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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 6, 6, 6, 14, 6, 2, 12, 12, 14], 'aut_gens': [[1, 2, 8], [5, 198, 876], [5, 294, 876], [673, 1202, 860], [1, 1014, 1144], [341, 770, 1016], [673, 1250, 424], [5, 530, 1116], [337, 434, 488], [341, 1298, 584], [677, 486, 680]], 'aut_group': None, 'aut_hash': 8078478873704631709, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21504, 'aut_permdeg': 46, 'aut_perms': [4781155106296875455965161225430828728988976205532078415946, 4770219604158099155853615928253856289923441724942504744844, 5468432716511852135224376035411778862605598216521292734369, 17671366926170684939896974213953882678514374777107378734, 441334535217213697885158557863605707115309647342467323759, 5436136083254093639661280946722882040166516903266829658433, 4705601829007962343959797220817621970359468326610245457148, 994360883918232944907121880114285848376270150637670893181, 441936396994089935087968975760884472915240013666249840934, 4330906513583247073447157128092711052942247160197980297506], 'aut_phi_ratio': 56.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 2, 1], [3, 1, 2, 1], [4, 2, 1, 2], [4, 8, 1, 1], [4, 14, 2, 1], [4, 28, 1, 1], [4, 28, 2, 1], [4, 56, 1, 1], [6, 1, 2, 3], [6, 4, 4, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 28, 2, 1], [12, 2, 2, 2], [12, 8, 2, 1], [12, 14, 4, 1], [12, 28, 2, 1], [12, 28, 4, 1], [12, 56, 2, 1], [14, 2, 3, 3], [14, 8, 6, 1], [21, 2, 6, 1], [24, 4, 4, 1], [24, 28, 4, 1], [28, 4, 3, 2], [28, 8, 6, 1], [42, 2, 6, 3], [42, 8, 12, 1], [56, 4, 12, 1], [84, 4, 6, 2], [84, 8, 12, 1], [168, 4, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_7.(C_2^5\\times C_6).C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '168.47', 'autcentquo_hash': 47, 'autcentquo_nilpotent': False, 'autcentquo_order': 168, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 2], [3, 1, 2], [4, 2, 2], [4, 8, 1], [4, 14, 2], [4, 28, 3], [4, 56, 1], [6, 1, 6], [6, 4, 4], [7, 2, 3], [8, 4, 2], [8, 28, 2], [12, 2, 4], [12, 8, 2], [12, 14, 4], [12, 28, 6], [12, 56, 2], [14, 2, 9], [14, 8, 6], [21, 2, 6], [24, 4, 4], [24, 28, 4], [28, 4, 6], [28, 8, 6], [42, 2, 18], [42, 8, 12], [56, 4, 12], [84, 4, 12], [84, 8, 12], [168, 4, 24]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '112.31', 'commutator_count': 1, 'commutator_label': '56.8', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4487, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['448.300', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 2], [3, 1, 2, 1], [4, 2, 1, 2], [4, 8, 1, 1], [4, 14, 2, 1], [4, 28, 1, 1], [4, 28, 2, 1], [4, 56, 1, 1], [6, 1, 2, 3], [6, 4, 2, 2], [7, 2, 3, 1], [8, 4, 2, 1], [8, 28, 2, 1], [12, 2, 2, 2], [12, 8, 2, 1], [12, 14, 4, 1], [12, 28, 2, 1], [12, 28, 4, 1], [12, 56, 2, 1], [14, 2, 3, 3], [14, 8, 3, 2], [21, 2, 6, 1], [24, 4, 4, 1], [24, 28, 4, 1], [28, 4, 3, 2], [28, 8, 6, 1], [42, 2, 6, 3], [42, 8, 6, 2], [56, 4, 12, 1], [84, 4, 6, 2], [84, 8, 12, 1], [168, 4, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 34944, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.54', 'hash': 4487, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 2, 28], 'inner_gens': [[1, 1010, 348], [337, 2, 440], [1013, 914, 8]], 'inner_hash': 31, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': None, 'inner_tex': 'D_4\\times D_7', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 102], [4, 57]], 'label': '1344.4487', 'linC_count': 384, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 72, 'linQ_dim': 14, 'linQ_dim_count': 8, 'linR_count': 252, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.(C6*Q8)', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 46, 'number_characteristic_subgroups': 74, 'number_conjugacy_classes': 183, 'number_divisions': 50, 'number_normal_subgroups': 82, 'number_subgroup_autclasses': 188, 'number_subgroup_classes': 204, 'number_subgroups': 936, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 11], [3, 2], [4, 180], [6, 22], [7, 6], [8, 64], [12, 360], [14, 66], [21, 12], [24, 128], [28, 72], [42, 132], [56, 48], [84, 144], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 768, 384, 0, 384, 784], 'outer_gens': [[5, 6, 684], [5, 102, 684], [673, 50, 1244], [1, 1206, 1336], [673, 1058, 232], [341, 1298, 584]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 192, 'outer_perms': [37251577883574125398372130486358937366874928751820771024958047744128772794060955449520645045165317839251864187084556023944690209469011095871193981059926637149079120502453831272564351345735760332717147448237842432925087693290245781375527305110595774535160286260021634936582296281480993666156073713652300154915138232659928881666174664009312008384625387402534, 46554114303123141893399786612092850485261532285159698397275546677915612096113089266406451954972156799039003466896052945568288466292928025441174668486015566043696742686769237469072032581663412603100059161419979859008764539617220917105581686740354152502424613678577921006047687849506171412668677081888356737239287623150386699856942550469162472903602113322713, 232586288012397454803969539309029797425483107555127207762418770737941613430632159791183136514678009380956073750990402495734277566060122842173437417692203953657193052599878084602526995259864022995470743885376646923681301444713233135467410768612297504156792886365663964868604666871443706709040834501027605952975650937337017246884253121011309298760031071352134, 204667828140708321391312348906374193177307075180031698051794918767659197594560538072222956003379470492082729386927071812638063045730558034104813793308036883924886286625885074003818155104091207345184195412993744716144950039060479023324435148011515052150069755088214492654461427993005097873524569632366589994338650055818109173796817938315690487281342708107366, 280893495156431627136928947174921522812808366439660749128040125217492677575870951533478615388965544892164055432219707833787127019514999469912809389903695686782084659644183728112786858446201744868988575767283902761782168027511872110582966410594866194545138596080451763140521220791059065482842035023714789148526220452847012776193932555704789411238401373231641, 11239829169797968215983611077860714077943972888266716678510311051963273423893140656292688508449451862659215627599884097528572047329984153808511206348703316332471956682358316344574680481741909674684233006114693259116678159581207154380864771802683269128371591091131224846898139120082227113031550006221674427682637615608419702178131882967719617049687120484414], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [6, 4], [8, 3], [12, 8], [16, 1], [24, 6], [48, 2]], 'representations': {'PC': {'code': 13479658134725920374909610356295317585701310989846559775499, 'gens': [1, 2, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 5408, 16161, 41, 11139, 7051, 91, 27524, 17612, 116, 9997, 141, 23310, 222, 36879]}, 'Perm': {'d': 26, 'gens': [1888326210495071944437864, 2587602948944973726412800, 16883614933103623098240000, 3, 33559447867886563983360000, 774405718732800, 48498388267952232529920000, 444984]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{28}.(C_6\\times Q_8)', 'transitive_degree': 672, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 116114178
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 4487, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 116114273
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 4487, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 4, 'size': 1}
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id: 116114284
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 4487, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 676, 'size': 1}
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id: 116114295
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 4487, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 672, 'size': 1}
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id: 116114306
{'aut_label': '2D', 'centralizer': '4.h1.a1', 'counter': 5, 'group_counter': 4487, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 841, 'size': 4}
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id: 116114317
{'aut_label': '2D', 'centralizer': '4.h1.a1', 'counter': 6, 'group_counter': 4487, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 845, 'size': 4}
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id: 116114328
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 4487, 'group_order': 1344, 'label': '3A1', 'order': 3, 'powers': [8, 1, 7], 'representative': 448, 'size': 1}
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id: 116114339
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 4487, 'group_order': 1344, 'label': '3A-1', 'order': 3, 'powers': [7, 1, 8], 'representative': 896, 'size': 1}
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id: 116114350
{'aut_label': '4A', 'centralizer': '2.f1.a1', 'counter': 9, 'group_counter': 4487, 'group_order': 1344, 'label': '4A', 'order': 4, 'powers': [4, 9, 9], 'representative': 336, 'size': 2}
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id: 116114179
{'aut_label': '4B', 'centralizer': '2.f1.a1', 'counter': 10, 'group_counter': 4487, 'group_order': 1344, 'label': '4B', 'order': 4, 'powers': [4, 10, 10], 'representative': 340, 'size': 2}
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id: 116114190
{'aut_label': '4C', 'centralizer': '8.f1.a1', 'counter': 11, 'group_counter': 4487, 'group_order': 1344, 'label': '4C', 'order': 4, 'powers': [3, 11, 11], 'representative': 1, 'size': 8}
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id: 116114201
{'aut_label': '4D1', 'centralizer': '14.b1.a1', 'counter': 12, 'group_counter': 4487, 'group_order': 1344, 'label': '4D1', 'order': 4, 'powers': [2, 13, 13], 'representative': 991, 'size': 14}
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id: 116114212
{'aut_label': '4D1', 'centralizer': '14.b1.a1', 'counter': 13, 'group_counter': 4487, 'group_order': 1344, 'label': '4D-1', 'order': 4, 'powers': [2, 12, 12], 'representative': 987, 'size': 14}
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id: 116114223
{'aut_label': '4E', 'centralizer': '28.f1.a1', 'counter': 14, 'group_counter': 4487, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [3, 14, 14], 'representative': 1135, 'size': 28}
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id: 116114234
{'aut_label': '4F1', 'centralizer': '28.d1.a1', 'counter': 15, 'group_counter': 4487, 'group_order': 1344, 'label': '4F1', 'order': 4, 'powers': [2, 16, 16], 'representative': 966, 'size': 28}
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id: 116114245
{'aut_label': '4F1', 'centralizer': '28.d1.a1', 'counter': 16, 'group_counter': 4487, 'group_order': 1344, 'label': '4F-1', 'order': 4, 'powers': [2, 15, 15], 'representative': 962, 'size': 28}
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id: 116114256
{'aut_label': '4G', 'centralizer': '56.h1.a1', 'counter': 17, 'group_counter': 4487, 'group_order': 1344, 'label': '4G', 'order': 4, 'powers': [2, 17, 17], 'representative': 746, 'size': 56}
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id: 116114267
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 4487, 'group_order': 1344, 'label': '6A1', 'order': 6, 'powers': [7, 2, 18], 'representative': 900, 'size': 1}
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id: 116114272
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 4487, 'group_order': 1344, 'label': '6A-1', 'order': 6, 'powers': [8, 2, 19], 'representative': 452, 'size': 1}
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id: 116114274
{'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 4487, 'group_order': 1344, 'label': '6B1', 'order': 6, 'powers': [8, 3, 20], 'representative': 1124, 'size': 1}
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id: 116114275
{'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 4487, 'group_order': 1344, 'label': '6B-1', 'order': 6, 'powers': [7, 3, 21], 'representative': 228, 'size': 1}
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id: 116114276
{'aut_label': '6C1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 4487, 'group_order': 1344, 'label': '6C1', 'order': 6, 'powers': [8, 4, 22], 'representative': 1120, 'size': 1}
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id: 116114277
{'aut_label': '6C1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 4487, 'group_order': 1344, 'label': '6C-1', 'order': 6, 'powers': [7, 4, 23], 'representative': 224, 'size': 1}
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id: 116114278
{'aut_label': '6D1', 'centralizer': '4.h1.a1', 'counter': 24, 'group_counter': 4487, 'group_order': 1344, 'label': '6D1', 'order': 6, 'powers': [7, 5, 24], 'representative': 393, 'size': 4}
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id: 116114279
{'aut_label': '6D1', 'centralizer': '4.h1.a1', 'counter': 25, 'group_counter': 4487, 'group_order': 1344, 'label': '6D-1', 'order': 6, 'powers': [8, 5, 25], 'representative': 1289, 'size': 4}
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id: 116114280
{'aut_label': '6D1', 'centralizer': '4.h1.a1', 'counter': 26, 'group_counter': 4487, 'group_order': 1344, 'label': '6E1', 'order': 6, 'powers': [7, 6, 26], 'representative': 397, 'size': 4}
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id: 116114281
{'aut_label': '6D1', 'centralizer': '4.h1.a1', 'counter': 27, 'group_counter': 4487, 'group_order': 1344, 'label': '6E-1', 'order': 6, 'powers': [8, 6, 27], 'representative': 1293, 'size': 4}
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id: 116114282
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 4487, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [29, 30, 1], 'representative': 384, 'size': 2}
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id: 116114283
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 4487, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [30, 28, 1], 'representative': 768, 'size': 2}
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id: 116114285
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 4487, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [28, 29, 1], 'representative': 1152, 'size': 2}
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id: 116114286
{'aut_label': '8A1', 'centralizer': '4.f1.a1', 'counter': 31, 'group_counter': 4487, 'group_order': 1344, 'label': '8A1', 'order': 8, 'powers': [9, 32, 31], 'representative': 168, 'size': 4}
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id: 116114287
{'aut_label': '8A1', 'centralizer': '4.f1.a1', 'counter': 32, 'group_counter': 4487, 'group_order': 1344, 'label': '8A3', 'order': 8, 'powers': [9, 31, 32], 'representative': 504, 'size': 4}
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id: 116114288
{'aut_label': '8B1', 'centralizer': '28.i1.a1', 'counter': 33, 'group_counter': 4487, 'group_order': 1344, 'label': '8B1', 'order': 8, 'powers': [9, 33, 34], 'representative': 627, 'size': 28}
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id: 116114289
{'aut_label': '8B1', 'centralizer': '28.i1.a1', 'counter': 34, 'group_counter': 4487, 'group_order': 1344, 'label': '8B-1', 'order': 8, 'powers': [9, 34, 33], 'representative': 291, 'size': 28}
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id: 116114290
{'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 35, 'group_counter': 4487, 'group_order': 1344, 'label': '12A1', 'order': 12, 'powers': [22, 9, 35], 'representative': 560, 'size': 2}
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id: 116114291
{'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 36, 'group_counter': 4487, 'group_order': 1344, 'label': '12A-1', 'order': 12, 'powers': [23, 9, 36], 'representative': 784, 'size': 2}
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id: 116114292
{'aut_label': '12B1', 'centralizer': '2.f1.a1', 'counter': 37, 'group_counter': 4487, 'group_order': 1344, 'label': '12B1', 'order': 12, 'powers': [23, 10, 37], 'representative': 116, 'size': 2}
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id: 116114293
{'aut_label': '12B1', 'centralizer': '2.f1.a1', 'counter': 38, 'group_counter': 4487, 'group_order': 1344, 'label': '12B-1', 'order': 12, 'powers': [22, 10, 38], 'representative': 1236, 'size': 2}
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id: 116114294
{'aut_label': '12C1', 'centralizer': '8.f1.a1', 'counter': 39, 'group_counter': 4487, 'group_order': 1344, 'label': '12C1', 'order': 12, 'powers': [21, 11, 39], 'representative': 1125, 'size': 8}
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id: 116114296
{'aut_label': '12C1', 'centralizer': '8.f1.a1', 'counter': 40, 'group_counter': 4487, 'group_order': 1344, 'label': '12C-1', 'order': 12, 'powers': [20, 11, 40], 'representative': 897, 'size': 8}
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id: 116114297
{'aut_label': '12D1', 'centralizer': '14.b1.a1', 'counter': 41, 'group_counter': 4487, 'group_order': 1344, 'label': '12D1', 'order': 12, 'powers': [18, 12, 44], 'representative': 91, 'size': 14}
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id: 116114298
{'aut_label': '12D1', 'centralizer': '14.b1.a1', 'counter': 42, 'group_counter': 4487, 'group_order': 1344, 'label': '12D-1', 'order': 12, 'powers': [19, 13, 43], 'representative': 59, 'size': 14}
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id: 116114299
{'aut_label': '12D1', 'centralizer': '14.b1.a1', 'counter': 43, 'group_counter': 4487, 'group_order': 1344, 'label': '12D5', 'order': 12, 'powers': [19, 12, 42], 'representative': 155, 'size': 14}
-
id: 116114300
{'aut_label': '12D1', 'centralizer': '14.b1.a1', 'counter': 44, 'group_counter': 4487, 'group_order': 1344, 'label': '12D-5', 'order': 12, 'powers': [18, 13, 41], 'representative': 95, 'size': 14}
-
id: 116114301
{'aut_label': '12E1', 'centralizer': '28.f1.a1', 'counter': 45, 'group_counter': 4487, 'group_order': 1344, 'label': '12E1', 'order': 12, 'powers': [20, 14, 45], 'representative': 11, 'size': 28}
-
id: 116114302
{'aut_label': '12E1', 'centralizer': '28.f1.a1', 'counter': 46, 'group_counter': 4487, 'group_order': 1344, 'label': '12E-1', 'order': 12, 'powers': [21, 14, 46], 'representative': 43, 'size': 28}
-
id: 116114303
{'aut_label': '12F1', 'centralizer': '28.d1.a1', 'counter': 47, 'group_counter': 4487, 'group_order': 1344, 'label': '12F1', 'order': 12, 'powers': [18, 15, 50], 'representative': 66, 'size': 28}
-
id: 116114304
{'aut_label': '12F1', 'centralizer': '28.d1.a1', 'counter': 48, 'group_counter': 4487, 'group_order': 1344, 'label': '12F-1', 'order': 12, 'powers': [19, 16, 49], 'representative': 38, 'size': 28}
-
id: 116114305
{'aut_label': '12F1', 'centralizer': '28.d1.a1', 'counter': 49, 'group_counter': 4487, 'group_order': 1344, 'label': '12F5', 'order': 12, 'powers': [19, 15, 48], 'representative': 34, 'size': 28}
-
id: 116114307
{'aut_label': '12F1', 'centralizer': '28.d1.a1', 'counter': 50, 'group_counter': 4487, 'group_order': 1344, 'label': '12F-5', 'order': 12, 'powers': [18, 16, 47], 'representative': 70, 'size': 28}
-
id: 116114308
{'aut_label': '12G1', 'centralizer': '56.h1.a1', 'counter': 51, 'group_counter': 4487, 'group_order': 1344, 'label': '12G1', 'order': 12, 'powers': [19, 17, 51], 'representative': 302, 'size': 56}
-
id: 116114309
{'aut_label': '12G1', 'centralizer': '56.h1.a1', 'counter': 52, 'group_counter': 4487, 'group_order': 1344, 'label': '12G-1', 'order': 12, 'powers': [18, 17, 52], 'representative': 1194, 'size': 56}
-
id: 116114310
{'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 53, 'group_counter': 4487, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [28, 54, 2], 'representative': 196, 'size': 2}
-
id: 116114311
{'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 54, 'group_counter': 4487, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [30, 55, 2], 'representative': 580, 'size': 2}
-
id: 116114312
{'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 55, 'group_counter': 4487, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [29, 53, 2], 'representative': 964, 'size': 2}
-
id: 116114313
{'aut_label': '14B1', 'centralizer': '2.a1.a1', 'counter': 56, 'group_counter': 4487, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [30, 57, 4], 'representative': 96, 'size': 2}
-
id: 116114314
{'aut_label': '14B1', 'centralizer': '2.a1.a1', 'counter': 57, 'group_counter': 4487, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [29, 58, 4], 'representative': 288, 'size': 2}
-
id: 116114315
{'aut_label': '14B1', 'centralizer': '2.a1.a1', 'counter': 58, 'group_counter': 4487, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [28, 56, 4], 'representative': 480, 'size': 2}
-
id: 116114316
{'aut_label': '14C1', 'centralizer': '2.a1.a1', 'counter': 59, 'group_counter': 4487, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [29, 60, 3], 'representative': 1060, 'size': 2}
-
id: 116114318
{'aut_label': '14C1', 'centralizer': '2.a1.a1', 'counter': 60, 'group_counter': 4487, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [28, 61, 3], 'representative': 484, 'size': 2}
-
id: 116114319
{'aut_label': '14C1', 'centralizer': '2.a1.a1', 'counter': 61, 'group_counter': 4487, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [30, 59, 3], 'representative': 1252, 'size': 2}
-
id: 116114320
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 62, 'group_counter': 4487, 'group_order': 1344, 'label': '14D1', 'order': 14, 'powers': [28, 63, 5], 'representative': 1033, 'size': 8}
-
id: 116114321
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 63, 'group_counter': 4487, 'group_order': 1344, 'label': '14D3', 'order': 14, 'powers': [30, 64, 5], 'representative': 73, 'size': 8}
-
id: 116114322
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 64, 'group_counter': 4487, 'group_order': 1344, 'label': '14D5', 'order': 14, 'powers': [29, 62, 5], 'representative': 457, 'size': 8}
-
id: 116114323
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 65, 'group_counter': 4487, 'group_order': 1344, 'label': '14E1', 'order': 14, 'powers': [28, 66, 6], 'representative': 1037, 'size': 8}
-
id: 116114324
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 66, 'group_counter': 4487, 'group_order': 1344, 'label': '14E3', 'order': 14, 'powers': [30, 67, 6], 'representative': 77, 'size': 8}
-
id: 116114325
{'aut_label': '14D1', 'centralizer': '8.e1.a1', 'counter': 67, 'group_counter': 4487, 'group_order': 1344, 'label': '14E5', 'order': 14, 'powers': [29, 65, 6], 'representative': 461, 'size': 8}
-
id: 116114326
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 68, 'group_counter': 4487, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [70, 28, 8], 'representative': 128, 'size': 2}
-
id: 116114327
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 69, 'group_counter': 4487, 'group_order': 1344, 'label': '21A-1', 'order': 21, 'powers': [71, 28, 7], 'representative': 1216, 'size': 2}
-
id: 116114329
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 70, 'group_counter': 4487, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [72, 29, 7], 'representative': 256, 'size': 2}
-
id: 116114330
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 71, 'group_counter': 4487, 'group_order': 1344, 'label': '21A-2', 'order': 21, 'powers': [73, 29, 8], 'representative': 1088, 'size': 2}
-
id: 116114331
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 72, 'group_counter': 4487, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [69, 30, 8], 'representative': 512, 'size': 2}
-
id: 116114332
{'aut_label': '21A1', 'centralizer': '2.a1.a1', 'counter': 73, 'group_counter': 4487, 'group_order': 1344, 'label': '21A-4', 'order': 21, 'powers': [68, 30, 7], 'representative': 832, 'size': 2}
-
id: 116114333
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 74, 'group_counter': 4487, 'group_order': 1344, 'label': '24A1', 'order': 24, 'powers': [36, 31, 74], 'representative': 56, 'size': 4}
-
id: 116114334
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 75, 'group_counter': 4487, 'group_order': 1344, 'label': '24A-1', 'order': 24, 'powers': [35, 31, 75], 'representative': 1288, 'size': 4}
-
id: 116114335
