Formats: - HTML - YAML - JSON - 2026-07-24T15:35:05.223065
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [8, 18, 6, 6], 'aut_gens': [[339786367000805117682586349328554681397243, 10631640421497648346633457090865944853364, 287207520660161682126837036330915041206916], [74452658171890248576389600376482201246665, 3531000600836836199328285919363455360, 96030973781143935560058681335557358570755], [244046279805734816150099627792401046905559, 148318118340737353408202910523263913564947, 319114901738819849757229553473367597940025], [52583455365195173277097040125362272801757, 265919005124012837001984377536439332019252, 64123040922535728365369764587819977058626], [159556495885534517139285736007165124971043, 148318118323053829447699524080758271068800, 319410126314715926912604821479533318997828]], 'aut_group': '2016.dd', 'aut_hash': 4903004512774377459, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1259712, 'aut_permdeg': 4401, 'aut_perms': 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'inner_order': 34992, 'inner_split': True, 'inner_tex': 'C_3^6.(S_3\\times Q_8)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 6], [4, 1], [8, 4], [16, 14], [24, 18], [48, 9]], 'label': '34992.gk', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.(S3*Q8)', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 60, 'number_divisions': 56, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 1238, 'number_subgroup_classes': 8892, 'number_subgroups': 2625788, 'old_label': None, 'order': 34992, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 999], [3, 2186], [4, 17496], [6, 5562], [12, 8748]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 3, 3], 'outer_gen_pows': [0, 0, 20962063216630126056741105524803512485065, 0], 'outer_gens': [[329748723196280008545379791039522317493240, 20670081841371406235870308097946992860323, 297835630063374581896514384496644288950772], [42545811551524220359730992341231945919198, 3785917745347912217250924713890588320, 191771069473791262605889341123441108111094], [233713394987563837291221602188789146957838, 3259656071899303100070414203805951603, 191771069456107350811177970334086263806450], [339786638345943444124665128330763193468108, 3259664609160757202292366690120558723, 307873816575249641364064649119288938935015]], 'outer_group': '36.10', 'outer_hash': 10, 'outer_nilpotent': False, 'outer_order': 36, 'outer_permdeg': 6, 'outer_perms': [136, 127, 676, 697], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1], [8, 4], [16, 6], [24, 18], [32, 4], [48, 9]], 'representations': {'PC': {'code': '123907834742372531956375189693094273519897593252030032832518414616020022415955592698442658305754709869029027994087538102676948426434271598713212458995756331617713788916128551326165985782056083592870207', 'gens': [1, 2, 4, 6, 7, 8, 9, 10, 11], 'pres': [11, -2, -2, -3, -2, -2, -3, 3, 3, 3, 3, 3, 112992, 617981, 56, 1065506, 42198, 439827, 275366, 121597, 124, 566284, 717435, 235976, 1976837, 291472, 127539, 7430, 313, 814985, 5572, 64103, 974, 1892359, 692754, 202781, 191880, 3219, 3198104, 496603, 665310, 21821, 10744, 976809, 604580, 790711, 118842, 35693, 2032821, 705704, 92487, 117666]}, 'Perm': {'d': 36, 'gens': [339786367000805117682586349328554681397243, 10631640421497648346633457090865944853364, 287207520660161682126837036330915041206916]}}, 'schur_multiplier': [6, 6], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(S_3\\times Q_8)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 160481694
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 167, 'group_order': 34992, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 160481705
      {'aut_label': '2A', 'centralizer': '27.A', 'counter': 2, 'group_counter': 167, 'group_order': 34992, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 148318118323054636030619223456470066416704, 'size': 27}
    • id: 160481716
      {'aut_label': '2B', 'centralizer': '243.C', 'counter': 3, 'group_counter': 167, 'group_order': 34992, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 148612816646422658531945544601838031828601, 'size': 243}
    • id: 160481727
      {'aut_label': '2C', 'centralizer': '729.a1', 'counter': 4, 'group_counter': 167, 'group_order': 34992, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 10333682468887900973706239821314349656269, 'size': 729}
    • id: 160481738
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 5, 'group_counter': 167, 'group_order': 34992, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 10628380774572399435841703605484685849744, 'size': 8}
    • id: 160481749
      {'aut_label': '3B', 'centralizer': '8.A', 'counter': 6, 'group_counter': 167, 'group_order': 34992, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 10628652136784860956425231524975061610480, 'size': 8}
    • id: 160481751
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 7, 'group_counter': 167, 'group_order': 34992, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 10628652136785279759096401461770986192884, 'size': 8}
    • id: 160481752
      {'aut_label': '3D', 'centralizer': '8.A', 'counter': 8, 'group_counter': 167, 'group_order': 34992, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 20666295941919359052059922281267695680148, 'size': 8}
    • id: 160481753
      {'aut_label': '3B', 'centralizer': '8.A', 'counter': 9, 'group_counter': 167, 'group_order': 34992, 'label': '3E', 'order': 3, 'powers': [9, 1], 'representative': 20666567286448296585164045580295983248644, 'size': 8}
    • id: 160481695
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 10, 'group_counter': 167, 'group_order': 34992, 'label': '3F', 'order': 3, 'powers': [10, 1], 'representative': 271371359111858934944111145713744880, 'size': 8}
    • id: 160481696
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 11, 'group_counter': 167, 'group_order': 34992, 'label': '3G', 'order': 3, 'powers': [11, 1], 'representative': 10628907027099616484555487653870021190960, 'size': 8}
    • id: 160481697
      {'aut_label': '3B', 'centralizer': '8.A', 'counter': 12, 'group_counter': 167, 'group_order': 34992, 'label': '3H', 'order': 3, 'powers': [12, 1], 'representative': 20666822194446576100773706329653031021364, 'size': 8}
    • id: 160481698
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 13, 'group_counter': 167, 'group_order': 34992, 'label': '3I', 'order': 3, 'powers': [13, 1], 'representative': 10628907036247073405829157056889932487107, 'size': 8}
    • id: 160481699
      {'aut_label': '3A', 'centralizer': '8.A', 'counter': 14, 'group_counter': 167, 'group_order': 34992, 'label': '3J', 'order': 3, 'powers': [14, 1], 'representative': 526261673867387065200240040673325360, 'size': 8}
    • id: 160481700
      {'aut_label': '3K', 'centralizer': '18.D', 'counter': 15, 'group_counter': 167, 'group_order': 34992, 'label': '3K', 'order': 3, 'powers': [15, 1], 'representative': 127648299896393861331249471116140758882625, 'size': 18}
    • id: 160481701
      {'aut_label': '3L', 'centralizer': '24.H', 'counter': 16, 'group_counter': 167, 'group_order': 34992, 'label': '3L', 'order': 3, 'powers': [16, 1], 'representative': 20666567286448684340684558296729548947760, 'size': 24}
    • id: 160481702
      {'aut_label': '3M', 'centralizer': '48.A', 'counter': 17, 'group_counter': 167, 'group_order': 34992, 'label': '3M', 'order': 3, 'powers': [17, 1], 'representative': 2554923812208813604, 'size': 48}
    • id: 160481703
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 18, 'group_counter': 167, 'group_order': 34992, 'label': '3N', 'order': 3, 'powers': [18, 1], 'representative': 26976018178130925657748, 'size': 48}
    • id: 160481704
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 19, 'group_counter': 167, 'group_order': 34992, 'label': '3O', 'order': 3, 'powers': [19, 1], 'representative': 418802673724860340371501603, 'size': 48}
    • id: 160481706
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 20, 'group_counter': 167, 'group_order': 34992, 'label': '3P', 'order': 3, 'powers': [20, 1], 'representative': 418802676036452106182864784, 'size': 48}
    • id: 160481707
      {'aut_label': '3Q', 'centralizer': '48.A', 'counter': 21, 'group_counter': 167, 'group_order': 34992, 'label': '3Q', 'order': 3, 'powers': [21, 1], 'representative': 418829652053584085160080884, 'size': 48}
    • id: 160481708
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 22, 'group_counter': 167, 'group_order': 34992, 'label': '3R', 'order': 3, 'powers': [22, 1], 'representative': 418854377758673049363117508, 'size': 48}
    • id: 160481709
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 23, 'group_counter': 167, 'group_order': 34992, 'label': '3S', 'order': 3, 'powers': [23, 1], 'representative': 9146650365329988205600944237507, 'size': 48}
    • id: 160481710
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 24, 'group_counter': 167, 'group_order': 34992, 'label': '3T', 'order': 3, 'powers': [24, 1], 'representative': 9146650390060315473535093482388, 'size': 48}
    • id: 160481711
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 25, 'group_counter': 167, 'group_order': 34992, 'label': '3U', 'order': 3, 'powers': [25, 1], 'representative': 9147069192729173776719626925604, 'size': 48}
    • id: 160481712
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 26, 'group_counter': 167, 'group_order': 34992, 'label': '3V', 'order': 3, 'powers': [26, 1], 'representative': 9147456948252241416697755655108, 'size': 48}
    • id: 160481713
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 27, 'group_counter': 167, 'group_order': 34992, 'label': '3W', 'order': 3, 'powers': [27, 1], 'representative': 271353676006725830743281778813674480, 'size': 48}
    • id: 160481714
      {'aut_label': '3N', 'centralizer': '48.A', 'counter': 28, 'group_counter': 167, 'group_order': 34992, 'label': '3X', 'order': 3, 'powers': [28, 1], 'representative': 271353676394481353810880166670480784, 'size': 48}
    • id: 160481715
      {'aut_label': '3M', 'centralizer': '48.A', 'counter': 29, 'group_counter': 167, 'group_order': 34992, 'label': '3Y', 'order': 3, 'powers': [29, 1], 'representative': 271362822238236782972772484815018484, 'size': 48}
    • id: 160481717
      {'aut_label': '3Z', 'centralizer': '144.A', 'counter': 30, 'group_counter': 167, 'group_order': 34992, 'label': '3Z', 'order': 3, 'powers': [30, 1], 'representative': 127648028533571623121447381237818148661121, 'size': 144}
    • id: 160481718
      {'aut_label': '3AA', 'centralizer': '144.BH', 'counter': 31, 'group_counter': 167, 'group_order': 34992, 'label': '3AA', 'order': 3, 'powers': [31, 1], 'representative': 127648028533571623146177952172644284834721, 'size': 144}
    • id: 160481719
      {'aut_label': '3AB1', 'centralizer': '144.BH', 'counter': 32, 'group_counter': 167, 'group_order': 34992, 'label': '3AB1', 'order': 3, 'powers': [33, 1], 'representative': 127648028533571623094469053225622572856385, 'size': 144}
