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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [22, 10, 110, 11], 'aut_gens': [[1, 10, 110], [1049, 110, 10], [1051, 20, 660], [11, 10, 770], [551, 10, 110]], 'aut_group': '24200.bg', 'aut_hash': 3957277396302200749, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24200, 'aut_permdeg': 242, 'aut_perms': [128752448633818362160790012152845115067871995360975010551768033360131482115503164698929655260319547538183665881677188092802834490480727524276270369563037932167558653050009004304691542986410023185477487314309142144058226949382883115284038458888934885526573331282849266036584107311823717136487452129666762976789376271222563800551007614901286727006032378398303970392681665179209750709821414957415305171392082047891294386313927422055132540035112291197784286836992029106873287742, 58811990310190613105397047279932204955380287640061730511247281961248574489325117663338475226215917128324817962195613609683643064858349661372163501734819189918672041937401859193702488265397363123438435972781792561949254719508902523317629185860103572214099678218147442632955060457646100412870470664590803634086368649869681288085473649655083301055869349459682903063466201251555222863376532585315747614860392014937542494364227315880435784036266533812387163399922684268383573192, 116918878992687092125980870420335873430636166584677098658384915169064683419034329733926808805779564206497265784286302599409181697872771966466177250963026191866278782320054349383541144941507224981629244987126025222179034650368028933168530832349939056125690316490950292113738124398259762398356606604909519530111499358388125306158665990635314756171128994253809665503285158103318135483124338990946311169791861906636351981101509343729869082325808145116311987913657920906406863306, 223949079963832821347897113073396041609480111836341491414313111222999879561003990832654990327802884169105423825064179742629453293652733513523427250561564792494895532942571316474916904771432017639892764495547973823512560560947262008968680225174954994228967906572330083248035603170420862148509536985336337140653287886053171884786000581980268590734590766367637530217349668335723196008647420988172332043911458250844267259023961911872350750534542776449232656897113328803860027781], 'aut_phi_ratio': 55.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 2, 2], [10, 121, 2, 2], [11, 10, 2, 1], [11, 10, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}\\wr C_2', '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': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 121, 1], [5, 121, 4], [10, 121, 4], [11, 10, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1210.10', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 4, 1], [10, 121, 4, 1], [11, 10, 1, 2], [11, 10, 5, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 110, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 10]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1210.10', 'hash': 10, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11, 11], 'inner_gens': [[1, 70, 880], [51, 10, 110], [441, 10, 110]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 1210, 'inner_split': False, 'inner_tex': 'C_{11}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 10, 'irrQ_degree': 50, 'irrQ_dim': 50, 'irrR_degree': 10, 'irrep_stats': [[1, 10], [10, 12]], 'label': '1210.10', 'linC_count': 10, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 10, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11:F11', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 22, 'number_divisions': 8, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 20, 'number_subgroups': 556, 'old_label': None, 'order': 1210, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 121], [5, 484], [10, 484], [11, 120]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [6, 5], 'outer_gens': [[1, 90, 660], [9, 660, 10]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [720, 41081], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [10, 2], [50, 2]], 'representations': {'PC': {'code': 88200547802529130399, 'gens': [1, 3, 4], 'pres': [4, -2, -5, -11, -11, 8, 842, 306, 14083, 7927]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [2143604792, 295918632, 1103176378, 418103038]}, 'Perm': {'d': 22, 'gens': [2446779061503273623, 5251477993144647437, 4738577, 58410722688808089600]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}:F_{11}', 'transitive_degree': 55, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 113320906
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10, 'group_order': 1210, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 113320917
{'aut_label': '2A', 'centralizer': '121.a1.a1', 'counter': 2, 'group_counter': 10, 'group_order': 1210, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 275, 'size': 121}
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id: 113320921
{'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 3, 'group_counter': 10, 'group_order': 1210, 'label': '5A1', 'order': 5, 'powers': [5, 1, 3], 'representative': 1086, 'size': 121}
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id: 113320922
{'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 4, 'group_counter': 10, 'group_order': 1210, 'label': '5A-1', 'order': 5, 'powers': [6, 1, 4], 'representative': 944, 'size': 121}
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id: 113320923
{'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 5, 'group_counter': 10, 'group_order': 1210, 'label': '5A2', 'order': 5, 'powers': [4, 1, 5], 'representative': 342, 'size': 121}
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id: 113320924
{'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 6, 'group_counter': 10, 'group_order': 1210, 'label': '5A-2', 'order': 5, 'powers': [3, 1, 6], 'representative': 798, 'size': 121}
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id: 113320925
{'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 7, 'group_counter': 10, 'group_order': 1210, 'label': '10A1', 'order': 10, 'powers': [3, 2, 7], 'representative': 693, 'size': 121}
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id: 113320926
{'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 8, 'group_counter': 10, 'group_order': 1210, 'label': '10A-1', 'order': 10, 'powers': [4, 2, 8], 'representative': 1147, 'size': 121}
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id: 113320927
{'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 9, 'group_counter': 10, 'group_order': 1210, 'label': '10A3', 'order': 10, 'powers': [6, 2, 9], 'representative': 659, 'size': 121}
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id: 113320907
{'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 10, 'group_counter': 10, 'group_order': 1210, 'label': '10A-3', 'order': 10, 'powers': [5, 2, 10], 'representative': 511, 'size': 121}
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id: 113320908
{'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 11, 'group_counter': 10, 'group_order': 1210, 'label': '11A', 'order': 11, 'powers': [11, 11, 1], 'representative': 110, 'size': 10}
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id: 113320909