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 76, 'group_counter': 4487, 'group_order': 1344, 'label': '24A5', 'order': 24, 'powers': [35, 32, 76], 'representative': 280, 'size': 4}
-
id: 116114336
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 77, 'group_counter': 4487, 'group_order': 1344, 'label': '24A-5', 'order': 24, 'powers': [36, 32, 77], 'representative': 1064, 'size': 4}
-
id: 116114337
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 78, 'group_counter': 4487, 'group_order': 1344, 'label': '24B1', 'order': 24, 'powers': [35, 33, 80], 'representative': 67, 'size': 28}
-
id: 116114338
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 79, 'group_counter': 4487, 'group_order': 1344, 'label': '24B-1', 'order': 24, 'powers': [36, 34, 81], 'representative': 35, 'size': 28}
-
id: 116114340
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 80, 'group_counter': 4487, 'group_order': 1344, 'label': '24B7', 'order': 24, 'powers': [35, 34, 78], 'representative': 19, 'size': 28}
-
id: 116114341
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 81, 'group_counter': 4487, 'group_order': 1344, 'label': '24B-7', 'order': 24, 'powers': [36, 33, 79], 'representative': 131, 'size': 28}
-
id: 116114342
{'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 82, 'group_counter': 4487, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [56, 83, 10], 'representative': 52, 'size': 4}
-
id: 116114343
{'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 83, 'group_counter': 4487, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [57, 84, 10], 'representative': 148, 'size': 4}
-
id: 116114344
{'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 84, 'group_counter': 4487, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [58, 82, 10], 'representative': 244, 'size': 4}
-
id: 116114345
{'aut_label': '28B1', 'centralizer': '4.f1.a1', 'counter': 85, 'group_counter': 4487, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [56, 86, 9], 'representative': 48, 'size': 4}
-
id: 116114346
{'aut_label': '28B1', 'centralizer': '4.f1.a1', 'counter': 86, 'group_counter': 4487, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [57, 87, 9], 'representative': 144, 'size': 4}
-
id: 116114347
{'aut_label': '28B1', 'centralizer': '4.f1.a1', 'counter': 87, 'group_counter': 4487, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [58, 85, 9], 'representative': 240, 'size': 4}
-
id: 116114348
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 88, 'group_counter': 4487, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [59, 89, 11], 'representative': 869, 'size': 8}
-
id: 116114349
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 89, 'group_counter': 4487, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [60, 91, 11], 'representative': 577, 'size': 8}
-
id: 116114351
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 90, 'group_counter': 4487, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [61, 93, 11], 'representative': 293, 'size': 8}
-
id: 116114352
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 91, 'group_counter': 4487, 'group_order': 1344, 'label': '28C9', 'order': 28, 'powers': [61, 88, 11], 'representative': 1061, 'size': 8}
-
id: 116114353
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 92, 'group_counter': 4487, 'group_order': 1344, 'label': '28C11', 'order': 28, 'powers': [60, 90, 11], 'representative': 769, 'size': 8}
-
id: 116114354
{'aut_label': '28C1', 'centralizer': '8.f1.a1', 'counter': 93, 'group_counter': 4487, 'group_order': 1344, 'label': '28C13', 'order': 28, 'powers': [59, 92, 11], 'representative': 485, 'size': 8}
-
id: 116114355
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 94, 'group_counter': 4487, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [68, 53, 19], 'representative': 68, 'size': 2}
-
id: 116114356
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 95, 'group_counter': 4487, 'group_order': 1344, 'label': '42A-1', 'order': 42, 'powers': [69, 53, 18], 'representative': 516, 'size': 2}
-
id: 116114357
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 96, 'group_counter': 4487, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [70, 55, 18], 'representative': 132, 'size': 2}
-
id: 116114358
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 97, 'group_counter': 4487, 'group_order': 1344, 'label': '42A-5', 'order': 42, 'powers': [71, 55, 19], 'representative': 1028, 'size': 2}
-
id: 116114359
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 98, 'group_counter': 4487, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [73, 54, 18], 'representative': 708, 'size': 2}
-
id: 116114360
{'aut_label': '42A1', 'centralizer': '2.a1.a1', 'counter': 99, 'group_counter': 4487, 'group_order': 1344, 'label': '42A-11', 'order': 42, 'powers': [72, 54, 19], 'representative': 260, 'size': 2}
-
id: 116114180
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 100, 'group_counter': 4487, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [73, 56, 23], 'representative': 32, 'size': 2}
-
id: 116114181
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 101, 'group_counter': 4487, 'group_order': 1344, 'label': '42B-1', 'order': 42, 'powers': [72, 56, 22], 'representative': 1312, 'size': 2}
-
id: 116114182
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 102, 'group_counter': 4487, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [68, 58, 22], 'representative': 160, 'size': 2}
-
id: 116114183
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 103, 'group_counter': 4487, 'group_order': 1344, 'label': '42B-5', 'order': 42, 'powers': [69, 58, 23], 'representative': 1184, 'size': 2}
-
id: 116114184
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 104, 'group_counter': 4487, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [71, 57, 22], 'representative': 352, 'size': 2}
-
id: 116114185
{'aut_label': '42B1', 'centralizer': '2.a1.a1', 'counter': 105, 'group_counter': 4487, 'group_order': 1344, 'label': '42B-11', 'order': 42, 'powers': [70, 57, 23], 'representative': 992, 'size': 2}
-
id: 116114186
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 106, 'group_counter': 4487, 'group_order': 1344, 'label': '42C1', 'order': 42, 'powers': [70, 59, 21], 'representative': 804, 'size': 2}
-
id: 116114187
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 107, 'group_counter': 4487, 'group_order': 1344, 'label': '42C-1', 'order': 42, 'powers': [71, 59, 20], 'representative': 548, 'size': 2}
-
id: 116114188
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 108, 'group_counter': 4487, 'group_order': 1344, 'label': '42C5', 'order': 42, 'powers': [72, 61, 20], 'representative': 1316, 'size': 2}
-
id: 116114189
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 109, 'group_counter': 4487, 'group_order': 1344, 'label': '42C-5', 'order': 42, 'powers': [73, 61, 21], 'representative': 36, 'size': 2}
-
id: 116114191
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 110, 'group_counter': 4487, 'group_order': 1344, 'label': '42C11', 'order': 42, 'powers': [68, 60, 20], 'representative': 740, 'size': 2}
-
id: 116114192
{'aut_label': '42C1', 'centralizer': '2.a1.a1', 'counter': 111, 'group_counter': 4487, 'group_order': 1344, 'label': '42C-11', 'order': 42, 'powers': [69, 60, 21], 'representative': 612, 'size': 2}
-
id: 116114193
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 112, 'group_counter': 4487, 'group_order': 1344, 'label': '42D1', 'order': 42, 'powers': [69, 62, 24], 'representative': 9, 'size': 8}
-
id: 116114194
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 113, 'group_counter': 4487, 'group_order': 1344, 'label': '42D-1', 'order': 42, 'powers': [68, 62, 25], 'representative': 233, 'size': 8}
-
id: 116114195
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 114, 'group_counter': 4487, 'group_order': 1344, 'label': '42D5', 'order': 42, 'powers': [71, 64, 25], 'representative': 41, 'size': 8}
-
id: 116114196
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 115, 'group_counter': 4487, 'group_order': 1344, 'label': '42D-5', 'order': 42, 'powers': [70, 64, 24], 'representative': 969, 'size': 8}
-
id: 116114197
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 116, 'group_counter': 4487, 'group_order': 1344, 'label': '42D11', 'order': 42, 'powers': [72, 63, 25], 'representative': 137, 'size': 8}
-
id: 116114198
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 117, 'group_counter': 4487, 'group_order': 1344, 'label': '42D-11', 'order': 42, 'powers': [73, 63, 24], 'representative': 201, 'size': 8}
-
id: 116114199
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 118, 'group_counter': 4487, 'group_order': 1344, 'label': '42E1', 'order': 42, 'powers': [69, 65, 26], 'representative': 13, 'size': 8}
-
id: 116114200
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 119, 'group_counter': 4487, 'group_order': 1344, 'label': '42E-1', 'order': 42, 'powers': [68, 65, 27], 'representative': 237, 'size': 8}
-
id: 116114202
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 120, 'group_counter': 4487, 'group_order': 1344, 'label': '42E5', 'order': 42, 'powers': [71, 67, 27], 'representative': 45, 'size': 8}
-
id: 116114203
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 121, 'group_counter': 4487, 'group_order': 1344, 'label': '42E-5', 'order': 42, 'powers': [70, 67, 26], 'representative': 153, 'size': 8}
-
id: 116114204
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 122, 'group_counter': 4487, 'group_order': 1344, 'label': '42E11', 'order': 42, 'powers': [72, 66, 27], 'representative': 89, 'size': 8}
-
id: 116114205
{'aut_label': '42D1', 'centralizer': '8.e1.a1', 'counter': 123, 'group_counter': 4487, 'group_order': 1344, 'label': '42E-11', 'order': 42, 'powers': [73, 66, 26], 'representative': 205, 'size': 8}
-
id: 116114206
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 124, 'group_counter': 4487, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [85, 125, 31], 'representative': 24, 'size': 4}
-
id: 116114207
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 125, 'group_counter': 4487, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [86, 127, 32], 'representative': 72, 'size': 4}
-
id: 116114208
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 126, 'group_counter': 4487, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [87, 130, 32], 'representative': 120, 'size': 4}
-
id: 116114209
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 127, 'group_counter': 4487, 'group_order': 1344, 'label': '56A9', 'order': 56, 'powers': [87, 135, 31], 'representative': 216, 'size': 4}
-
id: 116114210
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 128, 'group_counter': 4487, 'group_order': 1344, 'label': '56A11', 'order': 56, 'powers': [86, 133, 32], 'representative': 264, 'size': 4}
-
id: 116114211
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 129, 'group_counter': 4487, 'group_order': 1344, 'label': '56A13', 'order': 56, 'powers': [85, 131, 32], 'representative': 312, 'size': 4}
-
id: 116114213
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 130, 'group_counter': 4487, 'group_order': 1344, 'label': '56A15', 'order': 56, 'powers': [85, 128, 31], 'representative': 360, 'size': 4}
-
id: 116114214
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 131, 'group_counter': 4487, 'group_order': 1344, 'label': '56A17', 'order': 56, 'powers': [86, 126, 31], 'representative': 408, 'size': 4}
-
id: 116114215
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 132, 'group_counter': 4487, 'group_order': 1344, 'label': '56A19', 'order': 56, 'powers': [87, 124, 32], 'representative': 456, 'size': 4}
-
id: 116114216
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 133, 'group_counter': 4487, 'group_order': 1344, 'label': '56A23', 'order': 56, 'powers': [87, 129, 31], 'representative': 552, 'size': 4}
-
id: 116114217
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 134, 'group_counter': 4487, 'group_order': 1344, 'label': '56A25', 'order': 56, 'powers': [86, 132, 31], 'representative': 600, 'size': 4}
-
id: 116114218
{'aut_label': '56A1', 'centralizer': '4.f1.a1', 'counter': 135, 'group_counter': 4487, 'group_order': 1344, 'label': '56A27', 'order': 56, 'powers': [85, 134, 32], 'representative': 648, 'size': 4}
-
id: 116114219
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 136, 'group_counter': 4487, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [100, 82, 37], 'representative': 20, 'size': 4}
-
id: 116114220
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 137, 'group_counter': 4487, 'group_order': 1344, 'label': '84A-1', 'order': 84, 'powers': [101, 82, 38], 'representative': 468, 'size': 4}
-
id: 116114221
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 138, 'group_counter': 4487, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [102, 84, 38], 'representative': 84, 'size': 4}
-
id: 116114222
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 139, 'group_counter': 4487, 'group_order': 1344, 'label': '84A-5', 'order': 84, 'powers': [103, 84, 37], 'representative': 596, 'size': 4}
-
id: 116114224
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 140, 'group_counter': 4487, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [104, 83, 38], 'representative': 276, 'size': 4}
-
id: 116114225
{'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 141, 'group_counter': 4487, 'group_order': 1344, 'label': '84A-11', 'order': 84, 'powers': [105, 83, 37], 'representative': 404, 'size': 4}
-
id: 116114226
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 142, 'group_counter': 4487, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [100, 85, 36], 'representative': 16, 'size': 4}
-
id: 116114227
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 143, 'group_counter': 4487, 'group_order': 1344, 'label': '84B-1', 'order': 84, 'powers': [101, 85, 35], 'representative': 1328, 'size': 4}
-
id: 116114228
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 144, 'group_counter': 4487, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [102, 87, 35], 'representative': 80, 'size': 4}
-
id: 116114229
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 145, 'group_counter': 4487, 'group_order': 1344, 'label': '84B-5', 'order': 84, 'powers': [103, 87, 36], 'representative': 1264, 'size': 4}
-
id: 116114230
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 146, 'group_counter': 4487, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [104, 86, 35], 'representative': 176, 'size': 4}
-
id: 116114231
{'aut_label': '84B1', 'centralizer': '4.f1.a1', 'counter': 147, 'group_counter': 4487, 'group_order': 1344, 'label': '84B-11', 'order': 84, 'powers': [105, 86, 36], 'representative': 1168, 'size': 4}
-
id: 116114232
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 148, 'group_counter': 4487, 'group_order': 1344, 'label': '84C1', 'order': 84, 'powers': [106, 88, 39], 'representative': 65, 'size': 8}
-
id: 116114233
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 149, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-1', 'order': 84, 'powers': [107, 88, 40], 'representative': 513, 'size': 8}
-
id: 116114235
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 150, 'group_counter': 4487, 'group_order': 1344, 'label': '84C5', 'order': 84, 'powers': [108, 90, 40], 'representative': 321, 'size': 8}
-
id: 116114236
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 151, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-5', 'order': 84, 'powers': [109, 90, 39], 'representative': 17, 'size': 8}
-
id: 116114237
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 152, 'group_counter': 4487, 'group_order': 1344, 'label': '84C11', 'order': 84, 'powers': [110, 92, 40], 'representative': 37, 'size': 8}
-
id: 116114238
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 153, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-11', 'order': 84, 'powers': [111, 92, 39], 'representative': 641, 'size': 8}
-
id: 116114239
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 154, 'group_counter': 4487, 'group_order': 1344, 'label': '84C13', 'order': 84, 'powers': [106, 93, 39], 'representative': 69, 'size': 8}
-
id: 116114240
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 155, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-13', 'order': 84, 'powers': [107, 93, 40], 'representative': 609, 'size': 8}
-
id: 116114241
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 156, 'group_counter': 4487, 'group_order': 1344, 'label': '84C19', 'order': 84, 'powers': [109, 91, 39], 'representative': 209, 'size': 8}
-
id: 116114242
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 157, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-19', 'order': 84, 'powers': [108, 91, 40], 'representative': 129, 'size': 8}
-
id: 116114243
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 158, 'group_counter': 4487, 'group_order': 1344, 'label': '84C25', 'order': 84, 'powers': [111, 89, 39], 'representative': 257, 'size': 8}
-
id: 116114244
{'aut_label': '84C1', 'centralizer': '8.f1.a1', 'counter': 159, 'group_counter': 4487, 'group_order': 1344, 'label': '84C-25', 'order': 84, 'powers': [110, 89, 40], 'representative': 33, 'size': 8}
-
id: 116114246
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 160, 'group_counter': 4487, 'group_order': 1344, 'label': '168A1', 'order': 168, 'powers': [142, 124, 74], 'representative': 8, 'size': 4}
-
id: 116114247
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 161, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-1', 'order': 168, 'powers': [143, 124, 75], 'representative': 904, 'size': 4}
-
id: 116114248
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 162, 'group_counter': 4487, 'group_order': 1344, 'label': '168A5', 'order': 168, 'powers': [144, 126, 76], 'representative': 40, 'size': 4}
-
id: 116114249
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 163, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-5', 'order': 168, 'powers': [145, 126, 77], 'representative': 972, 'size': 4}
-
id: 116114250
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 164, 'group_counter': 4487, 'group_order': 1344, 'label': '168A11', 'order': 168, 'powers': [146, 128, 76], 'representative': 88, 'size': 4}
-
id: 116114251
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 165, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-11', 'order': 168, 'powers': [147, 128, 77], 'representative': 204, 'size': 4}
-
id: 116114252
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 166, 'group_counter': 4487, 'group_order': 1344, 'label': '168A13', 'order': 168, 'powers': [142, 129, 77], 'representative': 12, 'size': 4}
-
id: 116114253
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 167, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-13', 'order': 168, 'powers': [143, 129, 76], 'representative': 1000, 'size': 4}
-
id: 116114254
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 168, 'group_counter': 4487, 'group_order': 1344, 'label': '168A17', 'order': 168, 'powers': [146, 131, 75], 'representative': 136, 'size': 4}
-
id: 116114255
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 169, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-17', 'order': 168, 'powers': [147, 131, 74], 'representative': 584, 'size': 4}
-
id: 116114257
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 170, 'group_counter': 4487, 'group_order': 1344, 'label': '168A19', 'order': 168, 'powers': [145, 132, 77], 'representative': 152, 'size': 4}
-
id: 116114258
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 171, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-19', 'order': 168, 'powers': [144, 132, 76], 'representative': 1192, 'size': 4}
-
id: 116114259
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 172, 'group_counter': 4487, 'group_order': 1344, 'label': '168A23', 'order': 168, 'powers': [144, 133, 75], 'representative': 712, 'size': 4}
-
id: 116114260
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 173, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-23', 'order': 168, 'powers': [145, 133, 74], 'representative': 1160, 'size': 4}
-
id: 116114261
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 174, 'group_counter': 4487, 'group_order': 1344, 'label': '168A25', 'order': 168, 'powers': [147, 134, 74], 'representative': 200, 'size': 4}
-
id: 116114262
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 175, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-25', 'order': 168, 'powers': [146, 134, 75], 'representative': 1096, 'size': 4}
-
id: 116114263
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 176, 'group_counter': 4487, 'group_order': 1344, 'label': '168A29', 'order': 168, 'powers': [143, 135, 76], 'representative': 232, 'size': 4}
-
id: 116114264
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 177, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-29', 'order': 168, 'powers': [142, 135, 77], 'representative': 780, 'size': 4}
-
id: 116114265
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 178, 'group_counter': 4487, 'group_order': 1344, 'label': '168A41', 'order': 168, 'powers': [143, 130, 75], 'representative': 328, 'size': 4}
-
id: 116114266
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 179, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-41', 'order': 168, 'powers': [142, 130, 74], 'representative': 776, 'size': 4}
-
id: 116114268
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 180, 'group_counter': 4487, 'group_order': 1344, 'label': '168A47', 'order': 168, 'powers': [144, 127, 75], 'representative': 44, 'size': 4}
-
id: 116114269
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 181, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-47', 'order': 168, 'powers': [145, 127, 74], 'representative': 968, 'size': 4}
-
id: 116114270
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 182, 'group_counter': 4487, 'group_order': 1344, 'label': '168A53', 'order': 168, 'powers': [146, 125, 76], 'representative': 424, 'size': 4}
-
id: 116114271
{'aut_label': '168A1', 'centralizer': '4.f1.a1', 'counter': 183, 'group_counter': 4487, 'group_order': 1344, 'label': '168A-53', 'order': 168, 'powers': [147, 125, 77], 'representative': 588, 'size': 4}
-
gps_qchar • Show schema
Hide schema
-
id: 5818448
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1a', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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}
-
id: 5818459
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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}
-
id: 5818470
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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}
-
id: 5818481
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5818492
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5818494
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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}
-
id: 5818495
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 5818496
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5818497
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818449
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, -1, 2, 2, -2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818450
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, -1, 2, 2, -2, 2, 2, 2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818451
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, -1, 2, 2, 2, -2, -2, -2, 2, 2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818452
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818453
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -2, -2, -2, -2, -2, -2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818454
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -2, 2, 2, 2, 2, 2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818455
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818456
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, -2, -2, 0, -2, -2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818457
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 2, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818458
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818460
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2d', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818461