    • id: 160481720
      {'aut_label': '3AB1', 'centralizer': '144.BH', 'counter': 33, 'group_counter': 167, 'group_order': 34992, 'label': '3AB-1', 'order': 3, 'powers': [32, 1], 'representative': 127648028533572429677391306437068097438786, 'size': 144}
    • id: 160481721
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 34, 'group_counter': 167, 'group_order': 34992, 'label': '3AC1', 'order': 3, 'powers': [35, 1], 'representative': 127648028533571623121445070357614004114082, 'size': 144}
    • id: 160481722
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 35, 'group_counter': 167, 'group_order': 34992, 'label': '3AC-1', 'order': 3, 'powers': [34, 1], 'representative': 127648028533571623146175397960393742837266, 'size': 144}
    • id: 160481723
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 36, 'group_counter': 167, 'group_order': 34992, 'label': '3AD1', 'order': 3, 'powers': [37, 1], 'representative': 127648028533571623121449936496475946953029, 'size': 144}
    • id: 160481724
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 37, 'group_counter': 167, 'group_order': 34992, 'label': '3AD-1', 'order': 3, 'powers': [36, 1], 'representative': 127648028533571623146173085992192070072245, 'size': 144}
    • id: 160481725
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 38, 'group_counter': 167, 'group_order': 34992, 'label': '3AE1', 'order': 3, 'powers': [39, 1], 'representative': 127648028533572429677393617359130275803761, 'size': 144}
    • id: 160481726
      {'aut_label': '3AC1', 'centralizer': '144.BH', 'counter': 39, 'group_counter': 167, 'group_order': 34992, 'label': '3AE-1', 'order': 3, 'powers': [38, 1], 'representative': 127648028533572429677396171529535238024885, 'size': 144}
    • id: 160481728
      {'aut_label': '4A', 'centralizer': '1458.A', 'counter': 40, 'group_counter': 167, 'group_order': 34992, 'label': '4A', 'order': 4, 'powers': [4, 40], 'representative': 212138610095647454390875441037605252147469, 'size': 1458}
    • id: 160481729
      {'aut_label': '4A', 'centralizer': '1458.A', 'counter': 41, 'group_counter': 167, 'group_order': 34992, 'label': '4B', 'order': 4, 'powers': [4, 41], 'representative': 106074321674730142433907743279090278300949, 'size': 1458}
    • id: 160481730
      {'aut_label': '4A', 'centralizer': '1458.A', 'counter': 42, 'group_counter': 167, 'group_order': 34992, 'label': '4C', 'order': 4, 'powers': [4, 42], 'representative': 297832370699714447775302157921894171850196, 'size': 1458}
    • id: 160481731
      {'aut_label': '4D', 'centralizer': '4374.A', 'counter': 43, 'group_counter': 167, 'group_order': 34992, 'label': '4D', 'order': 4, 'powers': [4, 43], 'representative': 308169312513967956702268301128880373752254, 'size': 4374}
    • id: 160481732
      {'aut_label': '4D', 'centralizer': '4374.A', 'counter': 44, 'group_counter': 167, 'group_order': 34992, 'label': '4E', 'order': 4, 'powers': [4, 44], 'representative': 202103954309644571062097173016745852010172, 'size': 4374}
    • id: 160481733
      {'aut_label': '4D', 'centralizer': '4374.A', 'counter': 45, 'group_counter': 167, 'group_order': 34992, 'label': '4F', 'order': 4, 'powers': [4, 45], 'representative': 233716382997244270082366102399804631471330, 'size': 4374}
    • id: 160481734
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 46, 'group_counter': 167, 'group_order': 34992, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 138280203173391619202303576836250475722160, 'size': 216}
    • id: 160481735
      {'aut_label': '6B', 'centralizer': '216.A', 'counter': 47, 'group_counter': 167, 'group_order': 34992, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 138279676903180878166120119733590178973040, 'size': 216}
    • id: 160481736
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 48, 'group_counter': 167, 'group_order': 34992, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 20670081850518444302768773709871723292228, 'size': 216}
    • id: 160481737
      {'aut_label': '6D', 'centralizer': '216.A', 'counter': 49, 'group_counter': 167, 'group_order': 34992, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 127651551054290282312040355046494058102547, 'size': 216}
    • id: 160481739
      {'aut_label': '6B', 'centralizer': '216.A', 'counter': 50, 'group_counter': 167, 'group_order': 34992, 'label': '6E', 'order': 6, 'powers': [9, 2], 'representative': 148317592061380768616587736646250346102403, 'size': 216}
    • id: 160481740
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 51, 'group_counter': 167, 'group_order': 34992, 'label': '6F', 'order': 6, 'powers': [10, 2], 'representative': 148317592070527418981915169928132363459440, 'size': 216}
    • id: 160481741
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 52, 'group_counter': 167, 'group_order': 34992, 'label': '6G', 'order': 6, 'powers': [11, 2], 'representative': 127651296128607672201305887681062487139904, 'size': 216}
    • id: 160481742
      {'aut_label': '6B', 'centralizer': '216.A', 'counter': 53, 'group_counter': 167, 'group_order': 34992, 'label': '6H', 'order': 6, 'powers': [12, 2], 'representative': 255290624358587894514392360465779178099011, 'size': 216}
    • id: 160481743
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 54, 'group_counter': 167, 'group_order': 34992, 'label': '6I', 'order': 6, 'powers': [13, 2], 'representative': 148317592079063873853097693550953088100004, 'size': 216}
    • id: 160481744
      {'aut_label': '6A', 'centralizer': '216.A', 'counter': 55, 'group_counter': 167, 'group_order': 34992, 'label': '6J', 'order': 6, 'powers': [14, 2], 'representative': 138280203155708095266530760952041702595440, 'size': 216}
    • id: 160481745
      {'aut_label': '6K', 'centralizer': '1458.C', 'counter': 56, 'group_counter': 167, 'group_order': 34992, 'label': '6K', 'order': 6, 'powers': [15, 4], 'representative': 255591816128162381026078089361829273341565, 'size': 1458}
    • id: 160481746
      {'aut_label': '6L', 'centralizer': '1944.Y', 'counter': 57, 'group_counter': 167, 'group_order': 34992, 'label': '6L', 'order': 6, 'powers': [16, 3], 'representative': 137984962142671195599458745549640651941241, 'size': 1944}
    • id: 160481747
      {'aut_label': '12A', 'centralizer': '2916.F', 'counter': 58, 'group_counter': 167, 'group_order': 34992, 'label': '12A', 'order': 12, 'powers': [56, 40], 'representative': 340081862939523432996064296249088558679185, 'size': 2916}
    • id: 160481748
      {'aut_label': '12A', 'centralizer': '2916.F', 'counter': 59, 'group_counter': 167, 'group_order': 34992, 'label': '12B', 'order': 12, 'powers': [56, 41], 'representative': 361361151875354592684069016176343363632694, 'size': 2916}
    • id: 160481750
      {'aut_label': '12A', 'centralizer': '2916.F', 'counter': 60, 'group_counter': 167, 'group_order': 34992, 'label': '12C', 'order': 12, 'powers': [56, 42], 'representative': 180222520446946888608468430430987033076627, 'size': 2916}
  • gps_qchar • Show schema
    • id: 15773488
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773499
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773510
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773521
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773532
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773540
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773541
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773542
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.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], 'schur_index': 1}
    • id: 15773543
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1], 'schur_index': 1}
    • id: 15773489
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1], 'schur_index': 1}
    • id: 15773490
      {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 1], 'schur_index': 1}
    • id: 15773491
      {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 1], 'schur_index': 1}
    • id: 15773492
      {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2e', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0], 'schur_index': 2}
    • id: 15773493
      {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.2f', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0], 'schur_index': 2}
    • id: 15773494
      {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.4a', 'multiplicity': 1, 'nt': [24, 26], 'qdim': 4, 'qvalues': [4, 0, 0, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 2}
    • id: 15773495
      {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.8a', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
    • id: 15773496
      {'cdim': 8, 'counter': 17, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.8b', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773497
      {'cdim': 8, 'counter': 18, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.8c', 'multiplicity': 1, 'nt': [18, 64], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, -8, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773498
      {'cdim': 8, 'counter': 19, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.8d', 'multiplicity': 1, 'nt': [18, 64], 'qdim': 8, 'qvalues': [8, 0, -8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
    • id: 15773500
      {'cdim': 16, 'counter': 20, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16a', 'multiplicity': 1, 'nt': [18, 293], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, 16, -2, -2, -2, -2, 7, -2, -2, -2, 7, 7, -2, -2, -2, -2, -2, -2, -2, -2, 7, 7, -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], 'schur_index': 1}
    • id: 15773501
      {'cdim': 16, 'counter': 21, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16b', 'multiplicity': 1, 'nt': [18, 293], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, 16, -2, -2, -2, 7, -2, -2, -2, 7, -2, -2, -2, 7, -2, -2, -2, -2, -2, -2, -2, -2, 7, 7, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773502
      {'cdim': 16, 'counter': 22, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16c', 'multiplicity': 1, 'nt': [18, 293], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, 16, -2, -2, 7, -2, -2, -2, -2, -2, -2, -2, 7, -2, 7, -2, -2, -2, -2, -2, -2, -2, -2, -2, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773503
      {'cdim': 16, 'counter': 23, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16d', 'multiplicity': 1, 'nt': [18, 293], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, 16, -2, 7, -2, -2, -2, 7, -2, -2, -2, -2, -2, -2, -2, 7, -2, -2, 7, 7, -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], 'schur_index': 1}
    • id: 15773504
      {'cdim': 16, 'counter': 24, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16e', 'multiplicity': 1, 'nt': [24, 1335], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, -8, 16, -2, -2, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, -2, 1, -8, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773505