{'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 12, 'group_counter': 10, 'group_order': 1210, 'label': '11B', 'order': 11, 'powers': [12, 12, 1], 'representative': 10, 'size': 10}
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id: 113320910
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 13, 'group_counter': 10, 'group_order': 1210, 'label': '11C1', 'order': 11, 'powers': [14, 17, 1], 'representative': 120, 'size': 10}
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id: 113320911
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 14, 'group_counter': 10, 'group_order': 1210, 'label': '11C2', 'order': 11, 'powers': [16, 13, 1], 'representative': 240, 'size': 10}
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id: 113320912
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 15, 'group_counter': 10, 'group_order': 1210, 'label': '11C3', 'order': 11, 'powers': [17, 16, 1], 'representative': 360, 'size': 10}
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id: 113320913
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 16, 'group_counter': 10, 'group_order': 1210, 'label': '11C4', 'order': 11, 'powers': [15, 14, 1], 'representative': 560, 'size': 10}
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id: 113320914
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 17, 'group_counter': 10, 'group_order': 1210, 'label': '11C5', 'order': 11, 'powers': [13, 15, 1], 'representative': 340, 'size': 10}
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id: 113320915
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 18, 'group_counter': 10, 'group_order': 1210, 'label': '11D1', 'order': 11, 'powers': [19, 22, 1], 'representative': 230, 'size': 10}
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id: 113320916
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 19, 'group_counter': 10, 'group_order': 1210, 'label': '11D2', 'order': 11, 'powers': [21, 18, 1], 'representative': 460, 'size': 10}
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id: 113320918
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 20, 'group_counter': 10, 'group_order': 1210, 'label': '11D3', 'order': 11, 'powers': [22, 21, 1], 'representative': 780, 'size': 10}
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id: 113320919
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 21, 'group_counter': 10, 'group_order': 1210, 'label': '11D4', 'order': 11, 'powers': [20, 19, 1], 'representative': 570, 'size': 10}
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id: 113320920
{'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 22, 'group_counter': 10, 'group_order': 1210, 'label': '11D5', 'order': 11, 'powers': [18, 20, 1], 'representative': 350, 'size': 10}
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gps_qchar • Show schema
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id: 5192263
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.1a', '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], 'schur_index': 1}
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id: 5192264
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5192265
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.1c', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
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id: 5192266
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.1d', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
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id: 5192267
{'cdim': 10, 'counter': 5, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.10a', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1], 'schur_index': 1}
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id: 5192268
{'cdim': 10, 'counter': 6, 'faithful': False, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.10b', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5192269
{'cdim': 10, 'counter': 7, 'faithful': True, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.10c', 'multiplicity': 5, 'nt': [55, 0], 'qdim': 50, 'qvalues': [50, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 6, 6, -5, 6, -5, 6, -5, -5, 6, -5], 'schur_index': 1}
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id: 5192270
{'cdim': 10, 'counter': 8, 'faithful': True, 'group': '1210.10', 'group_order': 1210, 'image': None, 'label': '1210.10.10d', 'multiplicity': 5, 'nt': [55, 0], 'qdim': 50, 'qvalues': [50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -5, -5, -5, 6, -5, 6, -5, -5, 6, -5, 6], 'schur_index': 1}
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gps_char • Show schema
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id: 9598097
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1210, 'label': '1210.10.1a', '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]]]}
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id: 9598108
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 605, 'label': '1210.10.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 9598112
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 3, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.10.1c1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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: 9598113
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 4, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.10.1c2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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: 9598114
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.10.1c3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 9598115
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.10.1c4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 9598116
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.10.1d1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[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: 9598117
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.10.1d2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[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: 9598118
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.10.1d3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 9598098
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.10.1d4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 9598099
{'center': '110.a1.a1', 'center_index': 110, 'center_order': 11, 'counter': 11, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.a1', 'kernel_order': 11, 'label': '1210.10.10a', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 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]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 9598100
{'center': '110.a1.b1', 'center_index': 110, 'center_order': 11, 'counter': 12, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.b1', 'kernel_order': 11, 'label': '1210.10.10b', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[10, 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: 9598101
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10c1', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]]]}
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id: 9598102