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 4, -4, 4, -4, -4, -4, 4, -4, 4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818462
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2f', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -2, -2, -4, -4, 0, -4, -4, 4, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818463
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2g', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -2, -2, -4, -4, 0, 4, 4, -4, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818464
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2h', 'multiplicity': 2, 'nt': [24, 4], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -2, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 4, 4, 4, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, -4, -4, 4, -4, 4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818465
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2i', 'multiplicity': 2, 'nt': [24, 4], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, -2, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 4, 4, 4, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, -4, 4, 4, -4, -4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818483
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, -4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818466
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2j', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -1, -1, -1, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 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, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 5818467
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2k', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 6, 6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -6, -6, -6, -6, -1, -1, -1, 6, 6, 0, 0, 6, 6, 6, 6, -6, -6, 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, 1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5818468
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2l', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -6, -6, -6, -6, -1, -1, -1, -6, -6, 0, 0, 6, 6, 6, 6, 6, 6, 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, 1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 5818469
{'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2m', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -1, -1, -1, -6, -6, 0, 0, 6, 6, 6, 6, -6, -6, 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, -1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5818471
{'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2n', 'multiplicity': 4, 'nt': [16, 44], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -8, -8, -8, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, 8, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -8, -8, -8, -8, 8, -8, -8, 8, -8, 8, 8, 8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818472
{'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2o', 'multiplicity': 4, 'nt': [24, 17], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, -4, -4, 8, -8, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 8, -8, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, -4, 4, 4, -4, 4, -4, 4, 4, 4, -4, 4, -4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818484
{'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4b', 'multiplicity': 2, 'nt': [24, 114], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -8, -8, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818473
{'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2p', 'multiplicity': 6, 'nt': [21, 3], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, -6, -6, 12, 12, 12, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -2, -2, -2, 12, 12, 0, 0, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -6, -6, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818474
{'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2q', 'multiplicity': 6, 'nt': [42, 9], 'qdim': 12, 'qvalues': [12, 12, 12, 12, -12, -12, -6, -6, 12, 12, -12, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, 6, 6, 6, 6, -2, -2, -2, 12, 12, 0, 0, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, -6, -6, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 5818475
{'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2r', 'multiplicity': 6, 'nt': [42, 9], 'qdim': 12, 'qvalues': [12, 12, 12, 12, -12, -12, -6, -6, 12, 12, 12, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, 6, 6, 6, 6, -2, -2, -2, -12, -12, 0, 0, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818476
{'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2s', 'multiplicity': 6, 'nt': [42, 9], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, -6, -6, 12, 12, -12, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -2, -2, -2, -12, -12, 0, 0, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 5818477
{'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2t', 'multiplicity': 6, 'nt': [56, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, -12, 12, 12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, 12, 12, -12, -12, 12, -12, 12, -2, -2, -2, 0, 0, 0, 0, 12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818478
{'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2u', 'multiplicity': 6, 'nt': [56, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 12, -12, 12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, 12, 12, -12, 12, -12, 12, -12, -2, -2, -2, 0, 0, 0, 0, 12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818485
{'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4c', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 12, 12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818486
{'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4d', 'multiplicity': 3, 'nt': [56, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, 12, 12, -12, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818479
{'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2v', 'multiplicity': 8, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 8, 8, 8, 0, 0, 0, 0, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -16, -16, -16, 16, -16, 16, -16, -16, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 8, 8, 8, 8, -8, 8, 8, -8, 8, -8, -8, -8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818480
{'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2w', 'multiplicity': 12, 'nt': [168, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, -24, 24, -12, -12, -24, 24, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, -12, -12, 12, 12, -12, 12, -12, -4, -4, -4, 0, 0, 0, 0, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, -4, 4, -4, 4, 4, -4, -4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818482
{'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.2x', 'multiplicity': 12, 'nt': [168, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, 24, -24, -12, -12, -24, 24, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, -12, -12, 12, -12, 12, -12, 12, -4, -4, -4, 0, 0, 0, 0, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, -4, -4, 4, -4, -4, 4, 4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818487
{'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4e', 'multiplicity': 6, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, 24, -24, -24, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 24, -24, -24, -24, 24, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, 4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818488
{'cdim': 4, 'counter': 46, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4f', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, 24, 24, 0, 0, -12, -12, -24, -24, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -12, -12, -12, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818489
{'cdim': 4, 'counter': 47, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4g', 'multiplicity': 6, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -24, 24, -24, -24, -24, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, 4, 4, 4, -4, 4, 4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818490
{'cdim': 4, 'counter': 48, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4h', 'multiplicity': 6, 'nt': [168, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, 0, 0, -12, -12, 24, -24, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, -12, -12, 12, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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id: 5818491
{'cdim': 4, 'counter': 49, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4i', 'multiplicity': 12, 'nt': [168, 0], 'qdim': 48, 'qvalues': [48, 48, -48, -48, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -24, 24, 24, 24, -24, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 8, 8, -8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, -4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 5818493
{'cdim': 4, 'counter': 50, 'faithful': False, 'group': '1344.4487', 'group_order': 1344, 'image': None, 'label': '1344.4487.4j', 'multiplicity': 12, 'nt': [336, 0], 'qdim': 48, 'qvalues': [48, -48, 48, -48, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 24, -24, 24, 24, 24, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 8, 8, -8, 8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, -4, -4, 4, -4, -4, 4, -4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
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gps_char • Show schema
Hide schema
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id: 11774162
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id: 11774257
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id: 11774268
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id: 11774279
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id: 11774290
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id: 11774301
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id: 11774312
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id: 11774323
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id: 11774334
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id: 11774163
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id: 11774174
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id: 11774185
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id: 11774196
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id: 11774207
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.4487', 'group_counter': 4487, 'group_order': 1344, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.f1.a1', 'kernel_order': 224, 'label': '1344.4487.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]]]}
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id: 11774218
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id: 11774229
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id: 11774240
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id: 11774251
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id: 11774256
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id: 11774258
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id: 11774259
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id: 11774260
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id: 11774261
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id: 11774262
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id: 11774263
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id: 11774264
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id: 11774265
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id: 11774266
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id: 11774267
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id: 11774269
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id: 11774270
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id: 11774271
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id: 11774272
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id: 11774273
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id: 11774274
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id: 11774275
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id: 11774276
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id: 11774277
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id: 11774278
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id: 11774280
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id: 11774281
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id: 11774282
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id: 11774283
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id: 11774284
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id: 11774285
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id: 11774286
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id: 11774287
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id: 11774288
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id: 11774289
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id: 11774291
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id: 11774292
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id: 11774293
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id: 11774294
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id: 11774295
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id: 11774296
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id: 11774297
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id: 11774298
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id: 11774299
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id: 11774300
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id: 11774302
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 60, 'cyclotomic_n': 21, 'dim': 2, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.4487', 'group_counter': 4487, 'group_order': 1344, 'image': None, 'image_isoclass': '42.4', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.a1', 'kernel_order': 32, 'label': '1344.4487.2p2', 'nt': [21, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 7]], [[2, -7]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -7]], [[2, -7]], [[2, 7]], [[2, 7]], [[2, -7]], [[2, 7]], [[2, 7]], [[2, -7]], [[2, -7]], [[2, 7]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -7]], [[2, 7]], [[2, -7]], [[2, 7]], [[2, 7]], [[2, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 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id: 11774303
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id: 11774304
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id: 11774305
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id: 11774306
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id: 11774307
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id: 11774308
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id: 11774309
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id: 11774310
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id: 11774311
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id: 11774313
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id: 11774314
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id: 11774315
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id: 11774316
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id: 11774317
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id: 11774318
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id: 11774319
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id: 11774320
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id: 11774321
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id: 11774322
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id: 11774324
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id: 11774325
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id: 11774326
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id: 11774327
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id: 11774328
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id: 11774329
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id: 11774330
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id: 11774331
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id: 11774332
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id: 11774333
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id: 11774335
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id: 11774336
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id: 11774337
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id: 11774338
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id: 11774339
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id: 11774340
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id: 11774341
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id: 11774342
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id: 11774343
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id: 11774344
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id: 11774164
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id: 11774165
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id: 11774166
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id: 11774167
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id: 11774177
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-
id: 11774178
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id: 11774179
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id: 11774168
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id: 11774169
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id: 11774170
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id: 11774171
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id: 11774172
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id: 11774173
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id: 11774175
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id: 11774176
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id: 11774180
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id: 11774190
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id: 11774191
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id: 11774192
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-
id: 11774181
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id: 11774182
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-
id: 11774183
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id: 11774184
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id: 11774186
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id: 11774187
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id: 11774188
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id: 11774189
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id: 11774193
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id: 11774194
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id: 11774195
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id: 11774197
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id: 11774198
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id: 11774199
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id: 11774200
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id: 11774201
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id: 11774202
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id: 11774203
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id: 11774204
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id: 11774205
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id: 11774206
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id: 11774208
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id: 11774209
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id: 11774210
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id: 11774211
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id: 11774212
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id: 11774213
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id: 11774214
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id: 11774215
{'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 147, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.4487', 'group_counter': 4487, 'group_order': 1344, 'image': None, 'image_isoclass': '336.178', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.4487.4f6', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 7]], [[4, -7]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -7]], [[4, -7]], [[4, 7]], [[4, 7]], [[4, -7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -7]], [[-4, 7]], [[-4, -7]], [[-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 2], [2, 3], [-2, 5], [2, 7], [2, 10], [-2, -10]], [[2, 4], [2, 10]], [[2, 2], [2, 5]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 4], [-2, 5], [2, 6], [-2, 8], [-2, -10]], [[-2, 3], [-2, 10], [2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 5], [-2, 6], [-2, 7], [2, 8], [-2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 2], [2, 3], [-2, 5], [2, 7], [2, 10], [-2, -10]], [[2, 2], [2, 5]], [[-2, 3], [-2, 10], [2, -10]], [[2, 2], [2, 5]], [[2, 2], [2, 5]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 4], [-2, 5], [2, 6], [-2, 8], [-2, -10]], [[2, 0], [-2, 2], [2, 3], [-2, 5], [2, 7], [2, 10], [-2, -10]], [[-2, 3], [-2, 10], [2, -10]], [[2, 4], [2, 10]], [[2, 4], [2, 10]], [[2, 0], [-2, 2], [2, 3], [-2, 5], [2, 7], [2, 10], [-2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 5], [-2, 6], [-2, 7], [2, 8], [-2, 10], [2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 5], [-2, 6], [-2, 7], [2, 8], [-2, 10], [2, -10]], [[2, 4], [2, 10]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 4], [-2, 5], [2, 6], [-2, 8], [-2, -10]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 4], [-2, 5], [2, 6], [-2, 8], [-2, -10]], [[-2, 3], [-2, 10], [2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 5], [-2, 6], [-2, 7], [2, 8], [-2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 5], [2, 6], [2, 7], [-2, 8], [2, 10], [-2, -10]], [[-2, 0], [2, 2], [-2, 3], [2, 5], [-2, 7], [-2, 10], [2, -10]], [[-2, 4], [-2, 10]], [[-2, 4], [-2, 10]], [[-2, 2], [-2, 5]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 5], [2, 6], [2, 7], [-2, 8], [2, 10], [-2, -10]], [[-2, 0], [2, 2], [-2, 3], [2, 5], [-2, 7], [-2, 10], [2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 4], [2, 5], [-2, 6], [2, 8], [2, -10]], [[2, 3], [2, 10], [-2, -10]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 4], [2, 5], [-2, 6], [2, 8], [2, -10]], [[-2, 2], [-2, 5]], [[2, 3], [2, 10], [-2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 11774216
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id: 11774217
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id: 11774219
{'center': '112.a1.a1', 'center_index': 112, 'center_order': 12, 'counter': 150, 'cyclotomic_n': 56, 'dim': 4, 'faithful': False, 'field': [-8, 0, 24, 0, -10, 0, 1], 'group': '1344.4487', 'group_counter': 4487, 'group_order': 1344, 'image': None, 'image_isoclass': '224.107', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.4487.4g3', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[-2, 7], [-2, -7]], [[2, 7], [2, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[-2, 8], [-2, -8]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[-2, 4], [-2, -4]], [[2, 12], [2, -12]], [[-2, 12], [-2, -12]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[-2, 12], [-2, -12]], [[2, 8], [2, -8]], [[2, 8], [2, -8]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[-2, 7], [-2, -7]], [[-2, 7], [-2, -7]], [[2, 7], [2, -7]], [[2, 7], [2, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 8], [2, -8]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[-2, 8], [-2, -8]], [[-2, 8], [-2, -8]], [[2, 4], [2, -4]], [[-2, 12], [-2, -12]], [[2, 12], [2, -12]], [[2, 12], [2, -12]], [[-2, 4], [-2, -4]], [[2, 4], [2, -4]], [[-2, 4], [-2, -4]], [[-2, 12], [-2, -12]], [[2, 8], [2, -8]], [[-2, 8], [-2, -8]], [[2, 12], [2, -12]], [[2, 4], [2, -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, 5], [1, 9], [-1, 19], [1, 23]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[1, 5], [-1, 9], [1, 19], [-1, 23]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [1, 23]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[1, 5], [-1, 9], [1, 19], [-1, 23]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-1, 9], [1, 19], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [-1, 23]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [-1, 23]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [1, 23]], [[-1, 1], [-1, 3], [1, 7], [-1, 11], [1, 13], [-1, 19], [1, 23]], [[1, 1], [1, 3], [-1, 7], [1, 11], [-1, 13], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [1, 23]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[-1, 1], [-1, 3], [1, 5], [-1, 9], [-1, 11], [1, 13], [1, 21]], [[1, 1], [1, 3], [-1, 5], [1, 9], [1, 11], [-1, 13], [-1, 21]], [[-1, 5], [1, 9], [-1, 19], [1, 23]]]}