      {'cdim': 16, 'counter': 25, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16f', 'multiplicity': 1, 'nt': [24, 1335], 'qdim': 16, 'qvalues': [16, 0, 0, 0, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -8, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773511
      {'cdim': 24, 'counter': 30, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24a', 'multiplicity': 1, 'nt': [27, 529], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -3, -3, -3, -3, -3, -3, -3, 24, -3, -3, 0, 6, -3, -3, -3, 6, 6, -3, 6, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773512
      {'cdim': 24, 'counter': 31, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24b', 'multiplicity': 1, 'nt': [27, 529], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -3, -3, -3, -3, 24, -3, -3, -3, -3, -3, 0, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773513
      {'cdim': 24, 'counter': 32, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24c', 'multiplicity': 1, 'nt': [27, 529], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -3, 24, -3, -3, -3, -3, -3, -3, -3, -3, 0, 6, -3, 6, -3, -3, 6, -3, -3, -3, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773514
      {'cdim': 24, 'counter': 33, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24d', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -3, 6, -3, -3, -12, 15, -3, 6, 6, 0, 6, -3, -3, -3, 6, -3, -3, -3, -3, -3, -3, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 2, -1, -1, -4, 5, -1, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773515
      {'cdim': 24, 'counter': 34, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24e', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -3, 6, -3, -3, 15, -12, -3, 6, 6, 0, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 2, -1, -1, 5, -4, -1, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773516
      {'cdim': 24, 'counter': 35, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24f', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, 6, -3, -12, -3, -3, 6, 6, -3, -12, 15, 0, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -4, -1, -1, 2, 2, -1, -4, 5, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773517
      {'cdim': 24, 'counter': 36, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24g', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, 6, -3, -12, -3, -3, 6, 6, -3, 15, -12, 0, 6, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -4, -1, -1, 2, 2, -1, 5, -4, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773518
      {'cdim': 24, 'counter': 37, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24h', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, 6, -3, 15, -3, -3, 6, 6, -3, -12, -12, 0, 6, 6, -3, -3, -3, -3, -3, -3, 6, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 5, -1, -1, 2, 2, -1, -4, -4, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773519
      {'cdim': 24, 'counter': 38, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24i', 'multiplicity': 1, 'nt': [36, 13950], 'qdim': 24, 'qvalues': [24, 8, 0, 0, 15, -3, 6, -3, -3, -12, -12, -3, 6, 6, 0, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -1, 2, -1, -1, -4, -4, -1, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773520
      {'cdim': 24, 'counter': 39, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24j', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -3, -3, -3, -3, -3, -3, -3, 24, -3, -3, 0, 6, -3, -3, -3, 6, 6, -3, 6, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -8, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773522
      {'cdim': 24, 'counter': 40, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24k', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -3, -3, -3, -3, 24, -3, -3, -3, -3, -3, 0, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -8, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773523
      {'cdim': 24, 'counter': 41, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24l', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -3, 24, -3, -3, -3, -3, -3, -3, -3, -3, 0, 6, -3, 6, -3, -3, 6, -3, -3, -3, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -8, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773524
      {'cdim': 24, 'counter': 42, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24m', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -3, 6, -3, -3, -12, 15, -3, 6, 6, 0, 6, -3, -3, -3, 6, -3, -3, -3, -3, -3, -3, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, -2, 1, 1, 4, -5, 1, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773525
      {'cdim': 24, 'counter': 43, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24n', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -3, 6, -3, -3, 15, -12, -3, 6, 6, 0, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, -2, 1, 1, -5, 4, 1, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773526
      {'cdim': 24, 'counter': 44, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24o', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 6, -3, -12, -3, -3, 6, 6, -3, -12, 15, 0, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 4, 1, 1, -2, -2, 1, 4, -5, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773527
      {'cdim': 24, 'counter': 45, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24p', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 6, -3, -12, -3, -3, 6, 6, -3, 15, -12, 0, 6, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 4, 1, 1, -2, -2, 1, -5, 4, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773528
      {'cdim': 24, 'counter': 46, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24q', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 6, -3, 15, -3, -3, 6, 6, -3, -12, -12, 0, 6, 6, -3, -3, -3, -3, -3, -3, 6, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -5, 1, 1, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773529
      {'cdim': 24, 'counter': 47, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.24r', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 15, -3, 6, -3, -3, -12, -12, -3, 6, 6, 0, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 1, -2, 1, 1, 4, 4, 1, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773506
      {'cdim': 16, 'counter': 26, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16g', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, -4, -4, -4, 32, -4, -4, -4, -4, -4, -4, -16, -4, -4, -4, -4, 14, -4, -4, -4, 14, 14, -4, -4, -4, -4, 2, 2, 2, 2, -7, -7, 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], 'schur_index': 1}
    • id: 15773507
      {'cdim': 16, 'counter': 27, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16h', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, -4, -4, -4, 32, -4, -4, -4, -4, -4, -4, -16, -4, -4, -4, 14, -4, -4, -4, 14, -4, -4, -4, 14, -4, -4, 2, 2, 2, 2, 2, 2, -7, -7, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773508
      {'cdim': 16, 'counter': 28, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16i', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, -4, -4, -4, 32, -4, -4, -4, -4, -4, -4, -16, -4, -4, 14, -4, -4, -4, -4, -4, -4, -4, 14, -4, 14, -4, 2, 2, 2, 2, 2, 2, 2, 2, -7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773509
      {'cdim': 16, 'counter': 29, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.16j', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, -4, -4, -4, 32, -4, -4, -4, -4, -4, -4, -16, -4, 14, -4, -4, -4, 14, -4, -4, -4, -4, -4, -4, -4, 14, 2, 2, -7, -7, 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], 'schur_index': 1}
    • id: 15773530
      {'cdim': 48, 'counter': 48, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, 48, -6, -6, 0, -6, 3, 3, 3, -6, -6, 3, -6, 3, 3, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773531
      {'cdim': 48, 'counter': 49, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -6, -6, -6, -6, 48, -6, -6, -6, -6, -6, 0, -6, 3, 3, -6, 3, -6, 3, 3, -6, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773533
      {'cdim': 48, 'counter': 50, 'faithful': False, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48c', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -6, 48, -6, -6, -6, -6, -6, -6, -6, -6, 0, -6, 3, -6, 3, 3, -6, 3, 3, 3, -6, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773534
      {'cdim': 48, 'counter': 51, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -24, -6, 12, -6, -6, -24, 30, -6, 12, 12, 0, -6, 3, 3, 3, -6, 3, 3, 3, 3, 3, 3, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773535
      {'cdim': 48, 'counter': 52, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -24, -6, 12, -6, -6, 30, -24, -6, 12, 12, 0, -6, 3, -6, 3, 3, 3, 3, -6, -6, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773536
      {'cdim': 48, 'counter': 53, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48f', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, -6, -24, -6, -6, 12, 12, -6, -24, 30, 0, -6, -6, -6, -6, -6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773537
      {'cdim': 48, 'counter': 54, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48g', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, -6, -24, -6, -6, 12, 12, -6, 30, -24, 0, -6, -6, 3, 3, 3, 3, 3, -6, 3, -6, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773538
      {'cdim': 48, 'counter': 55, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48h', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, -6, 30, -6, -6, 12, 12, -6, -24, -24, 0, -6, -6, 3, 3, 3, 3, 3, 3, -6, 3, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15773539
      {'cdim': 48, 'counter': 56, 'faithful': True, 'group': '34992.gk', 'group_order': 34992, 'image': None, 'label': '34992.gk.48i', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 30, -6, 12, -6, -6, -24, -24, -6, 12, 12, 0, -6, 3, 3, -6, 3, 3, 3, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 35745571
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 34992, 'label': '34992.gk.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35745582
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
    • id: 35745593
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
    • id: 35745604
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35745615
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35745626
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
    • id: 35745628
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
    • id: 35745629
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gk.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35745630
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 5832, 'label': '34992.gk.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35745572
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 2916, 'label': '34992.gk.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
    • id: 35745573
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 2916, 'label': '34992.gk.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
    • id: 35745574