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10c2', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]]]}
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id: 9598103
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10c3', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]]]}
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id: 9598104
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10c4', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]]]}
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id: 9598105
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10c5', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]]]}
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id: 9598106
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10d1', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]]]}
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id: 9598107
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10d2', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]]]}
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id: 9598109
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10d3', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]]]}
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id: 9598110
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10d4', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]]]}
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id: 9598111
{'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1210.10', 'group_counter': 10, 'group_order': 1210, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 1, 'label': '1210.10.10d5', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 70213989
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1210, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '1210.10.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.10', 'subgroup_hash': 10, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70214000
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 605, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '1210.10.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.6', 'subgroup_hash': 6, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
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id: 70214002
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 242, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '1210.10.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70214003
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': True, 'core_order': 121, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 11, 'label': '1210.10.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 11}
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id: 70214004
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70214005
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.11.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70214006
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, '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': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
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id: 70214007
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.22.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, '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': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
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id: 70214008
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, '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: 70213990
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.55.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, '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: 70213991
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.55.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, '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: 70213992
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.55.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, '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: 70213993
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.10.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70213994
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.10.110.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
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id: 70213995
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1210.10.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.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': 110, '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': 0}
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id: 70213996
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1210.10.110.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, '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': 0}
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id: 70213997
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': True, 'direct': None, 'hall': 10, 'label': '1210.10.121.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '121.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': 121, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
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id: 70213998
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1210.10.242.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, '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: 70213999
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '1210.10.605.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.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': 605, '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': 2}
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id: 70214001
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 1210, 'characteristic': True, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1210.10.1210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1210.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1210.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1210, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], '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
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-
id: 70213989
{'ambient': '1210.10', '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': '1210.a1.a1', 'complements': ['1210.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1', '11.a1.a1', '11.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4632, 5869, 3607, 5333, 5257, 4925, 5859, 5037], 'generators': [5, 10, 110, 2], 'label': '1210.10.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1210.10', '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': '1210.10'}
-
id: 70213990
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.b1'], 'contains': ['110.a1.b1', '605.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5897, -1, 5848, -1, 4900, -1, 5317, -1], 'generators': [5, 10], 'label': '1210.10.55.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '55.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 70213991