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id: 11774220
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id: 11774221
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id: 11774222
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id: 11774223
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id: 11774224
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id: 11774225
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id: 11774226
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id: 11774227
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id: 11774228
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id: 11774230
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id: 11774239
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id: 11774241
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id: 11774242
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-
id: 11774231
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id: 11774232
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-
id: 11774233
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id: 11774234
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id: 11774235
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id: 11774236
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id: 11774237
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id: 11774238
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id: 11774243
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-
id: 11774253
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id: 11774254
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id: 11774255
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id: 11774244
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id: 11774245
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id: 11774246
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id: 11774247
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id: 11774248
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id: 11774249
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id: 11774250
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-
id: 11774252
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gps_subgroup_search • Show schema
Hide schema
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id: 72661038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.4487.1.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': '1344.4487', 'subgroup_hash': 4487, 'subgroup_order': 1344, 'subgroup_tex': 'C_{28}.(C_6\\times Q_8)', 'supersolvable': True, 'sylow': 0}
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id: 72661149
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.266', 'subgroup_hash': 266, 'subgroup_order': 672, 'subgroup_tex': 'D_4:C_{84}', 'supersolvable': True, 'sylow': 0}
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id: 72661165
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.827', 'subgroup_hash': 827, 'subgroup_order': 672, 'subgroup_tex': 'C_7:C_{12}\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 72661176
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.171', 'subgroup_hash': 171, 'subgroup_order': 672, 'subgroup_tex': 'C_{42}.D_8', 'supersolvable': True, 'sylow': 0}
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id: 72661187
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.783', 'subgroup_hash': 783, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.Q_8', 'supersolvable': True, 'sylow': 0}
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id: 72661198
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.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': '672.147', 'subgroup_hash': 147, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.Q_8', 'supersolvable': True, 'sylow': 0}
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id: 72661209
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.153', 'subgroup_hash': 153, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.D_4', 'supersolvable': True, 'sylow': 0}
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id: 72661220
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.157', 'subgroup_hash': 157, 'subgroup_order': 672, 'subgroup_tex': 'C_{168}:C_4', 'supersolvable': True, 'sylow': 0}
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id: 72661231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 448, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 14, 'label': '1344.4487.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '448.300', 'subgroup_hash': 300, 'subgroup_order': 448, 'subgroup_tex': '(C_2\\times C_8).D_{14}', 'supersolvable': True, 'sylow': 0}
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id: 72661039
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.205', 'subgroup_hash': 205, 'subgroup_order': 336, 'subgroup_tex': 'D_4\\times C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.108', 'subgroup_hash': 108, 'subgroup_order': 336, 'subgroup_tex': 'C_4:C_{84}', 'supersolvable': True, 'sylow': 0}
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id: 72661061
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 336, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.65', 'subgroup_hash': 65, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661072
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.67', 'subgroup_hash': 67, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661083
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.67', 'subgroup_hash': 67, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661094
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.109', 'subgroup_hash': 109, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{168}', 'supersolvable': True, 'sylow': 0}
-
id: 72661105
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 336, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.63', 'subgroup_hash': 63, 'subgroup_order': 336, 'subgroup_tex': 'C_{14}:C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 72661116
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 168, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.182', 'subgroup_hash': 182, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 72661127
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.73', 'subgroup_hash': 73, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661138
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.67', 'subgroup_hash': 67, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.66', 'subgroup_hash': 66, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661156
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 224, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '224.51', 'subgroup_hash': 51, 'subgroup_order': 224, 'subgroup_tex': 'D_4:C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661157
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '224.129', 'subgroup_hash': 129, 'subgroup_order': 224, 'subgroup_tex': 'C_2^3.D_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661158
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '224.38', 'subgroup_hash': 38, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}.D_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.85', 'subgroup_hash': 85, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661160
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.14', 'subgroup_hash': 14, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661161
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 224, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.20', 'subgroup_hash': 20, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.24', 'subgroup_hash': 24, 'subgroup_order': 224, 'subgroup_tex': 'C_{56}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661163
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.4487.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7.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': 7, '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': '192.911', 'subgroup_hash': 911, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times D_4.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661164
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 168, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 72661166
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 168, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661167
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 168, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661168
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 168, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
-
id: 72661169
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 168, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
-
id: 72661170
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 84, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.57', 'subgroup_hash': 57, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661171
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 84, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 72661172
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661173
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661174
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661175
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 84, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
-
id: 72661178
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 84, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
-
id: 72661179
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.4', 'subgroup_hash': 4, 'subgroup_order': 168, 'subgroup_tex': 'C_7:C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 72661180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 112, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661181
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 112, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.21', 'subgroup_hash': 21, 'subgroup_order': 112, 'subgroup_tex': 'C_4:C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661182
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.10', 'subgroup_hash': 10, 'subgroup_order': 112, 'subgroup_tex': 'C_{28}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661183
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.12', 'subgroup_hash': 12, 'subgroup_order': 112, 'subgroup_tex': 'C_{28}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661184
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.12', 'subgroup_hash': 12, 'subgroup_order': 112, 'subgroup_tex': 'C_{28}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661185
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 112, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
-
id: 72661186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.8', 'subgroup_hash': 8, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661188
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.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': 12, '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': '112.35', 'subgroup_hash': 35, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2.D_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661189
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.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': 12, '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': '112.18', 'subgroup_hash': 18, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661190
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.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': 12, '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': '112.12', 'subgroup_hash': 12, 'subgroup_order': 112, 'subgroup_tex': 'C_{28}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.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': 12, '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': '112.11', 'subgroup_hash': 11, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 96, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.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': 14, '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': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.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': 14, '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': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1.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': 14, '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': '96.172', 'subgroup_hash': 172, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661196
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.e1.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': 14, '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': '96.56', 'subgroup_hash': 56, 'subgroup_order': 96, 'subgroup_tex': 'C_8:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.f1.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': 14, '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': '96.55', 'subgroup_hash': 55, 'subgroup_order': 96, 'subgroup_tex': 'C_4:C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 72661199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.14.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.g1.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': 14, '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': '96.57', 'subgroup_hash': 57, 'subgroup_order': 96, 'subgroup_tex': 'C_8:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661200
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 84, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661201
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 72661202
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 72661203
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661204
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 42, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661205
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661206
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661207
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661208
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 72661210
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661211
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661212
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 72661213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.4487.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.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': 21, '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': '64.159', 'subgroup_hash': 159, 'subgroup_order': 64, 'subgroup_tex': 'D_4.Q_8', 'supersolvable': True, 'sylow': 2}
-
id: 72661214
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 56, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661215
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 56, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661216
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 56, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661218
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 56, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661219
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661221
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661222
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661223
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661224
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661225
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661226
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 28, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661227
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 28, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
-
id: 72661228
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
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id: 72661229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 48, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 72661230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 48, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661232
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 48, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
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id: 72661233
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.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': 28, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661234
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.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': 28, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661235
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1.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': 28, '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': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661236
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.g1.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': 28, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.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': 28, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661238
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.i1.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': 28, '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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
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id: 72661239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.j1.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': 28, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.k1.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': 28, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 72661241
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 42, 'counter': 99, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661040
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 42, 'counter': 100, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661041
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 42, 'counter': 101, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661042
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.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': 32, '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': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661043
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.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': 32, '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': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 72661044
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 32, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '42.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
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id: 72661045
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, '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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.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': 42, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1.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': 42, '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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1.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': 42, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f1.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': 42, '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.42.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1.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': 42, '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': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661052
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661053
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 112, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661054
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 113, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661055
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661056
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 14, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661057
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661058
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 14, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661059
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661060
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 72661062
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661063
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661064
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661065
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 24, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661066
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661067
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.56.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661068
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.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': 56, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661069
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661070
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661071
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661073
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.g1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661074
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661075
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.i1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661076
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.i1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661077
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.j1.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': 56, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661078
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.56.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.k1.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': 56, '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 72661079
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.56.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.l1.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': 56, '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 72661080
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 21, 'counter': 137, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.4487.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.159', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 159, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4.Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
-
id: 72661081
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661082
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661084
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661085
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661087
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 72661088
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661089
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661090
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661091
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661093
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 149, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661095
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 150, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 182, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661096