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 2916, 'label': '34992.gk.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35745575
      {'center': None, 'center_index': 4, 'center_order': 8748, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': -1, 'kernel': None, 'kernel_order': 4374, 'label': '34992.gk.2e', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745576
      {'center': None, 'center_index': 4, 'center_order': 8748, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': -1, 'kernel': None, 'kernel_order': 4374, 'label': '34992.gk.2f', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745577
      {'center': None, 'center_index': 24, 'center_order': 1458, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '48.40', 'image_order': 48, 'indicator': -1, 'kernel': None, 'kernel_order': 729, 'label': '34992.gk.4a', 'nt': [24, 26], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745578
      {'center': None, 'center_index': 72, 'center_order': 486, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 486, 'label': '34992.gk.8a', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745579
      {'center': None, 'center_index': 72, 'center_order': 486, 'counter': 17, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 486, 'label': '34992.gk.8b', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745580
      {'center': None, 'center_index': 72, 'center_order': 486, 'counter': 18, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '144.187', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gk.8c', 'nt': [18, 64], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745581
      {'center': None, 'center_index': 72, 'center_order': 486, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '144.187', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gk.8d', 'nt': [18, 64], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745583
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 20, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3536', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gk.16a', 'nt': [18, 293], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745584
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 21, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3536', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gk.16b', 'nt': [18, 293], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745585
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3536', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gk.16c', 'nt': [18, 293], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745586
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 23, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3536', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gk.16d', 'nt': [18, 293], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745587
      {'center': None, 'center_index': 432, 'center_order': 81, 'counter': 24, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '432.742', 'image_order': 432, 'indicator': 1, 'kernel': None, 'kernel_order': 81, 'label': '34992.gk.16e', 'nt': [24, 1335], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745588
      {'center': None, 'center_index': 432, 'center_order': 81, 'counter': 25, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '432.742', 'image_order': 432, 'indicator': 1, 'kernel': None, 'kernel_order': 81, 'label': '34992.gk.16f', 'nt': [24, 1335], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745589
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 26, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16g1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-5, 0], [-3, 1]], [[-2, 0], [3, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745590
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 27, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16g2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 1]], [[-5, 0], [-3, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745591
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 28, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16h1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[-5, 0], [-3, 1]], [[-2, 0], [3, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745592
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16h2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [3, 1]], [[-5, 0], [-3, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745594
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 30, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16i1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [3, 1]], [[-5, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745595
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 31, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16i2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[-5, 0], [-3, 1]], [[-2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745596
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 32, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16j1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-8, 0], [-9, 1]], [[1, 0], [9, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745597
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 33, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.16j2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[1, 0], [9, 1]], [[-8, 0], [-9, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745598
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 34, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24a', 'nt': [27, 529], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745599
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 35, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24b', 'nt': [27, 529], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745600
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 36, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24c', 'nt': [27, 529], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745601
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24d', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[15, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745602
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24e', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745603
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24f', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[15, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745605
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24g', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[15, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745606
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24h', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745607
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24i', 'nt': [36, 13950], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745608
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24j', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745609
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24k', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745610
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.24l', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745611
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 46, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24m', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[15, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[-5, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745612
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 47, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24n', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-5, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745613
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 48, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24o', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[15, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745614
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 49, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24p', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[15, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-5, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745616
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 50, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24q', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745617
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 51, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.24r', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745618
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 52, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.48a', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745619
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 53, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.48b', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745620
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 54, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gk.48c', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745621
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48d', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-24, 0]], [[30, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745622
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 56, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48e', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[30, 0]], [[-24, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745623
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48f', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-24, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-24, 0]], [[30, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745624
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 58, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48g', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-24, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[30, 0]], [[-24, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745625
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 59, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48h', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[30, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-24, 0]], [[-24, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35745627
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 60, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gk', 'group_counter': 167, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gk', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gk.48i', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[30, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-24, 0]], [[-24, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 1238 matching records in this table.