{'ambient': '1210.10', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['110.b1.a1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8839, -1, 8659, -1, 745, -1, 1609, -1], 'generators': [5, 120], 'label': '1210.10.55.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '55.b1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
-
id: 70213992
{'ambient': '1210.10', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['110.b1.b1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8839, -1, 7506, -1, 745, -1, 459, -1], 'generators': [5, 230], 'label': '1210.10.55.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.b1', 'old_label': '55.b1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
-
id: 70213993
{'ambient': '1210.10', 'aut_centralizer_order': 1210, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2420, 'centralizer': '10.a1.a1', 'complements': ['11.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4288, 4977, 3697, 3666, 5782, 4925, 4076, 3396], 'generators': [110], 'label': '1210.10.110.a1.a1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 70213994
{'ambient': '1210.10', 'aut_centralizer_order': 1210, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2420, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.b1', '55.a1.b1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4288, 4977, 5991, 7333, 5782, 4925, 5252, 6679], 'generators': [10], 'label': '1210.10.110.a1.b1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.b1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 70213995
{'ambient': '1210.10', 'aut_centralizer_order': 242, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2420, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '55.b1.a1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7369, -1, 9345, -1, 2424, -1, 2009, -1], 'generators': [120], 'label': '1210.10.110.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '110.b1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 70213996
{'ambient': '1210.10', 'aut_centralizer_order': 242, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2420, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '55.b1.b1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7369, -1, 8205, -1, 2424, -1, 872, -1], 'generators': [230], 'label': '1210.10.110.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '110.b1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 70213997
{'ambient': '1210.10', 'aut_centralizer_order': 100, 'aut_label': '121.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12100, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.a1.b1'], 'contains': ['242.a1.a1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2702, -1, 2791, -1, 9265, -1, 8004, -1], 'generators': [5, 2], 'label': '1210.10.121.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '121.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 70213998
{'ambient': '1210.10', 'aut_centralizer_order': 100, 'aut_label': '242.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12100, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.a1.b1', '121.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2702, -1, 2299, -1, 7461, -1, 7332, -1], 'generators': [2], 'label': '1210.10.242.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 70213999
{'ambient': '1210.10', 'aut_centralizer_order': 200, 'aut_label': '605.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.a1.b1', '55.b1.a1', '55.b1.b1', '121.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5691, -1, 5991, -1, 4103, -1, 3043, -1], 'generators': [5], 'label': '1210.10.605.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 70214000
{'ambient': '1210.10', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 1, 'centralizer': '1210.a1.a1', 'complements': ['605.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '22.a1.a1', '22.a1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4632, 2864, 3024, 6458, 5257, 2276, 6596, 7724], 'generators': [2, 110, 10], 'label': '1210.10.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
-
id: 70214001
{'ambient': '1210.10', 'aut_centralizer_order': None, 'aut_label': '1210.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': ['110.a1.a1', '110.a1.b1', '110.b1.a1', '110.b1.b1', '242.a1.a1', '605.a1.a1'], 'contains': [], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4817, 4977, 7299, 5500, 4942, 4925, 3559, 5037], 'generators': [], 'label': '1210.10.1210.a1.a1', 'mobius_quo': 1, 'mobius_sub': 121, 'normal_closure': '1210.a1.a1', 'normal_contained_in': ['110.a1.a1', '110.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1210.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 70214002
{'ambient': '1210.10', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 1, 'centralizer': '1210.a1.a1', 'complements': ['242.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '55.a1.a1', '55.a1.b1', '55.b1.a1', '55.b1.b1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7277, 7136, 5939, 2667, 2256, 7612, 3224, 2388], 'generators': [5, 110, 10], 'label': '1210.10.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
-
id: 70214003
{'ambient': '1210.10', 'aut_centralizer_order': 121, 'aut_label': '10.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '200.31', 'aut_weyl_index': 121, 'centralizer': '10.a1.a1', 'complements': ['121.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['110.a1.a1', '110.a1.b1', '110.b1.a1', '110.b1.b1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5368, 4977, 8620, 4291, 2823, 4925, 4037, 5037], 'generators': [10, 110], 'label': '1210.10.10.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['110.a1.a1', '110.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 70214004
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '55.a1.a1', '121.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2978, -1, 1924, -1, 7649, -1, 5123, -1], 'generators': [5, 110, 2], 'label': '1210.10.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 70214005
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.b1', '55.a1.b1', '121.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [2978, -1, 3892, -1, 7649, -1, 8068, -1], 'generators': [5, 10, 2], 'label': '1210.10.11.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '11.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 70214006
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '242.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1161, -1, 655, -1, 7083, -1, 6660, -1], 'generators': [2, 110], 'label': '1210.10.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 70214007
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.b1'], 'contains': ['110.a1.b1', '242.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [1161, -1, 3193, -1, 7083, -1, 9348, -1], 'generators': [2, 10], 'label': '1210.10.22.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '22.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 70214008
{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '605.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5897, -1, 3697, -1, 4900, -1, 2758, -1], 'generators': [5, 110], 'label': '1210.10.55.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