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 151, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.169', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 169, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661097
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.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': 96, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661098
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.96.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.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': 96, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 72661099
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 12, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661100
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 12, 'counter': 155, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661101
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 12, 'counter': 156, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661102
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1.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': 112, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661103
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661104
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.f1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661106
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661107
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.h1.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': 112, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661108
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 6, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.i1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661109
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.112.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 72661110
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.k1.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': 112, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661111
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.112.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.k1.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': 112, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661112
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 8, 'counter': 166, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.54', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{21}:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{21}:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661115
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.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': 168, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 72661117
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661118
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661119
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661120
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661121
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661122
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661123
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661124
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.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': 168, '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': 0}
-
id: 72661125
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.k1.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': 168, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661126
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.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': 168, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 72661128
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 180, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.4487.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.911', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 911, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4.Q_8', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
-
id: 72661129
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 6, 'counter': 181, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.109', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661130
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 6, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.107', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 107, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661131
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 6, 'counter': 183, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.73', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 73, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661132
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.d1.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': 224, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661133
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 185, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.224.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.d1.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': 224, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 72661134
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.4487.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.178', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 178, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 72661135
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 187, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.179', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 179, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661136
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 188, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.174', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 174, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{42}:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661137
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.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': 336, '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}
-
id: 72661139
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661140
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.f1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661141
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.g1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661142
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.h1.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': 336, '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}
-
id: 72661143
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661144
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 72661145
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1.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': 336, '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}
-
id: 72661146
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.4487.336.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1.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': 336, '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}
-
id: 72661147
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 3, 'counter': 198, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '1344.4487.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '448.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '448.300', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 300, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2\\times C_8).D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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id: 72661148
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 199, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.807', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 807, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 72661151
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 200, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.805', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 805, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}.D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 72661152
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 201, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.4487.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.771', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 771, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2\\times C_{42}):Q_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 72661153
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.d1.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': 672, '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: 72661154
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.4487.672.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.d1.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': 672, '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: 72661155
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.4487', 'ambient_counter': 4487, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(C_6\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.4487.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1344.4487', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4487, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{28}.(C_6\\times Q_8)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 72661126
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.l1.a1', '84.i1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8596, -1, 8893, -1, 8941, -1, 8794, -1], 'generators': [3], 'label': '1344.4487.168.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.e1.a1', 'old_label': '168.l1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661144
{'ambient': '1344.4487', 'aut_centralizer_order': 768, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.j1.a1', '168.f1.a1'], 'contains': ['672.b1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [751, -1, 4291, -1, 4534, -1, 3242, -1], 'generators': [367], 'label': '1344.4487.336.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '336.j1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661038
{'ambient': '1344.4487', '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': '112.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 4063, 7912, 4621, 7042, 4210, 7369, 5831], 'generators': [1, 676, 672, 168, 1008, 192, 2, 448], 'label': '1344.4487.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '112.31', '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': '112.31'}
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id: 72661039
{'ambient': '1344.4487', 'aut_centralizer_order': 112, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1531', 'aut_weyl_index': 112, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.j1.a1', '12.a1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7061, 470, 6023, 1056, 6699, 9008, 6753, 1064], 'generators': [841, 672, 1008, 448, 676, 192], 'label': '1344.4487.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.b1', '8.d1.a1', '12.a1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 72661040
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [378, 8871, 1895, 9094, 3707, 3179, 2981, 6427], 'generators': [676, 192, 448], 'label': '1344.4487.32.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '224.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661041
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '32.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6070, 6791, 2961, 7105, 5949, 4218, 6097, 4952], 'generators': [672, 192, 448], 'label': '1344.4487.32.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '224.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661042
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.h1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [959, -1, 1590, -1, 2628, -1, 2465, -1], 'generators': [841, 192, 448], 'label': '1344.4487.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.a1', 'projective_image': '448.300', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661043
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.h1.a1', '16.k1.b1'], 'contains': ['64.a1.a1', '96.d1.b1', '224.d1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [959, -1, 727, -1, 2628, -1, 2348, -1], 'generators': [505, 192, 448], 'label': '1344.4487.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.b1', 'projective_image': '448.300', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 72661044
{'ambient': '1344.4487', 'aut_centralizer_order': 336, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.c1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9164, 824, 9440, 1172, 8340, 8510, 8821, 2535], 'generators': [1, 168], 'label': '1344.4487.42.a1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1', '14.a1.a1'], 'normal_contains': ['84.a1.a1', '84.b1.a1', '84.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 72661045
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.e1.a1', '84.f1.a1', '84.g1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6443, -1, 6950, -1, 5062, -1, 5483, -1], 'generators': [841, 2, 1008], 'label': '1344.4487.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 72661046
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.h1.a1', '84.i1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8935, -1, 8912, -1, 8207, -1, 8481, -1], 'generators': [841, 1038], 'label': '1344.4487.42.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 72661047
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.f1.a1', '84.h1.a1', '84.j1.a1', '84.k1.a1'], 'core': '84.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5249, -1, 7819, -1, 5882, -1, 6080, -1], 'generators': [1, 1038, 1008], 'label': '1344.4487.42.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 72661048
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.g1.a1', '84.i1.a1'], 'core': '84.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8510, -1, 9301, -1, 8474, -1, 8018, -1], 'generators': [1, 2], 'label': '1344.4487.42.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661049
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.51', 'aut_weyl_index': 672, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.f1.a1', '84.i1.a1'], 'core': '84.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9517, -1, 9584, -1, 8608, -1, 8943, -1], 'generators': [3, 168], 'label': '1344.4487.42.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.f1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661050
{'ambient': '1344.4487', 'aut_centralizer_order': 112, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1531', 'aut_weyl_index': 112, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '12.b1.a1', '28.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6156, 1745, 7002, 2071, 6959, 7582, 6515, 3672], 'generators': [1, 672, 448, 192, 1008, 676], 'label': '1344.4487.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661051
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.261', 'aut_weyl_index': 336, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.g1.a1', '84.h1.a1'], 'core': '84.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8226, -1, 8404, -1, 6433, -1, 8140, -1], 'generators': [2, 168], 'label': '1344.4487.42.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.g1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661052
{'ambient': '1344.4487', 'aut_centralizer_order': 3584, 'aut_label': '48.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3499, 7740, 4502, 7639, 4088, 3698, 4040, 5948], 'generators': [676, 192, 672], 'label': '1344.4487.48.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.b1.a1', '96.c1.a1', '96.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.10', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661053
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '48.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1'], 'contains': ['96.c1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7921, 5907, 8167, 6306, 8112, 5141, 8239, 4618], 'generators': [1008, 672, 192], 'label': '1344.4487.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.c1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '672.771', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661054
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '48.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['96.c1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6529, 3918, 7385, 3886, 6836, 5867, 7542, 3212], 'generators': [340, 672, 192], 'label': '1344.4487.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.d1.b1', '24.d1.a1'], 'normal_contains': ['96.c1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '672.771', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661055
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.e1.a1', '24.i1.a1', '24.i1.a2'], 'contains': ['96.a1.a1', '96.d1.a1', '96.d1.b1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2782, -1, 1641, -1, 2183, -1, 1941, -1], 'generators': [841, 192, 4], 'label': '1344.4487.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.d1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661056
{'ambient': '1344.4487', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 256, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.b1.a1', '24.i1.a1', '24.i1.a2'], 'contains': ['96.a1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3158, -1, 811, -1, 1671, -1, 1351, -1], 'generators': [703, 192, 4], 'label': '1344.4487.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.e1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661057
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 256, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.g1.a1', '24.i1.a1', '24.i1.a2'], 'contains': ['96.a1.a1', '336.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3300, -1, 1052, -1, 1538, -1, 1473, -1], 'generators': [2, 192, 4], 'label': '1344.4487.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.f1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661058
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 256, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.h1.a1'], 'contains': ['96.a1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1211, -1, 1457, -1, 2497, -1, 2228, -1], 'generators': [1038, 192, 4], 'label': '1344.4487.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.g1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661059
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.e1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.d1.b1', '336.h1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1880, -1, 3457, -1, 3404, -1, 2814, -1], 'generators': [841, 192, 676], 'label': '1344.4487.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.h1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661060
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '336.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [222, -1, 5038, -1, 5166, -1, 4324, -1], 'generators': [1, 676, 192], 'label': '1344.4487.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.i1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661061
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.c1.a1', '28.f1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4996, 8620, 5766, 8870, 5319, 363, 5134, 9665], 'generators': [367, 192, 448, 676, 1008, 672], 'label': '1344.4487.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661062
{'ambient': '1344.4487', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 256, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.c1.a1'], 'contains': ['96.b1.a1', '336.j1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [773, -1, 4800, -1, 4599, -1, 3218, -1], 'generators': [367, 192, 676], 'label': '1344.4487.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '48.j1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661063
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.d1.a1', '24.e1.a1', '24.j1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '336.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6842, -1, 5728, -1, 6132, -1, 6482, -1], 'generators': [841, 192, 672], 'label': '1344.4487.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661064
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.d1.b1', '24.e1.a1', '24.j1.a1'], 'contains': ['96.c1.a1', '96.d1.b1', '336.k1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6842, -1, 5438, -1, 6132, -1, 6265, -1], 'generators': [505, 192, 672], 'label': '1344.4487.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.k1.b1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661065
{'ambient': '1344.4487', 'aut_centralizer_order': 5376, 'aut_label': '56.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.f1.a1', '28.g1.a1', '28.h1.a1', '28.i1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6129, 5372, 6592, 4869, 7102, 6328, 6547, 4284], 'generators': [676, 1008, 448, 672], 'label': '1344.4487.56.a1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661066
{'ambient': '1344.4487', 'aut_centralizer_order': 672, 'aut_label': '56.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.a1.a1'], 'contains': ['112.c1.a1', '112.k1.a1', '168.b1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7011, 1570, 6321, 1748, 6555, 9033, 7357, 426], 'generators': [841, 340, 448, 672], 'label': '1344.4487.56.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.d1.a1', '28.a1.a1'], 'normal_contains': ['112.c1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661067
{'ambient': '1344.4487', 'aut_centralizer_order': 672, 'aut_label': '56.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '28.a1.a1'], 'contains': ['112.c1.a1', '112.k1.b1', '168.b1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7011, 1570, 5795, 279, 6555, 9033, 6992, 1467], 'generators': [505, 340, 448, 672], 'label': '1344.4487.56.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.b1.b1', 'normal_contained_in': ['8.d1.b1', '28.a1.a1'], 'normal_contains': ['112.c1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.b1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661068
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.a1.a1', '28.d1.a1', '28.e1.a1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.h1.a1', '112.k1.a1', '112.k1.b1', '168.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4329, -1, 3080, -1, 2971, -1, 3379, -1], 'generators': [841, 676, 672, 448], 'label': '1344.4487.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '56.c1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661069
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.b1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.i1.a1', '168.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1065, -1, 4366, -1, 5339, -1, 4977, -1], 'generators': [1, 672, 448, 676], 'label': '1344.4487.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '56.d1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661070
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.d1.a1', '28.f1.a1', '28.j1.a1'], 'contains': ['112.a1.a1', '112.e1.a1', '168.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2650, -1, 2395, -1, 2016, -1, 2513, -1], 'generators': [703, 672, 448, 4], 'label': '1344.4487.56.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.e1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661071
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.e1.a1', '28.f1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.j1.a1', '168.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1749, -1, 3966, -1, 4732, -1, 4171, -1], 'generators': [367, 672, 448, 676], 'label': '1344.4487.56.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.f1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661072
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 16, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '12.d1.a1', '28.g1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5854, 7651, 6391, 5645, 4796, 6073, 5613, 8297], 'generators': [2, 192, 448, 4, 1008, 672], 'label': '1344.4487.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661073