    • id: 202369230
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 34992, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '34992.gk.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.gk', 'subgroup_hash': 5851871792559871295, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.(S_3\\times Q_8)', 'supersolvable': False, 'sylow': 0}
    • id: 202369580
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 17496, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4639547612117297113, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^5.C_3:S_3.C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 202369691
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 17496, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2619031437592766887, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.C_3.Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369802
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4675216169102337661, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.C_{12}.C_2', 'supersolvable': False, 'sylow': 0}
    • id: 202369913
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5832, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, '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': '11664.de', 'subgroup_hash': 1928245259206718905, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.(C_2\\times Q_8)', 'supersolvable': False, 'sylow': 0}
    • id: 202370024
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 8748, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4290897417716872382, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^5.C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202370135
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8748, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7900436537566606106, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370246
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8748, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6056940396142048557, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^3.C_3^4.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370357
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.nf', 'subgroup_hash': 8308808951802383450, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369231
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '5832.mh', 'subgroup_hash': 4065257348453030750, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 202369342
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '5832.nf', 'subgroup_hash': 8308808951802383450, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369453
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 4374, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4429614544072327677, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^4.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 202369503
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8244745585140392873, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^5.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369514
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5596956082708510582, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^6.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369525
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.9.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, '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': '3888.dz', 'subgroup_hash': 8113302298439337365, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369536
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.9.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, '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': None, 'subgroup_hash': 4223036449862934994, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4.D_6.C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 202369547
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202369558
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1458, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8062918463383090919, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369569
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7515333107384866523, 'subgroup_order': 2916, 'subgroup_tex': 'C_3.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369581
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7640976462238486466, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4.C_3:S_3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 202369592
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1458, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202369603
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '34992.gk.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, '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': ['F', 'L2', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9106', 'subgroup_hash': 5920808883286947445, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\times C_3^4:C_3', 'supersolvable': True, 'sylow': 3}
    • id: 202369614
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.3904', 'subgroup_hash': 3904, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 202369625
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.2310', 'subgroup_hash': 2310, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 202369636
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.3931', 'subgroup_hash': 3931, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369647
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.3930', 'subgroup_hash': 3930, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369658
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.2336', 'subgroup_hash': 2336, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202369669
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202369680
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.2336', 'subgroup_hash': 2336, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202369692
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202369703
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1458, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1795', 'subgroup_hash': 1795, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369714
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1762', 'subgroup_hash': 1762, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369725
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1762', 'subgroup_hash': 1762, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369736
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1794', 'subgroup_hash': 1794, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369747
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 486, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369758
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1469', 'subgroup_hash': 1469, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369769
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1469', 'subgroup_hash': 1469, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369780
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1797', 'subgroup_hash': 1797, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369791
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1758', 'subgroup_hash': 1758, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369803
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369814
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369825
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369836
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1758', 'subgroup_hash': 1758, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369847
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.27.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, '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': '1296.3581', 'subgroup_hash': 3581, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202369858
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.27.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, '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': '1296.3536', 'subgroup_hash': 3536, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2\\times Q_8)', 'supersolvable': False, 'sylow': 0}
    • id: 202369869
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.27.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, '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': '1296.3536', 'subgroup_hash': 3536, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2\\times Q_8)', 'supersolvable': False, 'sylow': 0}
    • id: 202369880
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.890', 'subgroup_hash': 890, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369891
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.890', 'subgroup_hash': 890, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369902
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369914
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369925
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369936
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369947
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369958
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369969
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202369980
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.456', 'subgroup_hash': 456, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202369991
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.882', 'subgroup_hash': 882, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370002
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.883', 'subgroup_hash': 883, 'subgroup_order': 972, 'subgroup_tex': 'C_3^5:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370013
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370025
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370036
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370047
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370058
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370069
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370080
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.36.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202370091
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 729, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 202370102
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370113
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370124
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370136
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370147
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370158
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370169
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.498', 'subgroup_hash': 498, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370180
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.48.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.498', 'subgroup_hash': 498, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370191
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.745', 'subgroup_hash': 745, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202370202
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 202370213
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 202370224
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 202370235
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370247
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370258
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370269
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370280
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370291
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370302
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370313
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370324
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.54.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202370335
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 486, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370346
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 486, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370358
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.256', 'subgroup_hash': 256, 'subgroup_order': 486, 'subgroup_tex': 'S_3\\times C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 202370369
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.256', 'subgroup_hash': 256, 'subgroup_order': 486, 'subgroup_tex': 'S_3\\times C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 202370380
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.256', 'subgroup_hash': 256, 'subgroup_order': 486, 'subgroup_tex': 'S_3\\times C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 202370391
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370402
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370413
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370424
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370435
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202370446
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202370457
