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a1', 'old_label': '14685.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14685.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 269273620
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '14685.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['29370.a1.a1', '44055.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [5555, -1, 5616, -1, 5814, -1, 5823, -1], 'generators': [27352688, 394358], 'label': '352440.a.14685.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a2', 'old_label': '14685.a1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14685.a1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 269273621
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '16020.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8010.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '8010.a1.a1', '8010.b1.a1', '8010.b1.a2'], 'contains': ['32040.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [1943, -1, 2245, -1, 2976, -1, 2299, -1], 'generators': [28270118, 31707850], 'label': '352440.a.16020.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '16020.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16020.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 269273622
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['180.a1.a1', '990.a1.a1', '8010.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3098, -1, 2303, -1, 2666, -1, 2059, -1], 'generators': [41931774, 3861174], 'label': '352440.a.90.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3916.b'}
-
id: 269273623
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '16020.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8010.b1.a1'], 'contains': ['32040.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 8010, 'diagramx': [3575, -1, 2884, -1, 3929, -1, 3035, -1], 'generators': [7881213, 24610602], 'label': '352440.a.16020.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8010.b1.a1', 'old_label': '16020.b1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16020.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
-
id: 269273624
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '16020.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8010.b1.a2'], 'contains': ['32040.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 8010, 'diagramx': [3575, -1, 3522, -1, 3929, -1, 4375, -1], 'generators': [48257334, 7881213], 'label': '352440.a.16020.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8010.b1.a2', 'old_label': '16020.b1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16020.b1.a2', 'subgroup_fusion': None, 'weyl_group': '22.1'}
-
id: 269273625
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '19580.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3916.a1.a1'], 'contains': ['39160.a1.a1', '58740.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 19580, 'diagramx': [8149, -1, 7949, -1, 8769, -1, 8304, -1], 'generators': [10495275, 39161458, 7718692], 'label': '352440.a.19580.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '19580.a1.a1', 'old_label': '19580.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19580.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
-
id: 269273626
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '23496.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7832.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7832.a1.a1', '11748.a1.a1'], 'contains': ['70488.a1.a1', '117480.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [9515, -1, 9656, -1, 8480, -1, 8966, -1], 'generators': [22014087, 19819213], 'label': '352440.a.23496.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '23496.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23496.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 269273627
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '29370.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5874.a1.a1', '14685.a1.a2'], 'contains': ['88110.b1.a2', '117480.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [6059, -1, 6844, -1, 5814, -1, 5823, -1], 'generators': [39903005, 17255118, 26162402], 'label': '352440.a.29370.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a2', 'old_label': '29370.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '29370.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 269273628
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '29370.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5874.a1.a2', '14685.a1.a1'], 'contains': ['88110.b1.a1', '117480.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [6059, -1, 6298, -1, 5814, -1, 5227, -1], 'generators': [22805506, 47933553, 51347142], 'label': '352440.a.29370.a1.a2', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a1', 'old_label': '29370.a1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '29370.a1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 269273629
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '32040.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8010.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '16020.a1.a1', '16020.b1.a1', '16020.b1.a2'], 'contains': ['352440.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [1530, -1, 2116, -1, 3448, -1, 3035, -1], 'generators': [31707850], 'label': '352440.a.32040.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '32040.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32040.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 269273630
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '35244.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5874.a1.a1', '5874.a1.a2', '11748.a1.a1'], 'contains': ['70488.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 35244, 'diagramx': [7801, -1, 8192, -1, 6445, -1, 7667, -1], 'generators': [39161458, 19819213], 'label': '352440.a.35244.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35244.a1.a1', 'old_label': '35244.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '35244.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 269273631
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '39160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7832.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7832.a1.a1', '19580.a1.a1'], 'contains': ['117480.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [8781, -1, 8738, -1, 9336, -1, 8304, -1], 'generators': [10495275, 7718692], 'label': '352440.a.39160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '39160.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '39160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 269273632
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '44055.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4005.a1.a1', '14685.a1.a1', '14685.a1.a2'], 'contains': ['88110.a1.a1', '88110.b1.a1', '88110.b1.a2'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 44055, 'diagramx': [4684, -1, 4527, -1, 5043, -1, 4632, -1], 'generators': [46870983, 38330288, 24610602], 'label': '352440.a.44055.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44055.a1.a1', 'old_label': '44055.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44055.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 269273633