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.d1.a1', '28.e1.a1', '28.g1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '168.g1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4638, -1, 2161, -1, 1551, -1, 2296, -1], 'generators': [2, 672, 448, 4], 'label': '1344.4487.56.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.g1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661074
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '56.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.h1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.g1.a1', '168.h1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1318, -1, 2795, -1, 3874, -1, 4761, -1], 'generators': [1038, 672, 448, 4], 'label': '1344.4487.56.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.h1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661075
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.d1.a1'], 'contains': ['112.d1.a1', '112.e1.a1', '112.f1.a1', '168.i1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3670, -1, 470, -1, 105, -1, 313, -1], 'generators': [841, 2, 448, 4], 'label': '1344.4487.56.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '56.i1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661076
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a2', '28.d1.a1'], 'contains': ['112.d1.a1', '112.e1.a1', '112.f1.a1', '168.i1.a2'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3670, -1, 180, -1, 105, -1, 96, -1], 'generators': [169, 2, 448, 4], 'label': '1344.4487.56.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '56.i1.a2', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661077
{'ambient': '1344.4487', 'aut_centralizer_order': 672, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.a1.a1'], 'contains': ['112.b1.a1', '112.k1.a1', '112.k1.b1', '168.j1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7637, -1, 5184, -1, 7891, -1, 7175, -1], 'generators': [841, 1008, 448, 672], 'label': '1344.4487.56.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '56.j1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661078
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.c1.a1'], 'contains': ['112.b1.a1', '168.k1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9823, -1, 8844, -1, 8785, -1, 9167, -1], 'generators': [168, 448, 336, 672], 'label': '1344.4487.56.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '56.k1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661079
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '28.i1.a1'], 'contains': ['112.b1.a1', '168.l1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8484, -1, 8608, -1, 9182, -1, 8869, -1], 'generators': [3, 448, 1008, 672], 'label': '1344.4487.56.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.e1.a1', 'old_label': '56.l1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661080
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '2.a1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.b1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [585, 9165, 1142, 8827, 3303, 3179, 2580, 6180], 'generators': [448, 192], 'label': '1344.4487.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.c1.a1', '32.a1.a1'], 'normal_contains': ['192.a1.a1', '448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '448.300', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.9', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661081
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '84.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.a1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1', '168.c1.a1', '168.j1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7922, 750, 7878, 812, 7320, 8456, 7657, 2509], 'generators': [841, 676, 1008], 'label': '1344.4487.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.a1.a1', '28.a1.a1', '42.a1.a1'], 'normal_contains': ['168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661082
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '84.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.b1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.a1'], 'core': '84.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5717, 2463, 8278, 2342, 7724, 7417, 6839, 3797], 'generators': [1, 1008], 'label': '1344.4487.84.b1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.b1.a1', 'normal_contained_in': ['12.b1.a1', '28.b1.a1', '42.a1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661083
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 16, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '12.e1.a1', '28.h1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5554, 6492, 6724, 7007, 6023, 2177, 6092, 4409], 'generators': [1038, 192, 448, 4, 1008, 672], 'label': '1344.4487.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661084
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '84.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.c1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.k1.a1'], 'core': '84.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9581, 3103, 9372, 3264, 8290, 6947, 9018, 3364], 'generators': [676, 168], 'label': '1344.4487.84.c1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.c1.a1', 'normal_contained_in': ['12.f1.a1', '28.c1.a1', '42.a1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '336.178', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.2', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661085
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.d1.a1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.e1.a1', '168.g1.a1', '168.i1.a1', '168.i1.a2'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4790, -1, 2959, -1, 1783, -1, 2726, -1], 'generators': [841, 2, 672], 'label': '1344.4487.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.d1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661086
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.e1.a1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.f1.a1', '168.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4353, -1, 4712, -1, 3436, -1, 4355, -1], 'generators': [505, 2], 'label': '1344.4487.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.e1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661087
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.f1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.e1.a1', '168.f1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5210, -1, 7319, -1, 6261, -1, 5826, -1], 'generators': [367, 1008], 'label': '1344.4487.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.f1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661088
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.g1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.g1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7265, -1, 7139, -1, 6135, -1, 6377, -1], 'generators': [2, 1008], 'label': '1344.4487.84.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.g1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661089
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1344, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.h1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.h1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5860, -1, 7604, -1, 6388, -1, 6717, -1], 'generators': [1038, 1008], 'label': '1344.4487.84.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.h1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661090
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2688, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.i1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.l1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8846, -1, 9100, -1, 8615, -1, 8720, -1], 'generators': [3, 676], 'label': '1344.4487.84.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.i1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661091
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.j1.a1', '42.d1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.h1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2831, -1, 5079, -1, 4303, -1, 5370, -1], 'generators': [1009, 1038], 'label': '1344.4487.84.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '84.j1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661092
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.k1.a1', '42.d1.a1'], 'contains': ['168.d1.a1', '168.f1.a1', '168.h1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2335, -1, 6372, -1, 5763, -1, 5710, -1], 'generators': [1, 1038], 'label': '1344.4487.84.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '84.k1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661093
{'ambient': '1344.4487', 'aut_centralizer_order': 3584, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3127, 9480, 1372, 8388, 2289, 2816, 2038, 6788], 'generators': [4, 192], 'label': '1344.4487.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '672.807', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.26', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661094
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.231', 'aut_weyl_index': 224, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '12.f1.a1', '28.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9598, 2848, 9385, 2926, 9185, 6827, 9373, 2976], 'generators': [676, 672, 448, 192, 168, 336], 'label': '1344.4487.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.f1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '112.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661095
{'ambient': '1344.4487', 'aut_centralizer_order': 3584, 'aut_label': '96.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1290, 8596, 4021, 9183, 3964, 3838, 3135, 5846], 'generators': [676, 192], 'label': '1344.4487.96.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '672.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '672.805', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.25', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661096
{'ambient': '1344.4487', 'aut_centralizer_order': 3584, 'aut_label': '96.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.k1.a1', '48.k1.b1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6424, 6572, 5453, 7082, 6077, 4498, 6269, 4926], 'generators': [672, 192], 'label': '1344.4487.96.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['32.c1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '672.771', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.21', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661097
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.d1.a1', '48.h1.a1', '48.k1.a1'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1970, -1, 2237, -1, 3431, -1, 2814, -1], 'generators': [841, 192], 'label': '1344.4487.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.d1.a1', 'projective_image': '1344.4487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661098
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.d1.a1', '48.h1.a1', '48.k1.b1'], 'contains': ['192.a1.a1', '672.d1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1970, -1, 2110, -1, 3431, -1, 2697, -1], 'generators': [505, 192], 'label': '1344.4487.96.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.d1.b1', 'projective_image': '1344.4487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661099
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '112.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.c1.a1', '56.d1.a1', '56.e1.a1', '56.f1.a1', '56.g1.a1', '56.h1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '224.c1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1747, 7740, 2618, 7588, 3870, 4679, 3731, 5378], 'generators': [676, 672, 448], 'label': '1344.4487.112.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['224.b1.a1', '224.c1.a1', '224.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '112.31', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.31', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661100
{'ambient': '1344.4487', 'aut_centralizer_order': 5376, 'aut_label': '112.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.j1.a1', '56.k1.a1', '56.l1.a1'], 'contains': ['224.c1.a1', '336.b1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8029, 5877, 6769, 6094, 7984, 5504, 7907, 4284], 'generators': [1008, 448, 672], 'label': '1344.4487.112.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1'], 'normal_contains': ['224.c1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '224.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.7', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661101
{'ambient': '1344.4487', 'aut_centralizer_order': 5376, 'aut_label': '112.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.b1.a1', '56.b1.b1'], 'contains': ['224.c1.a1', '336.c1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5782, 4993, 6006, 4869, 6603, 6790, 6918, 2877], 'generators': [340, 448, 672], 'label': '1344.4487.112.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1', '56.b1.b1', '56.b1.a1'], 'normal_contains': ['224.c1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '224.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.3', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661102
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.c1.a1', '56.i1.a1', '56.i1.a2'], 'contains': ['224.a1.a1', '224.d1.a1', '224.d1.b1', '336.d1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2988, -1, 709, -1, 1837, -1, 1625, -1], 'generators': [841, 4, 448], 'label': '1344.4487.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '112.d1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661103
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.e1.a1', '56.i1.a1', '56.i1.a2'], 'contains': ['224.a1.a1', '336.e1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2637, -1, 50, -1, 1407, -1, 585, -1], 'generators': [703, 448, 4], 'label': '1344.4487.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.e1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661104
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.g1.a1', '56.i1.a1', '56.i1.a2'], 'contains': ['224.a1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3658, -1, 351, -1, 1081, -1, 812, -1], 'generators': [2, 448, 4], 'label': '1344.4487.112.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '112.f1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661105
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '12.g1.a1', '28.i1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8081, 5212, 8811, 8027, 9432, 3657, 8763, 7145], 'generators': [3, 192, 448, 1008, 676, 672], 'label': '1344.4487.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661106
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '56.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.h1.a1'], 'contains': ['224.a1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [878, -1, 1340, -1, 2366, -1, 2109, -1], 'generators': [1038, 448, 4], 'label': '1344.4487.112.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.k1.a1', 'old_label': '112.g1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661107
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.c1.a1'], 'contains': ['224.b1.a1', '224.d1.a1', '224.d1.b1', '336.h1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1346, -1, 1894, -1, 3186, -1, 2614, -1], 'generators': [841, 676, 448], 'label': '1344.4487.112.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '112.h1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661108
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.d1.a1'], 'contains': ['224.b1.a1', '336.i1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [55, -1, 4225, -1, 5039, -1, 4207, -1], 'generators': [1, 448, 676], 'label': '1344.4487.112.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '112.i1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661109
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.f1.a1'], 'contains': ['224.b1.a1', '336.j1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [490, -1, 3963, -1, 4469, -1, 3098, -1], 'generators': [367, 448, 676], 'label': '1344.4487.112.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '112.j1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661110
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.b1.a1', '56.c1.a1', '56.j1.a1'], 'contains': ['224.c1.a1', '224.d1.a1', '336.k1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6073, -1, 3694, -1, 5786, -1, 5948, -1], 'generators': [841, 672, 448], 'label': '1344.4487.112.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.k1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661111
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '56.b1.b1', '56.c1.a1', '56.j1.a1'], 'contains': ['224.c1.a1', '224.d1.b1', '336.k1.b1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6073, -1, 3444, -1, 5786, -1, 5767, -1], 'generators': [505, 672, 448], 'label': '1344.4487.112.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.k1.b1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661112
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '168.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.b1.a1', '84.c1.a1', '84.f1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6892, 4267, 7841, 3699, 7211, 6328, 7067, 3827], 'generators': [676, 1008], 'label': '1344.4487.168.a1.a1', 'mobius_quo': 0, 'mobius_sub': -56, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.b1.a1', '84.c1.a1'], 'normal_contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.12', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661113
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '168.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2688, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.b1.a1', '84.a1.a1'], 'contains': ['336.c1.a1', '336.k1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7324, 1064, 6648, 1425, 6719, 8171, 7397, 1334], 'generators': [841, 340], 'label': '1344.4487.168.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': ['24.d1.a1', '56.b1.a1', '84.a1.a1'], 'normal_contains': ['336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661114
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '168.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2688, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '56.b1.b1', '84.a1.a1'], 'contains': ['336.c1.a1', '336.k1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7324, 1064, 6544, 362, 6719, 8171, 7205, 2250], 'generators': [505, 340], 'label': '1344.4487.168.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': ['24.d1.b1', '56.b1.b1', '84.a1.a1'], 'normal_contains': ['336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.b1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661115
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.c1.a1', '84.a1.a1', '84.d1.a1', '84.e1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.h1.a1', '336.k1.a1', '336.k1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4522, -1, 4304, -1, 3583, -1, 3876, -1], 'generators': [841, 676, 672], 'label': '1344.4487.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.c1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661116
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 16, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.g1.a1', '8.i1.a1', '8.i1.a2', '12.h1.a1', '28.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3491, -1, 1996, -1, 2070, -1, 2404, -1], 'generators': [841, 192, 672, 448, 2, 4], 'label': '1344.4487.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.h1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661117
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.d1.a1', '84.b1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.i1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2193, -1, 5547, -1, 5339, -1, 5374, -1], 'generators': [1, 672], 'label': '1344.4487.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '168.d1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661118
{'ambient': '1344.4487', 'aut_centralizer_order': 768, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.e1.a1', '84.d1.a1', '84.f1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.e1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4326, -1, 2952, -1, 2989, -1, 3550, -1], 'generators': [703, 672], 'label': '1344.4487.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.e1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661119
{'ambient': '1344.4487', 'aut_centralizer_order': 768, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.f1.a1', '84.e1.a1', '84.f1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.j1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2909, -1, 5297, -1, 4765, -1, 4473, -1], 'generators': [367, 672], 'label': '1344.4487.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.f1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661120
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.g1.a1', '84.d1.a1', '84.e1.a1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.f1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4816, -1, 3820, -1, 2791, -1, 3370, -1], 'generators': [2, 672], 'label': '1344.4487.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.g1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661121
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '56.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.h1.a1', '84.h1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2404, -1, 4992, -1, 4306, -1, 5193, -1], 'generators': [1038, 672], 'label': '1344.4487.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '168.h1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661122
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.i1.a1', '84.d1.a1'], 'contains': ['336.d1.a1', '336.e1.a1', '336.f1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3992, -1, 1207, -1, 1244, -1, 1199, -1], 'generators': [841, 2], 'label': '1344.4487.168.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '168.i1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661123
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a2', '56.i1.a2', '84.d1.a1'], 'contains': ['336.d1.a1', '336.e1.a1', '336.f1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3992, -1, 957, -1, 1244, -1, 1018, -1], 'generators': [169, 2], 'label': '1344.4487.168.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '168.i1.a2', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661124
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2688, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.j1.a1', '84.a1.a1'], 'contains': ['336.b1.a1', '336.k1.a1', '336.k1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7439, -1, 6084, -1, 7868, -1, 7301, -1], 'generators': [841, 1008], 'label': '1344.4487.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.j1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661125
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5376, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.k1.a1', '84.c1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9750, -1, 9191, -1, 8400, -1, 9092, -1], 'generators': [168], 'label': '1344.4487.168.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '168.k1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661127
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 16, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.g1.a1', '12.i1.a1', '28.e1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2659, -1, 3685, -1, 2967, -1, 3366, -1], 'generators': [505, 192, 448, 4, 2, 672], 'label': '1344.4487.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661128
{'ambient': '1344.4487', 'aut_centralizer_order': 3584, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3584, 'centralizer': '2.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.d1.b1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1907, 9165, 2182, 8968, 3529, 3278, 2877, 6089], 'generators': [192], 'label': '1344.4487.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.b1.a1', '96.c1.a1', '96.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1344.4487', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.52', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661129