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202369232
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gk', 'ambient_counter': 167, 'ambient_order': 34992, 'ambient_tex': 'C_3^6.(S_3\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gk.72.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 1238 matching records in this table.
    • id: 202369230
      {'ambient': '34992.gk', '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': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.A', '2.B', '2.C', '3.a1', '9.A', '9.B'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9684, 6318, 9644, 3247], 'generators': [10631640421497648346633457090865944853364, 265924700981089824612497257486013004984243, 287207520660161682126837036330915041206916, 10628380783110079667891945245656009369843, 339786367000805117682586349328554681397243, 295241030720035824849169818559470203785, 9146650338356281619235829943283, 20666295950456232649488742324945953488788, 526279357810177215774797298686100004, 9146650338351416191655337984144, 806582922253211364573312003], 'label': '34992.gk.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.A', '2.B', '2.C'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '4032.cr'}
    • id: 202369231
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.A', '3.a1'], 'contains': ['12.A', '12.B', '12.E', '54.A', '54.B', '54.C', '54.D'], 'core': '12.A', 'coset_action_label': None, 'count': 9, 'diagramx': [9558, -1, 9068, -1], 'generators': [10631640421497648346633457090865944853364, 10628380783110079667891945245656009369843, 106068888939343826035254314259324930948455, 295241030720035824849169818559470203785, 9146650338356281619235829943283, 20666295950456232649488742324945953488788, 526279357810177215774797298686100004, 9146650338351416191655337984144, 806582922253211364573312003], 'label': '34992.gk.6.B', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': '5000.cl'}
    • id: 202369232
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.D', '36.D'], 'contains': ['144.Y', '216.H', '216.I', '216.S', '216.T', '216.U', '216.BB', '216.BC'], 'core': '3888.A', 'coset_action_label': None, 'count': 36, 'diagramx': [3187, -1, 4912, -1], 'generators': [10631640421497648346633457090865944853364, 9147456921278534830332641360884, 20666295950456232649488742324945953488788, 526279357810177215774797298686100004, 10628380783109691887640861971087360640244, 9146650338351416191655337984144], 'label': '34992.gk.72.M', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.B', 'old_label': '72.m1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.M', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202369233
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.D', '648.K', '648.P', '648.U', '648.Z', '972.O'], 'contains': ['3888.C', '5832.A', '5832.D'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1944, -1, 4166, -1], 'generators': [3785917745347912217250924713890588320, 526261673867387065200240040673325360, 255296320207126814112601361622871674510864], 'label': '34992.gk.1944.I', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '1944.i1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.I', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369234
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.E', '648.G', '648.L', '648.M', '648.Q', '648.R', '648.V', '648.BA', '648.BN', '972.I'], 'contains': ['3888.D', '5832.A', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [2900, -1, 5049, -1], 'generators': [526270820936528085474734892998784240, 806582922253211364573312003, 3259656072287108074303896037790574963], 'label': '34992.gk.1944.J', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.j1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.J', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369235
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.F', '648.M', '648.R', '648.W', '648.BA', '648.BN', '972.J'], 'contains': ['3888.E', '5832.A', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2941, -1, 5082, -1], 'generators': [3259646925636769722888792367526766867, 9147069141022586128451262566548, 526279357810177213463205545328768000], 'label': '34992.gk.1944.K', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.k1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.K', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369236
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.H', '648.I', '648.N', '648.O', '648.S', '648.T', '648.X', '648.BB'], 'contains': ['3888.L', '5832.A', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [236, -1, 1070, -1], 'generators': [10631911783710109867216985052201900389764, 20666822212130487868504194224683767943203, 265924446055408021109412815676148899035667], 'label': '34992.gk.1944.L', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.l1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.L', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369237
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.J', '648.O', '648.T', '648.Y', '648.BB'], 'contains': ['3888.P', '5832.A', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [189, -1, 1114, -1], 'generators': [255296065307665796001649933292197483701123, 10632166691708777163077729076127596892083, 10628907036247073405829157056889932487107], 'label': '34992.gk.1944.M', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.m1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.M', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369238
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.D', '648.K', '648.P', '648.BC', '648.BH', '972.P'], 'contains': ['3888.V', '5832.B', '5832.D'], 'core': '34992.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2068, -1, 4193, -1], 'generators': [526279358197957466858071867334829603, 3531018284360848406748582805097381764, 255296320207126814112601361622871674510864], 'label': '34992.gk.1944.N', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '1944.n1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.N', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369239
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.E', '648.G', '648.L', '648.M', '648.R', '648.BD', '648.BI', '648.BO', '972.K'], 'contains': ['3888.W', '5832.B', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [2970, -1, 5022, -1], 'generators': [10631640412350998008282041987195681045268, 10628380783109691887640861971087360640244, 20666822212130487868501882632917956569604], 'label': '34992.gk.1944.O', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.o1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.O', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369240
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.F', '648.L', '648.Q', '648.BE', '648.BI', '648.BO', '972.L'], 'contains': ['3888.X', '5832.B', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2914, -1, 4996, -1], 'generators': [20666822194446963881022479058595362777748, 10628380774572818238512873542280610432148, 10631640430034521995761445561518274837124], 'label': '34992.gk.1944.P', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.p1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.P', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369241
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.H', '648.I', '648.N', '648.O', '648.T', '648.BF', '648.BJ'], 'contains': ['3888.BE', '5832.B', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [168, -1, 1011, -1], 'generators': [526270820936528087786368491935891908, 3259656071480525152050684673217262960, 275962616130752841362132853161800181457987], 'label': '34992.gk.1944.Q', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.q1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.Q', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369242
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.J', '648.N', '648.S', '648.BG', '648.BJ'], 'contains': ['3888.BI', '5832.B', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [294, -1, 1140, -1], 'generators': [20670081850518056549493707525448802665124, 20666822194446576100773706329653031021364, 265924446064555090250435400716347325531764], 'label': '34992.gk.1944.R', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.r1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.R', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369243
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.B', '36.I'], 'contains': ['144.BA', '216.L', '216.N', '216.O', '216.Q', '216.V'], 'core': '34992.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1162, -1, 3071, -1], 'generators': [9147069141027451555776446672880, 9147069141022586128451262566548, 10631640421498036126884540365434593582963, 275962361222754980676172690361166748808884, 526279357810177215774797298686100004, 10628380783109691887640861971087360640244], 'label': '34992.gk.72.N', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '72.n1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.N', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369244
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.D', '648.U', '648.BC', '648.BK', '648.BP', '972.Q'], 'contains': ['3888.BK', '5832.C', '5832.D'], 'core': '34992.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [812, -1, 3214, -1], 'generators': [526279357810177215774797298686100004, 255296065307665796026375638381161686818723, 3259656071480525152050684673217262960], 'label': '34992.gk.1944.S', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '1944.s1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.S', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369245
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.E', '648.F', '648.V', '648.BD', '648.BL', '648.BR', '972.M'], 'contains': ['3888.BL', '5832.C', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2860, -1, 4791, -1], 'generators': [526270820517725414304798352382054643, 20666822194446963881024789604221679750963, 10631911775173236218088996581549570406004], 'label': '34992.gk.1944.T', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.t1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.T', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369246
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.G', '648.W', '648.BE', '648.BL', '648.BP', '648.BQ', '648.BR', '972.N'], 'contains': ['3888.BM', '5832.C', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [936, -1, 3586, -1], 'generators': [526279357810177215774797298686100004, 17684330570406523300984971344644, 3259656071480525152050684673217262960], 'label': '34992.gk.1944.U', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.A', 'old_label': '1944.u1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.U', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369247
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.H', '648.Y', '648.BG', '648.BM', '648.BP'], 'contains': ['3888.BZ', '5832.C', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [775, -1, 1793, -1], 'generators': [265924700963405912844766770636866454609984, 10628907036246266822906903845525359175104, 10632166691707970580155475864763023580080], 'label': '34992.gk.1944.V', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.v1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.V', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369248
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.I', '648.J', '648.X', '648.BF', '648.BM', '648.BQ'], 'contains': ['3888.CA', '5832.C', '5832.F'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [37, -1, 984, -1], 'generators': [265924446064554671447764230779819162843763, 20666822194446963881024789604221679750963, 10631911775173236218088996581549570406004], 'label': '34992.gk.1944.W', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '1944.v2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.W', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 202369249
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.BN', '648.BO', '648.BR', '972.R'], 'contains': ['3888.CJ', '5832.E'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3059, -1, 5134, -1], 'generators': [526270820517725414304798352382054643, 3259656071480525152050684673217262960, 526279357391401518310358882801625744], 'label': '34992.gk.1944.X', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1944.w1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.X', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369250
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.Y', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.BS', '648.BT', '648.BU', '972.R'], 'contains': ['3888.CJ', '5832.G'], 'core': '34992.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [4497, -1, 5383, -1], 'generators': [526270820517725414304798352382054643, 20965322872091829840960829206593966365706, 526279357391401518310358882801625744], 'label': '34992.gk.1944.Y', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.C', 'old_label': '1944.x1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.Y', 'subgroup_fusion': None, 'weyl_group': '8.4'}
    • id: 202369251