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1'], 'contains': ['360.a1.a1', '1980.a1.a1', '16020.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [1824, -1, 1313, -1, 685, -1, 529, -1], 'generators': [28270118, 923016, 31707850], 'label': '352440.a.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3916.b'}
-
id: 269273634
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '58740.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5874.a1.a1', '5874.a1.a2', '11748.a1.a1', '14685.a1.a1', '14685.a1.a2', '19580.a1.a1'], 'contains': ['117480.a1.a1', '176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 58740, 'diagramx': [6343, -1, 6570, -1, 7623, -1, 7031, -1], 'generators': [39161458, 7718692], 'label': '352440.a.58740.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '58740.a1.a1', 'old_label': '58740.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '58740.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 269273635
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '70488.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7832.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['23496.a1.a1', '35244.a1.a1'], 'contains': ['352440.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [9679, -1, 9749, -1, 6445, -1, 7667, -1], 'generators': [19819213], 'label': '352440.a.70488.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '70488.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70488.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 269273636
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '88110.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8010.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['990.a1.a1', '8010.a1.a1', '44055.a1.a1'], 'contains': ['176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [3025, -1, 1987, -1, 4797, -1, 3705, -1], 'generators': [46870983, 5970176], 'label': '352440.a.88110.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '88110.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 269273637
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '88110.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '88110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8010.b1.a1', '29370.a1.a2', '44055.a1.a1'], 'contains': ['176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [4510, -1, 4304, -1, 5621, -1, 5087, -1], 'generators': [46870983, 24610602], 'label': '352440.a.88110.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a1', 'old_label': '88110.b1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 269273638
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '88110.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '88110.b1.a2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8010.b1.a2', '29370.a1.a1', '44055.a1.a1'], 'contains': ['176220.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 14685, 'diagramx': [4510, -1, 5208, -1, 5621, -1, 5765, -1], 'generators': [48257334, 46870983], 'label': '352440.a.88110.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14685.a1.a2', 'old_label': '88110.b1.a2', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88110.b1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 269273639
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '117480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7832.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['23496.a1.a1', '29370.a1.a1', '29370.a1.a2', '39160.a1.a1', '58740.a1.a1'], 'contains': ['352440.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [6949, -1, 8464, -1, 7623, -1, 6799, -1], 'generators': [7718692], 'label': '352440.a.117480.a1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '117480.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '117480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 269273640
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '176220.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4005.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1980.a1.a1', '16020.a1.a1', '16020.b1.a1', '16020.b1.a2', '35244.a1.a1', '58740.a1.a1', '88110.a1.a1', '88110.b1.a1', '88110.b1.a2'], 'contains': ['352440.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [3575, -1, 3658, -1, 4797, -1, 4375, -1], 'generators': [48257334], 'label': '352440.a.176220.a1.a1', 'mobius_quo': None, 'mobius_sub': -220, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '176220.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 269273641
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '352440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3960.a1.a1', '32040.a1.a1', '70488.a1.a1', '117480.a1.a1', '176220.a1.a1'], 'contains': [], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3575, 5000, 3658, 5000, 4797, 5000, 4375, 5000], 'generators': [], 'label': '352440.a.352440.a1.a1', 'mobius_quo': 1, 'mobius_sub': 704880, 'normal_closure': '352440.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '352440.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '352440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 269273645
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '3916.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '352440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['7832.a1.a1', '11748.a1.a1', '19580.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 3916, 'diagramx': [7965, -1, 8393, -1, 8330, -1, 8635, -1], 'generators': [58314587, 56001035], 'label': '352440.a.3916.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3916.a1.a1', 'old_label': '3916.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3916.a1.a1', 'subgroup_fusion': None, 'weyl_group': '90.3'}
-
id: 269273646
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '3960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '1980.a1.a1'], 'contains': ['352440.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [321, -1, 251, -1, 2024, -1, 1563, -1], 'generators': [923016], 'label': '352440.a.3960.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '3960.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.2'}
-
id: 269273647
{'ambient': '352440.a', 'aut_centralizer_order': None, 'aut_label': '4005.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '176220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8010.a1.a1', '8010.b1.a1', '8010.b1.a2', '44055.a1.a1'], 'core': '352440.a1.a1', 'coset_action_label': None, 'count': 4005, 'diagramx': [4373, -1, 3881, -1, 4722, -1, 3962, -1], 'generators': [58314587, 48257334], 'label': '352440.a.4005.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4005.a1.a1', 'old_label': '4005.a1.a1', 'projective_image': '352440.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4005.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