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '224.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.d1.a1', '112.e1.a1', '112.f1.a1', '112.g1.a1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1747, 8880, 474, 7822, 2019, 3508, 1805, 6484], 'generators': [4, 448], 'label': '1344.4487.224.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1'], 'normal_contains': ['448.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '224.109', 'quotient_action_image': '1.1', 'quotient_action_kernel': '224.109', 'quotient_action_kernel_order': 224, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661130
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '224.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.a1.a1', '112.h1.a1', '112.i1.a1', '112.j1.a1'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [504, 7971, 2589, 8837, 3848, 4168, 3029, 5542], 'generators': [676, 448], 'label': '1344.4487.224.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.b1.a1', 'normal_contained_in': ['32.b1.a1', '112.a1.a1'], 'normal_contains': ['448.a1.a1', '672.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.b1.a1', 'projective_image': '224.107', 'quotient_action_image': '1.1', 'quotient_action_kernel': '224.107', 'quotient_action_kernel_order': 224, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661131
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '224.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.k1.a1', '112.k1.b1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5782, 6791, 3550, 6674, 5841, 5166, 5944, 4622], 'generators': [672, 448], 'label': '1344.4487.224.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.c1.a1', 'normal_contained_in': ['32.c1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1'], 'normal_contains': ['448.a1.a1', '672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.c1.a1', 'projective_image': '224.73', 'quotient_action_image': '1.1', 'quotient_action_kernel': '224.73', 'quotient_action_kernel_order': 224, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661132
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.d1.a1', '112.h1.a1', '112.k1.a1'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1917, -1, 1807, -1, 3186, -1, 2473, -1], 'generators': [841, 448], 'label': '1344.4487.224.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '224.d1.a1', 'projective_image': '448.300', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661133
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '112.d1.a1', '112.h1.a1', '112.k1.b1'], 'contains': ['448.a1.a1', '672.d1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1917, -1, 1034, -1, 3186, -1, 2377, -1], 'generators': [505, 448], 'label': '1344.4487.224.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '224.d1.b1', 'projective_image': '448.300', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661134
{'ambient': '1344.4487', 'aut_centralizer_order': 21504, 'aut_label': '336.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1', '168.h1.a1'], 'contains': ['672.a1.a1', '672.b1.a1', '672.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4063, 7286, 4919, 7302, 4088, 4848, 3959, 5249], 'generators': [676, 672], 'label': '1344.4487.336.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.b1.a1', '672.c1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.178', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661135
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '336.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1', '168.j1.a1', '168.k1.a1', '168.l1.a1'], 'contains': ['672.c1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8029, 5592, 7841, 5917, 7984, 5483, 7907, 4329], 'generators': [1008], 'label': '1344.4487.336.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1'], 'normal_contains': ['672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '672.771', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.28', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661136
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '336.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1'], 'contains': ['672.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6639, 4267, 6241, 2698, 6719, 6328, 7136, 3044], 'generators': [340], 'label': '1344.4487.336.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normal_contains': ['672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '672.771', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.24', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661137
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.d1.a1', '168.c1.a1', '168.i1.a1', '168.i1.a2'], 'contains': ['672.a1.a1', '672.d1.a1', '672.d1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3142, -1, 1629, -1, 2166, -1, 1925, -1], 'generators': [841, 4], 'label': '1344.4487.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '336.d1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661138
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 16, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.h1.a1', '12.j1.a1', '28.j1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2060, -1, 3314, -1, 3634, -1, 4132, -1], 'generators': [1009, 192, 448, 676, 1038, 672], 'label': '1344.4487.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661139
{'ambient': '1344.4487', 'aut_centralizer_order': 768, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.e1.a1', '168.e1.a1', '168.i1.a1', '168.i1.a2'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3481, -1, 747, -1, 1671, -1, 1275, -1], 'generators': [703], 'label': '1344.4487.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.e1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661140
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.f1.a1', '168.g1.a1', '168.i1.a1', '168.i1.a2'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3914, -1, 1410, -1, 1538, -1, 1421, -1], 'generators': [2], 'label': '1344.4487.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '336.f1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661141
{'ambient': '1344.4487', 'aut_centralizer_order': 384, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '56.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.g1.a1', '168.h1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [874, -1, 1740, -1, 2442, -1, 2178, -1], 'generators': [1038], 'label': '1344.4487.336.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.k1.a1', 'old_label': '336.g1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661142
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.h1.a1', '168.c1.a1'], 'contains': ['672.b1.a1', '672.d1.a1', '672.d1.b1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1780, -1, 3152, -1, 3554, -1, 2927, -1], 'generators': [841, 676], 'label': '1344.4487.336.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '336.h1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661143
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.i1.a1', '168.d1.a1'], 'contains': ['672.b1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [61, -1, 4690, -1, 5102, -1, 4266, -1], 'generators': [1], 'label': '1344.4487.336.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '336.i1.a1', 'projective_image': '672.805', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661145
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.b1.a1', '168.c1.a1', '168.j1.a1'], 'contains': ['672.c1.a1', '672.d1.a1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6759, -1, 4801, -1, 5953, -1, 6156, -1], 'generators': [841, 672], 'label': '1344.4487.336.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.k1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661146
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '112.k1.b1', '168.b1.b1', '168.c1.a1', '168.j1.a1'], 'contains': ['672.c1.a1', '672.d1.b1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6759, -1, 4580, -1, 5953, -1, 6047, -1], 'generators': [505, 672], 'label': '1344.4487.336.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.k1.b1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661147
{'ambient': '1344.4487', 'aut_centralizer_order': 10752, 'aut_label': '448.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1', '224.d1.a1', '224.d1.b1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1630, 8505, 1355, 8457, 3308, 3871, 2580, 5815], 'generators': [448], 'label': '1344.4487.448.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '448.a1.a1', 'normal_contained_in': ['64.a1.a1', '224.b1.a1', '224.c1.a1', '224.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '448.a1.a1', 'projective_image': '448.300', 'quotient_action_image': '1.1', 'quotient_action_kernel': '448.300', 'quotient_action_kernel_order': 448, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661148
{'ambient': '1344.4487', 'aut_centralizer_order': 21504, 'aut_label': '672.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.d1.a1', '336.e1.a1', '336.f1.a1', '336.g1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3260, 8830, 1516, 8153, 2228, 3575, 1982, 6423], 'generators': [4], 'label': '1344.4487.672.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '672.807', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.807', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661149
{'ambient': '1344.4487', 'aut_centralizer_order': 28, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.56083', 'aut_weyl_index': 28, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '6.a1.a1', '14.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9104, 1070, 8443, 1986, 7682, 7953, 8203, 2653], 'generators': [1, 1008, 448, 192, 168, 672, 676], 'label': '1344.4487.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '6.a1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661150
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 16, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.h1.a1', '12.k1.a1', '28.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1747, -1, 4531, -1, 4230, -1, 4480, -1], 'generators': [1, 192, 448, 676, 1038, 672], 'label': '1344.4487.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.k1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661151
{'ambient': '1344.4487', 'aut_centralizer_order': 21504, 'aut_label': '672.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1', '336.h1.a1', '336.i1.a1', '336.j1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [975, 8201, 3890, 8803, 3964, 4168, 3135, 5542], 'generators': [676], 'label': '1344.4487.672.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.b1.a1', 'normal_contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.b1.a1', 'projective_image': '672.805', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.805', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661152
{'ambient': '1344.4487', 'aut_centralizer_order': 21504, 'aut_label': '672.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.c1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.k1.a1', '336.k1.b1'], 'contains': ['1344.a1.a1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5938, 6462, 4872, 6819, 5953, 5005, 6101, 4774], 'generators': [672], 'label': '1344.4487.672.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.c1.a1', 'normal_contained_in': ['96.c1.a1', '224.c1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.c1.a1', 'projective_image': '672.771', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.771', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661153
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.d1.a1', '336.h1.a1', '336.k1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2003, -1, 2452, -1, 3425, -1, 2782, -1], 'generators': [841], 'label': '1344.4487.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '672.d1.a1', 'projective_image': '1344.4487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661154
{'ambient': '1344.4487', 'aut_centralizer_order': 2688, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21504, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.b1', '224.d1.b1', '336.d1.a1', '336.h1.a1', '336.k1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2003, -1, 2291, -1, 3425, -1, 2686, -1], 'generators': [505], 'label': '1344.4487.672.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '672.d1.b1', 'projective_image': '1344.4487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661155
{'ambient': '1344.4487', 'aut_centralizer_order': None, 'aut_label': '1344.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': ['192.a1.a1', '448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1', '672.d1.a1', '672.d1.b1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1956, 8505, 2291, 8457, 3477, 3871, 2782, 5815], 'generators': [], 'label': '1344.4487.1344.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['192.a1.a1', '448.a1.a1', '672.b1.a1', '672.c1.a1', '672.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': '1344.4487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 72661156
{'ambient': '1344.4487', 'aut_centralizer_order': 56, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20154', 'aut_weyl_index': 56, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.f1.a1', '42.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9268, 1084, 9742, 1850, 8345, 8324, 8985, 2330], 'generators': [1, 672, 192, 676, 168, 1008], 'label': '1344.4487.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.f1.a1', '42.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661157
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ek', 'aut_weyl_index': 8, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.h1.a1', '12.i1.a1', '42.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6278, 6972, 6943, 3942, 5057, 4836, 5853, 8981], 'generators': [841, 192, 1008, 4, 2, 672], 'label': '1344.4487.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661158
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ek', 'aut_weyl_index': 8, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.g1.a1', '42.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8667, 2738, 8624, 5486, 8093, 2944, 8310, 5116], 'generators': [841, 192, 340, 1008, 1038, 672], 'label': '1344.4487.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.e1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661159
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ek', 'aut_weyl_index': 8, 'centralizer': '112.a1.a1', 'complements': ['224.d1.a1', '224.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1', '12.j1.a1', '12.k1.a1', '42.d1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5191, 4088, 7485, 6193, 5792, 1018, 6303, 6142], 'generators': [1, 192, 1008, 676, 1038, 672], 'label': '1344.4487.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661226
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 448, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.a1.a1'], 'contains': ['48.b1.a1', '48.k1.a1', '48.k1.b1', '168.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7860, -1, 7536, -1, 8090, -1, 8239, -1], 'generators': [841, 192, 672, 1008], 'label': '1344.4487.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661160
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ek', 'aut_weyl_index': 8, 'centralizer': '112.a1.a1', 'complements': ['224.d1.a1', '224.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.g1.a1', '42.e1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8310, 3484, 9125, 3274, 8553, 5426, 7954, 6602], 'generators': [1, 192, 676, 1008, 2, 672], 'label': '1344.4487.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.d1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661161
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '6.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 16, 'centralizer': '56.a1.a1', 'complements': ['224.d1.a1', '224.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1', '42.f1.a1'], 'core': '6.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9043, 4892, 9950, 7480, 8971, 1525, 9177, 7697], 'generators': [3, 192, 676, 1008, 168, 672], 'label': '1344.4487.6.f1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.f1.a1', 'normal_contained_in': ['2.f1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661162
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ek', 'aut_weyl_index': 8, 'centralizer': '112.a1.a1', 'complements': ['224.d1.a1', '224.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1', '42.g1.a1'], 'core': '6.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7736, 5497, 8410, 4611, 6492, 4247, 8112, 5682], 'generators': [2, 192, 4, 1008, 168, 672], 'label': '1344.4487.6.g1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.g1.a1', 'normal_contained_in': ['2.g1.a1', '3.a1.a1'], 'normal_contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '336.178', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661163
{'ambient': '1344.4487', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '512.10494202', 'aut_weyl_index': 42, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1', '14.e1.a1', '14.f1.a1', '14.g1.a1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8403, -1, 7860, -1, 6789, -1, 6870, -1], 'generators': [1, 1008, 676, 2, 672, 168, 448], 'label': '1344.4487.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661164
{'ambient': '1344.4487', 'aut_centralizer_order': 896, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6119, 7147, 6573, 7105, 7057, 4581, 6813, 5530], 'generators': [676, 448, 192, 1008, 672], 'label': '1344.4487.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '112.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661165
{'ambient': '1344.4487', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.h1.a1', '4.i1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5554, 7611, 5882, 4110, 4927, 5570, 5374, 8483], 'generators': [841, 672, 1008, 448, 2, 192, 4], 'label': '1344.4487.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661166
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '28.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '24.b1.a1', '56.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2618, 9200, 2162, 8939, 2328, 853, 2516, 8331], 'generators': [703, 448, 4, 672, 192], 'label': '1344.4487.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661167
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '24.c1.a1', '56.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1820, 8365, 3903, 9721, 3945, 1542, 3484, 8966], 'generators': [367, 448, 676, 672, 192], 'label': '1344.4487.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661168
{'ambient': '1344.4487', 'aut_centralizer_order': 112, 'aut_label': '8.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 224, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '24.d1.a1', '56.b1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6728, 934, 5969, 2075, 6619, 9037, 7847, 277], 'generators': [841, 448, 192, 340, 672], 'label': '1344.4487.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '24.d1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661169
{'ambient': '1344.4487', 'aut_centralizer_order': 112, 'aut_label': '8.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 224, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.c1.a1', '16.k1.b1', '24.d1.b1', '56.b1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6728, 934, 5625, 419, 6619, 9037, 7411, 1425], 'generators': [505, 448, 192, 340, 672], 'label': '1344.4487.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '24.d1.b1', '56.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661170
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.52', 'aut_weyl_index': 448, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.h1.a1', '16.k1.a1', '16.k1.b1', '24.e1.a1', '56.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2345, -1, 3033, -1, 2584, -1, 3000, -1], 'generators': [841, 672, 448, 676, 192], 'label': '1344.4487.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.e1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661171
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.52', 'aut_weyl_index': 448, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '24.f1.a1', '56.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1229, -1, 4195, -1, 4185, -1, 4306, -1], 'generators': [1, 448, 192, 672, 676], 'label': '1344.4487.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.f1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661172
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '24.g1.a1', '56.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3491, -1, 1922, -1, 1811, -1, 2293, -1], 'generators': [2, 448, 4, 672, 192], 'label': '1344.4487.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.g1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661173
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '24.h1.a1', '56.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1485, -1, 2780, -1, 3287, -1, 3864, -1], 'generators': [1038, 448, 4, 672, 192], 'label': '1344.4487.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.h1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661174
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.i1.a1', '56.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2877, -1, 950, -1, 709, -1, 1143, -1], 'generators': [841, 448, 4, 2, 192], 'label': '1344.4487.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.i1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661175
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.i1.a2', '56.i1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2877, -1, 660, -1, 709, -1, 865, -1], 'generators': [169, 448, 4, 2, 192], 'label': '1344.4487.8.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.i1.a2', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a2', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661176
{'ambient': '1344.4487', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1', '6.c1.a1', '14.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 2264, 8121, 6178, 7356, 3748, 7667, 3877], 'generators': [841, 672, 448, 340, 1038, 192, 1008], 'label': '1344.4487.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661177
{'ambient': '1344.4487', 'aut_centralizer_order': 112, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 224, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.k1.b1', '24.j1.a1', '56.j1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7394, -1, 5048, -1, 8020, -1, 7629, -1], 'generators': [841, 448, 192, 1008, 672], 'label': '1344.4487.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.j1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661178
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.52', 'aut_weyl_index': 448, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.b1.a1', '24.k1.a1', '56.k1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9926, -1, 9342, -1, 9700, -1, 9947, -1], 'generators': [168, 192, 336, 448, 672], 'label': '1344.4487.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.k1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661179
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.b1.a1', '24.l1.a1', '56.l1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8561, -1, 8989, -1, 9892, -1, 9555, -1], 'generators': [3, 1008, 672, 448, 192], 'label': '1344.4487.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.l1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661180
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.221', 'aut_weyl_index': 224, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.j1.a1', '84.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7570, 365, 7784, 1425, 7538, 6617, 8310, 2049], 'generators': [841, 1008, 192, 676, 672], 'label': '1344.4487.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'normal_contains': ['24.a1.a1', '24.d1.b1', '24.d1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661181
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.221', 'aut_weyl_index': 224, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '84.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5728, 2558, 8587, 3203, 7779, 5933, 7190, 4903], 'generators': [1, 192, 676, 1008, 672], 'label': '1344.4487.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '84.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661182
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '84.f1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5058, 7226, 7271, 7348, 5693, 2230, 5685, 7697], 'generators': [367, 676, 672, 1008, 192], 'label': '1344.4487.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661183