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.BS', '648.BV', '648.BX', '648.BY', '648.BZ', '648.CA', '648.CB', '648.CC', '648.CE', '972.I'], 'contains': ['3888.D', '5832.G', '5832.H'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [3793, -1, 5315, -1], 'generators': [526270820936528085474734892998784240, 806582922253211364573312003, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.Z', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.Z', 'old_label': '1944.y1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.Z', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369252
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.BS', '648.BW', '648.BZ', '648.CB', '648.CD', '648.CE', '972.J'], 'contains': ['3888.E', '5832.G', '5832.H'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [3897, -1, 5342, -1], 'generators': [9147069141022586128451262566548, 526279357810177213463205545328768000, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.Z', 'old_label': '1944.z1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BA', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369253
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.BT', '648.BV', '648.BX', '648.BY', '648.BZ', '648.CB', '648.CF', '648.CH', '972.K'], 'contains': ['3888.W', '5832.G', '5832.I'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [3999, -1, 5288, -1], 'generators': [10628380783109691887640861971087360640244, 20666822212130487868501882632917956569604, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BA', 'old_label': '1944.ba1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BB', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369254
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.C'], 'contains': ['144.BC', '216.N', '216.P', '216.R', '216.W'], 'core': '34992.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [483, -1, 999, -1], 'generators': [526279357810177215774797298686100004, 10631640421497229543962287154070020270960, 265924700981089824612497257486013004984243, 9147456921273669403019911296147, 10628380783109691887640861971087360640244, 9146650338356281619235829943283], 'label': '34992.gk.72.O', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.C', 'old_label': '72.o1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.O', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369255
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.BT', '648.BW', '648.BY', '648.CA', '648.CG', '648.CH', '972.L'], 'contains': ['3888.X', '5832.G', '5832.I'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [4046, -1, 5262, -1], 'generators': [20666822194446963881022479058595362777748, 10628380774572818238512873542280610432148, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BA', 'old_label': '1944.bb1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BC', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369256
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.BU', '648.BV', '648.BW', '648.CC', '648.CF', '648.CL', '972.M'], 'contains': ['3888.BL', '5832.G', '5832.J'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [3353, -1, 5170, -1], 'generators': [526270820517725414304798352382054643, 10628380783110079667891945245656009369843, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BD', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BB', 'old_label': '1944.bc1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BD', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369257
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.BU', '648.BX', '648.CD', '648.CG', '648.CI', '648.CJ', '648.CK', '648.CL', '972.N'], 'contains': ['3888.BM', '5832.G', '5832.J'], 'core': '34992.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [2701, -1, 4325, -1], 'generators': [526279357810177215774797298686100004, 17684330570406523300984971344644, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BB', 'old_label': '1944.bd1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BE', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369258
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.CM', '648.CO', '648.CP', '648.CQ', '648.CS', '972.O'], 'contains': ['3888.C', '5832.H', '5832.K', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [2172, -1, 4284, -1], 'generators': [526261673867387065200240040673325360, 275962361222754174093250437149814629538480, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.O', 'old_label': '1944.be1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BF', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369259
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.CN', '648.CO', '648.CP', '648.CR', '648.CS'], 'contains': ['3888.O', '5832.H', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [2335, -1, 4248, -1], 'generators': [526261673867387065200240040673325360, 265924446073091963847857044787086652514724, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.BG', 'old_label': '1944.bf1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BG', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369260
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.BV', '648.BW', '648.BX', '648.CM', '648.CN', '648.CT', '648.CU', '648.CV', '972.A'], 'contains': ['3888.Q', '5832.H', '5832.I', '5832.J'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [3129, -1, 4516, -1], 'generators': [9146650338351416191655337984144, 10628907036246266822906903845525359175104, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.K', 'old_label': '1944.bg1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BH', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369261
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.BY', '648.BZ', '648.CO', '648.CU', '648.CV', '972.B'], 'contains': ['3888.R', '5832.H', '5832.I'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [3251, -1, 4832, -1], 'generators': [9146650338351416191655337984144, 20666822194446157298102536392857106438960, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BI', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.L', 'old_label': '1944.bh1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BI', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369262
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.CA', '648.CB', '648.CP', '648.CU', '648.CV', '972.C'], 'contains': ['3888.S', '5832.H', '5832.I'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [3268, -1, 4814, -1], 'generators': [526261673867387065200240040673325360, 10628380774572818238512873542280610432148, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.M', 'old_label': '1944.bi1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BJ', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369263
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.CC', '648.CD', '648.CQ', '648.CR', '648.CT', '648.CV', '972.D'], 'contains': ['3888.T', '5832.H', '5832.J'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2871, -1, 4365, -1], 'generators': [526261674286189736370176836597907764, 10628380765426555680412540625193921177603, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.N', 'old_label': '1944.bj1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BK', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369264
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.CE', '648.CS', '648.CV', '972.E'], 'contains': ['3888.U', '5832.H'], 'core': '34992.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [3704, -1, 5225, -1], 'generators': [9147456921273669403019911296147, 20666822194446157298102536392857106438960, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.B', 'old_label': '1944.bk1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BL', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 202369265
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.A', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.D', '36.E'], 'contains': ['144.BE', '216.M', '216.N', '216.S', '216.T', '216.U', '216.X', '216.Y'], 'core': '34992.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2878, -1, 4949, -1], 'generators': [10628380783110079667891945245656009369843, 526279357391374544604860502761517600, 20666295950456232649488742324945953488788, 9146650338351416191655337984144, 9146650338356281619235829943283, 10632166674025253175598325501805003100227], 'label': '34992.gk.72.P', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.B', 'old_label': '72.p1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.P', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202369266
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.CM', '648.CO', '648.CP', '648.CW', '648.CY', '972.P'], 'contains': ['3888.V', '5832.I', '5832.K', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [2193, -1, 4302, -1], 'generators': [526270820936528087786368491935891908, 275962361222754174093250437149814629538480, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.P', 'old_label': '1944.bl1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BM', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369267
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.CN', '648.CO', '648.CP', '648.CX', '648.CY'], 'contains': ['3888.BH', '5832.I', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [2307, -1, 4266, -1], 'generators': [526279358197957466858071867334829603, 265924446073091963847857044787086652514724, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.BN', 'old_label': '1944.bm1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BN', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369268
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.CF', '648.CG', '648.CT', '648.CU', '648.CW', '648.CX', '972.F'], 'contains': ['3888.BJ', '5832.I', '5832.J'], 'core': '34992.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2711, -1, 4347, -1], 'generators': [10628380783110079667891945245656009369843, 526270821324308338869643060584621507, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.P', 'old_label': '1944.bn1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BO', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369269
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.CH', '648.CU', '648.CY', '972.G'], 'contains': ['3888.A', '5832.I'], 'core': '3888.A', 'coset_action_label': None, 'count': 81, 'diagramx': [4182, -1, 5192, -1], 'generators': [526270820936528087786368491935891908, 10628380783109691887640861971087360640244, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.B', 'old_label': '1944.bo1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BP', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369270
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.CI', '648.CM', '648.CQ', '648.CW', '648.CZ', '972.Q'], 'contains': ['3888.BK', '5832.J', '5832.K'], 'core': '34992.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [946, -1, 3370, -1], 'generators': [526279357810177215774797298686100004, 275962361222754174093250437149814629538480, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BC', 'old_label': '1944.bp1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BQ', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 202369271
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.CJ', '648.CM', '648.CN', '648.CR', '648.CX', '648.DA'], 'contains': ['3888.BX', '5832.J', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [2287, -1, 3334, -1], 'generators': [526279357810177215774797298686100004, 298500669108380115792016598290387402829, 265924446064554283615806803146927783036224], 'label': '34992.gk.1944.BR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.CJ', 'old_label': '1944.bq1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BR', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369272
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.CK', '648.CN', '648.CQ', '648.CW', '648.DA'], 'contains': ['3888.BY', '5832.J', '5832.L'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [1369, -1, 3352, -1], 'generators': [526279357810177215774797298686100004, 275962361240438085860980925045100674313123, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.CK', 'old_label': '1944.bq2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BS', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369273
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.X', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.CL', '648.CT', '648.CZ', '648.DA', '972.H'], 'contains': ['3888.B', '5832.J'], 'core': '3888.B', 'coset_action_label': None, 'count': 27, 'diagramx': [2497, -1, 3635, -1], 'generators': [526279357810177215774797298686100004, 10628380783110079667891945245656009369843, 298500669108380115792016598290387402829], 'label': '34992.gk.1944.BT', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.C', 'old_label': '1944.br1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BT', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369274
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.D', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.DB', '648.DC', '648.DD', '648.DE', '648.DF', '972.O'], 'contains': ['3888.C', '5832.M', '5832.N'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [2032, -1, 4442, -1], 'generators': [265924972334765024651997437268666620971680, 526261673867387065200240040673325360, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BU', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.O', 'old_label': '1944.bs1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BU', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369275