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 32, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '84.g1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6938, 5707, 7066, 4635, 5485, 3999, 6625, 7153], 'generators': [2, 4, 672, 1008, 192], 'label': '1344.4487.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1', '6.e1.a1', '6.g1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661184
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '12.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 32, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '84.h1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6008, 5112, 8327, 5191, 6279, 2820, 7000, 6066], 'generators': [1038, 4, 672, 1008, 192], 'label': '1344.4487.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.e1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661185
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 448, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '84.c1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9582, 3573, 9901, 3975, 9031, 5252, 9775, 4276], 'generators': [676, 192, 336, 168, 672], 'label': '1344.4487.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'normal_contains': ['24.a1.a1', '84.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '336.178', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661186
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '12.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 64, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.l1.a1', '84.i1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9073, 4398, 9610, 5861, 9508, 3410, 9333, 6610], 'generators': [3, 1008, 672, 676, 192], 'label': '1344.4487.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.g1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661187
{'ambient': '1344.4487', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': ['672.d1.a1', '672.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.j1.a1', '4.k1.a1', '6.d1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5027, 4552, 6472, 7236, 5685, 1266, 5759, 5473], 'generators': [1, 672, 1008, 448, 1038, 192, 676], 'label': '1344.4487.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661188
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.g1.a1', '24.i1.a1', '24.i1.a2', '84.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4313, -1, 2777, -1, 2070, -1, 2752, -1], 'generators': [841, 672, 4, 2, 192], 'label': '1344.4487.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661189
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.g1.a1', '84.e1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4015, -1, 4547, -1, 3079, -1, 3674, -1], 'generators': [505, 4, 672, 2, 192], 'label': '1344.4487.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661190
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '24.h1.a1', '84.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3311, -1, 4840, -1, 3737, -1, 4715, -1], 'generators': [1009, 676, 672, 1038, 192], 'label': '1344.4487.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.j1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661191
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 32, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.h1.a1', '84.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2912, -1, 5169, -1, 4633, -1, 4874, -1], 'generators': [1, 676, 672, 1038, 192], 'label': '1344.4487.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.k1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661192
{'ambient': '1344.4487', 'aut_centralizer_order': 168, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9138, 1159, 8584, 952, 7599, 9693, 7764, 1695], 'generators': [1, 672, 1008, 168, 448, 676], 'label': '1344.4487.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661193
{'ambient': '1344.4487', 'aut_centralizer_order': 24, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.a1', '28.e1.a1', '28.f1.a1', '28.g1.a1', '42.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6402, -1, 5570, -1, 4535, -1, 4896, -1], 'generators': [841, 672, 4, 2, 1008, 448], 'label': '1344.4487.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661194
{'ambient': '1344.4487', 'aut_centralizer_order': 24, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.h1.a1', '28.i1.a1', '42.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8469, -1, 8127, -1, 7356, -1, 7418, -1], 'generators': [841, 672, 1008, 1038, 448, 340], 'label': '1344.4487.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661195
{'ambient': '1344.4487', 'aut_centralizer_order': 24, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.f1.a1', '28.h1.a1', '28.j1.a1', '28.k1.a1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5117, -1, 6244, -1, 5581, -1, 5374, -1], 'generators': [1, 672, 676, 1038, 1008, 448], 'label': '1344.4487.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661196
{'ambient': '1344.4487', 'aut_centralizer_order': 24, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.g1.a1', '28.i1.a1', '42.e1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8034, -1, 7561, -1, 7842, -1, 6974, -1], 'generators': [1, 672, 1008, 2, 448, 676], 'label': '1344.4487.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661197
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.267', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.f1.a1', '28.i1.a1', '42.f1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9454, -1, 9096, -1, 8761, -1, 8540, -1], 'generators': [3, 672, 1008, 168, 448, 676], 'label': '1344.4487.14.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.f1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661198
{'ambient': '1344.4487', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': ['672.d1.a1', '672.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7960, 3573, 7722, 2912, 7964, 6469, 7111, 6902], 'generators': [1, 672, 448, 676, 2, 192, 1008], 'label': '1344.4487.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661199
{'ambient': '1344.4487', 'aut_centralizer_order': 24, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 168, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.g1.a1', '28.h1.a1', '42.g1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7542, -1, 7321, -1, 6285, -1, 7196, -1], 'generators': [2, 672, 1008, 168, 448, 4], 'label': '1344.4487.14.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.g1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661200
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1658, 8680, 2414, 8294, 3637, 3018, 3592, 6575], 'generators': [676, 448, 192, 672], 'label': '1344.4487.16.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.b1.a1', '32.c1.a1', '32.a1.a1', '48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661201
{'ambient': '1344.4487', 'aut_centralizer_order': 896, 'aut_label': '16.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.c1.a1', '48.b1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7841, 6652, 7081, 6955, 8452, 4589, 8571, 5382], 'generators': [1008, 192, 672, 448], 'label': '1344.4487.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.a1', '48.b1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '224.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661202
{'ambient': '1344.4487', 'aut_centralizer_order': 896, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.c1.a1', '48.c1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5676, 4448, 5699, 6188, 6719, 5809, 7507, 2938], 'generators': [340, 192, 672, 448], 'label': '1344.4487.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.b1', '8.d1.a1'], 'normal_contains': ['32.c1.a1', '48.c1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '224.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661203
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.i1.a1', '8.i1.a2'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '48.d1.a1', '112.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1911, -1, 959, -1, 1071, -1, 1418, -1], 'generators': [841, 448, 192, 4], 'label': '1344.4487.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.d1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661204
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.i1.a1', '8.i1.a2'], 'contains': ['32.a1.a1', '48.e1.a1', '112.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2288, -1, 634, -1, 831, -1, 533, -1], 'generators': [703, 4, 192, 448], 'label': '1344.4487.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.e1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661205
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.i1.a1', '8.i1.a2'], 'contains': ['32.a1.a1', '48.f1.a1', '112.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2604, -1, 393, -1, 345, -1, 755, -1], 'generators': [2, 4, 192, 448], 'label': '1344.4487.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.f1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661206
{'ambient': '1344.4487', 'aut_centralizer_order': 32, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1'], 'contains': ['32.a1.a1', '48.g1.a1', '112.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [725, -1, 1205, -1, 1311, -1, 1638, -1], 'generators': [1038, 4, 192, 448], 'label': '1344.4487.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.g1.a1', 'projective_image': '224.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661207
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.d1.b1', '48.h1.a1', '112.h1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [981, -1, 1744, -1, 2738, -1, 1857, -1], 'generators': [841, 448, 192, 676], 'label': '1344.4487.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.h1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661208
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.b1.a1', '48.i1.a1', '112.i1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [126, -1, 4014, -1, 5156, -1, 4004, -1], 'generators': [1, 192, 676, 448], 'label': '1344.4487.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.i1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661227
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.f1.a1'], 'contains': ['48.b1.a1', '168.k1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9945, -1, 9901, -1, 8968, -1, 9603, -1], 'generators': [168, 336, 672, 192], 'label': '1344.4487.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '24.k1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661209
{'ambient': '1344.4487', 'aut_centralizer_order': 8, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ei', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['672.d1.a1', '672.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '6.f1.a1', '14.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9416, 5542, 9204, 8162, 8865, 2082, 8651, 7647], 'generators': [3, 672, 448, 676, 168, 192, 1008], 'label': '1344.4487.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '6.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661210
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.a1', '48.j1.a1', '112.j1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [409, -1, 3777, -1, 4492, -1, 2077, -1], 'generators': [367, 676, 192, 448], 'label': '1344.4487.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.j1.a1', 'projective_image': '224.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661211
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.e1.a1', '8.j1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '48.k1.a1', '112.k1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5872, -1, 3267, -1, 5949, -1, 6206, -1], 'generators': [841, 448, 192, 672], 'label': '1344.4487.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.k1.a1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661212
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.e1.a1', '8.j1.a1'], 'contains': ['32.c1.a1', '32.d1.b1', '48.k1.b1', '112.k1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5872, -1, 3033, -1, 5949, -1, 5990, -1], 'generators': [505, 448, 192, 672], 'label': '1344.4487.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.k1.b1', 'projective_image': '224.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661213
{'ambient': '1344.4487', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 84, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.g1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9111, -1, 9093, -1, 7167, -1, 7591, -1], 'generators': [1, 2, 168], 'label': '1344.4487.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661214
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '24.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6646, 5372, 8114, 4522, 7538, 5137, 7857, 4903], 'generators': [676, 192, 672, 1008], 'label': '1344.4487.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661215
{'ambient': '1344.4487', 'aut_centralizer_order': 128, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '28.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.h1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '168.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4072, 7791, 2724, 7283, 2499, 2230, 3163, 5948], 'generators': [703, 4, 192, 672], 'label': '1344.4487.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661216
{'ambient': '1344.4487', 'aut_centralizer_order': 128, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1', '12.i1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '168.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3153, 6956, 4916, 9127, 4972, 3698, 4541, 7697], 'generators': [367, 676, 192, 672], 'label': '1344.4487.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661217
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '24.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 448, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1'], 'contains': ['48.c1.a1', '48.k1.a1', '168.b1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7293, 470, 7734, 1663, 6884, 7891, 8421, 946], 'generators': [841, 192, 672, 340], 'label': '1344.4487.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.d1.a1', '12.a1.a1'], 'normal_contains': ['48.c1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661218
{'ambient': '1344.4487', 'aut_centralizer_order': 224, 'aut_label': '24.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 448, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.a1.a1'], 'contains': ['48.c1.a1', '48.k1.b1', '168.b1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7293, 470, 7229, 307, 6884, 7891, 8056, 1988], 'generators': [505, 192, 672, 340], 'label': '1344.4487.24.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': ['8.d1.b1', '12.a1.a1'], 'normal_contains': ['48.c1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661219
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.a1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.h1.a1', '48.k1.a1', '48.k1.b1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3799, -1, 4555, -1, 3220, -1, 3823, -1], 'generators': [841, 672, 192, 676], 'label': '1344.4487.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661220
{'ambient': '1344.4487', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': ['672.d1.a1', '672.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7577, 6522, 7419, 5130, 6389, 4671, 7369, 4728], 'generators': [2, 672, 448, 4, 168, 192, 1008], 'label': '1344.4487.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '112.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
-
id: 72661221
{'ambient': '1344.4487', 'aut_centralizer_order': 448, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 896, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.b1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.i1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2581, -1, 5372, -1, 5576, -1, 5540, -1], 'generators': [1, 192, 676, 672], 'label': '1344.4487.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.f1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661222
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.d1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '168.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4565, -1, 3290, -1, 2256, -1, 2941, -1], 'generators': [2, 4, 192, 672], 'label': '1344.4487.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
-
id: 72661223
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.e1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '168.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2837, -1, 3977, -1, 4114, -1, 5197, -1], 'generators': [1038, 4, 192, 672], 'label': '1344.4487.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.h1.a1', 'projective_image': '336.178', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
-
id: 72661224
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.h1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.f1.a1', '168.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3469, -1, 1276, -1, 588, -1, 1199, -1], 'generators': [841, 4, 192, 2], 'label': '1344.4487.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.i1.a1', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661225
{'ambient': '1344.4487', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a2', '12.h1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.f1.a1', '168.i1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3469, -1, 1036, -1, 588, -1, 977, -1], 'generators': [169, 4, 192, 2], 'label': '1344.4487.24.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.i1.a2', 'projective_image': '672.807', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a2', 'subgroup_fusion': None, 'weyl_group': '14.1'}
-
id: 72661228
{'ambient': '1344.4487', 'aut_centralizer_order': 64, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.g1.a1'], 'contains': ['48.b1.a1', '168.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8746, -1, 9772, -1, 9367, -1, 9310, -1], 'generators': [3, 672, 192, 1008], 'label': '1344.4487.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.l1.a1', 'projective_image': '672.771', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
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id: 72661229
{'ambient': '1344.4487', 'aut_centralizer_order': 672, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 672, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.b1.b1', '56.c1.a1', '56.j1.a1', '84.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7358, 1070, 5908, 634, 6838, 9660, 6455, 851], 'generators': [841, 672, 676, 1008, 448], 'label': '1344.4487.28.a1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.b1.b1', '56.b1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
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id: 72661230
{'ambient': '1344.4487', 'aut_centralizer_order': 672, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 672, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.a1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.d1.a1', '84.b1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5724, 2208, 6931, 2440, 7296, 7973, 6253, 3649], 'generators': [1, 672, 1008, 448, 676], 'label': '1344.4487.28.b1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.b1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 72661231
{'ambient': '1344.4487', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '112.a1.a1', 'complements': ['448.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '21.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8749, 3858, 8624, 4434, 7042, 2857, 7954, 6192], 'generators': [1, 672, 168, 676, 2, 192, 1008], 'label': '1344.4487.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
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id: 72661232
{'ambient': '1344.4487', 'aut_centralizer_order': 1344, 'aut_label': '28.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.k1.a1', '84.c1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9650, 3224, 9096, 3567, 8794, 7293, 9114, 3022], 'generators': [676, 672, 168, 448, 336], 'label': '1344.4487.28.c1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '112.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 72661233
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.51', 'aut_weyl_index': 672, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.e1.a1', '56.g1.a1', '56.i1.a1', '56.i1.a2', '84.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4492, -1, 2237, -1, 1555, -1, 2059, -1], 'generators': [841, 4, 2, 672, 448], 'label': '1344.4487.28.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.d1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 72661234
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.51', 'aut_weyl_index': 672, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.f1.a1', '56.g1.a1', '84.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4145, -1, 3377, -1, 2855, -1, 3247, -1], 'generators': [505, 672, 2, 448, 4], 'label': '1344.4487.28.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.e1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661235
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '28.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.e1.a1', '56.f1.a1', '84.f1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5115, -1, 5636, -1, 5280, -1, 5061, -1], 'generators': [367, 672, 1008, 448, 676], 'label': '1344.4487.28.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.f1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661236
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.46', 'aut_weyl_index': 672, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.g1.a1', '84.g1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6710, -1, 6235, -1, 4841, -1, 5281, -1], 'generators': [2, 672, 1008, 448, 4], 'label': '1344.4487.28.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.g1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 72661237
{'ambient': '1344.4487', 'aut_centralizer_order': 96, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.46', 'aut_weyl_index': 672, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.c1.a1', '14.d1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.h1.a1', '84.h1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6041, -1, 6583, -1, 6071, -1, 5907, -1], 'generators': [1038, 672, 1008, 448, 4], 'label': '1344.4487.28.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.h1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 72661238
{'ambient': '1344.4487', 'aut_centralizer_order': 192, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1344, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.c1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.l1.a1', '84.i1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8392, -1, 8532, -1, 9268, -1, 8651, -1], 'generators': [3, 672, 676, 448, 1008], 'label': '1344.4487.28.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.i1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 72661239
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.51', 'aut_weyl_index': 672, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.d1.a1'], 'contains': ['56.d1.a1', '56.e1.a1', '56.h1.a1', '84.j1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2045, -1, 3741, -1, 3529, -1, 4086, -1], 'generators': [1009, 672, 1038, 448, 676], 'label': '1344.4487.28.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.j1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661240
{'ambient': '1344.4487', 'aut_centralizer_order': 48, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.51', 'aut_weyl_index': 672, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.d1.a1'], 'contains': ['56.d1.a1', '56.f1.a1', '56.h1.a1', '84.k1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1786, -1, 4252, -1, 4425, -1, 4525, -1], 'generators': [1, 672, 1038, 448, 676], 'label': '1344.4487.28.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.k1.a1', 'projective_image': '112.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 72661241
{'ambient': '1344.4487', 'aut_centralizer_order': 1792, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1792, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1231, 9635, 388, 8589, 2000, 2816, 1774, 6762], 'generators': [4, 192, 448], 'label': '1344.4487.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '224.109', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.8', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}