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.D', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.DB', '648.DC', '648.DD', '648.DG', '648.DH', '972.P'], 'contains': ['3888.V', '5832.M', '5832.O'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [2048, -1, 4469, -1], 'generators': [265924972334765024651997437268666620971680, 526279358197957466858071867334829603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BV', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.P', 'old_label': '1944.bt1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BV', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369276
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '24.G', '24.H', '36.C'], 'contains': ['144.O', '216.BG', '216.BJ', '216.BL', '216.BN', '216.BS', '216.BT'], 'core': '432.B', 'coset_action_label': None, 'count': 36, 'diagramx': [3057, -1, 4415, -1], 'generators': [526279357810177215774797298686100004, 10628380783110079667891945245656009369843, 9147456921278534830332641360884, 9146650338351416191655337984144, 20965322872091829840960829206593966365706, 20666295950455813846817572388150028906384], 'label': '34992.gk.72.Q', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.C', 'old_label': '72.q1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Q', 'subgroup_fusion': None, 'weyl_group': '108.44'}
    • id: 202369277
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DB', '648.DE', '648.DG', '648.DI', '648.DJ', '648.DK', '648.DL', '648.DM', '648.DN', '972.Q'], 'contains': ['3888.BK', '5832.M', '5832.P'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [1564, -1, 3865, -1], 'generators': [526279357810177215774797298686100004, 265924446064555090198729056358279902306628, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.Q', 'old_label': '1944.bu1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BW', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 202369278
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DO', '648.DT', '648.DU', '648.DV', '648.DW', '648.DX', '648.DY', '648.DZ', '648.EA', '648.EB', '648.ET', '648.EV', '648.FB', '648.FC', '648.FF', '648.FG', '648.FJ', '648.FO', '972.I'], 'contains': ['3888.D', '5832.N', '5832.Q', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [7187, -1, 7641, -1], 'generators': [9147456921273669403019911296147, 9146650338356281619235829943283, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.I', 'old_label': '1944.bv1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BX', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369279
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.DP', '648.DQ', '648.DR', '648.DS', '648.EA', '648.EB', '648.EU', '648.FC', '648.FG', '648.FK', '648.FO', '972.J'], 'contains': ['3888.E', '5832.N', '5832.Q', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [7266, -1, 7623, -1], 'generators': [9147069141022586128451262566548, 526279357810177213463205545328768000, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.J', 'old_label': '1944.bw1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BY', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369280
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DP', '648.DQ', '648.DT', '648.DU', '648.DV', '648.EG', '648.EH', '648.EI', '648.EJ', '648.EK', '648.EL', '648.EM', '648.EN', '648.EO', '648.EW', '648.EX', '648.FB', '648.FD', '648.FF', '648.FH', '648.FL', '648.FP'], 'contains': ['3888.F', '5832.N', '5832.R', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [7485, -1, 8273, -1], 'generators': [10628380765426555680417407140491725418388, 526279357391374544604860502761517600, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.BZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.BZ', 'old_label': '1944.bx1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.BZ', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369281
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DP', '648.DS', '648.DU', '648.DW', '648.DX', '648.ED', '648.EF', '648.EG', '648.EI', '648.EL', '648.EM', '648.EQ', '648.ER', '648.ES', '648.EW', '648.EY', '648.FD', '648.FE', '648.FG', '648.FI', '648.FL', '648.FO', '648.FP'], 'contains': ['3888.G', '5832.N', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [8171, -1, 8382, -1], 'generators': [526279357391374544604860502761517600, 9146650338356281619235829943283, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CA', 'old_label': '1944.by1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CA', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369282
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DQ', '648.DS', '648.DT', '648.DW', '648.DY', '648.ED', '648.EE', '648.EG', '648.EH', '648.EK', '648.EN', '648.EP', '648.EQ', '648.ES', '648.EW', '648.EY', '648.FC', '648.FE', '648.FH', '648.FI', '648.FL', '648.FO', '648.FP'], 'contains': ['3888.H', '5832.N', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [8163, -1, 8364, -1], 'generators': [526279357391374544604860502761517600, 20666295950456232701192776179245209770240, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CB', 'old_label': '1944.by2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CB', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369283
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DO', '648.DR', '648.DZ', '648.EA', '648.EC', '648.EK', '648.EL', '648.EM', '648.EN', '648.EO', '648.EP', '648.EQ', '648.ER', '648.ES', '648.ET', '648.EZ', '648.FD', '648.FE', '648.FH', '648.FI', '648.FJ', '648.FP'], 'contains': ['3888.I', '5832.N', '5832.R', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [8707, -1, 8436, -1], 'generators': [526279357391374544604860502761517600, 20666295932772708713713372604922615978384, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CC', 'old_label': '1944.bz1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CC', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369284
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DT', '648.DU', '648.DV', '648.DW', '648.DX', '648.DY', '648.EK', '648.EL', '648.EM', '648.EN', '648.EO', '648.EP', '648.EQ', '648.ER', '648.ES', '648.FA', '648.FC', '648.FD', '648.FG', '648.FH', '648.FM', '648.FO', '648.FP'], 'contains': ['3888.J', '5832.N', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [7748, -1, 8400, -1], 'generators': [20666822203593614219373894162265626585844, 9147069141022586128451262566548, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CD', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CD', 'old_label': '1944.ca1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CD', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369285
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.DO', '648.DZ', '648.EC', '648.ED', '648.EE', '648.EF', '648.EG', '648.EH', '648.EI', '648.EJ', '648.EU', '648.FD', '648.FH', '648.FN', '648.FP'], 'contains': ['3888.K', '5832.N', '5832.S', '5832.T', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [7808, -1, 8291, -1], 'generators': [9147069141022586128451262566548, 295241030720035824849169818559470203785, 10628380783110079667896810714814319210244], 'label': '34992.gk.1944.CE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CE', 'old_label': '1944.cb1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CE', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369286
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DB', '648.ET', '648.EU', '648.EV', '648.EW', '648.EX', '648.EY', '648.EZ', '648.FA', '648.FQ', '648.FR', '648.FS', '972.A'], 'contains': ['3888.Q', '5832.N', '5832.O', '5832.P'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [3207, -1, 7007, -1], 'generators': [10628380783110079667891945245656009369843, 526261674286189736370176836597907764, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.R', 'old_label': '1944.cc1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CF', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369287
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.H', '36.D'], 'contains': ['144.Y', '216.BG', '216.BH', '216.BI', '216.BL', '216.BM', '216.BU', '216.BV'], 'core': '3888.A', 'coset_action_label': None, 'count': 108, 'diagramx': [4056, -1, 5457, -1], 'generators': [271371359918441854642440543658029364, 20666822203593614167669861395963898521603, 526279358197957466858071867334829603, 10628380783109691887640861971087360640244, 9146650338351416191655337984144, 20965322872091829840960829206593966365706], 'label': '34992.gk.72.R', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '72.r1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.R', 'subgroup_fusion': None, 'weyl_group': '108.44'}
    • id: 202369288
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DC', '648.FB', '648.FC', '648.FD', '648.FE', '648.FR', '648.FS', '972.B'], 'contains': ['3888.R', '5832.N', '5832.O'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [4917, -1, 7148, -1], 'generators': [9146650338351416191655337984144, 295241030720035824849169818559470203785, 20666822194446157298102536392857106438960], 'label': '34992.gk.1944.CG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.S', 'old_label': '1944.cd1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CG', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369289
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.DD', '648.FF', '648.FG', '648.FH', '648.FI', '648.FR', '648.FS', '972.C'], 'contains': ['3888.S', '5832.N', '5832.O'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [4808, -1, 7112, -1], 'generators': [526261673867387065200240040673325360, 10628380774572818238512873542280610432148, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.T', 'old_label': '1944.ce1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CH', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369290
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.DE', '648.FJ', '648.FK', '648.FL', '648.FM', '648.FN', '648.FQ', '648.FS', '972.D'], 'contains': ['3888.T', '5832.N', '5832.P'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [3161, -1, 6971, -1], 'generators': [526261674286189736370176836597907764, 10628380765426555680412540625193921177603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CI', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.U', 'old_label': '1944.cf1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CI', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369291
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DF', '648.FO', '648.FP', '648.FS', '972.E', '972.S', '972.T'], 'contains': ['3888.U', '5832.N'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [7302, -1, 7659, -1], 'generators': [526261673867387065200240040673325360, 10628380765425749097490287413829347865600, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.A', 'old_label': '1944.cg1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CJ', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 202369292
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.ET', '648.EV', '648.FB', '648.FC', '648.FG', '648.FX', '648.FY', '648.FZ', '648.GA', '648.GB', '648.GC', '648.GD', '648.GE', '648.GP', '648.GU', '972.K'], 'contains': ['3888.W', '5832.O', '5832.Q', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 8748, 'diagramx': [7293, -1, 7605, -1], 'generators': [10628380783109691887640861971087360640244, 20666822212130487868501882632917956569604, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.K', 'old_label': '1944.ch1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CK', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369293
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.EU', '648.FB', '648.FF', '648.FT', '648.FU', '648.FV', '648.FW', '648.GC', '648.GE', '648.GQ', '648.GU', '972.L'], 'contains': ['3888.X', '5832.O', '5832.Q', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [7226, -1, 7440, -1], 'generators': [20666822194446963881022479058595362777748, 10628380774572818238512873542280610432148, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.L', 'old_label': '1944.ci1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CL', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369294
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.EW', '648.EX', '648.FB', '648.FD', '648.FH', '648.FV', '648.FW', '648.FY', '648.FZ', '648.GF', '648.GG', '648.GJ', '648.GK', '648.GL', '648.GR', '648.GU'], 'contains': ['3888.Y', '5832.O', '5832.R', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [7934, -1, 8047, -1], 'generators': [20666295950456232701192776179245209770240, 526270820936528087786368491935891908, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CM', 'old_label': '1944.cj1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CM', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369295
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.EW', '648.EY', '648.FC', '648.FD', '648.FE', '648.FG', '648.FH', '648.FT', '648.FV', '648.FY', '648.GA', '648.GB', '648.GF', '648.GG', '648.GI', '648.GJ', '648.GK', '648.GM', '648.GN', '648.GO', '648.GR', '648.GV'], 'contains': ['3888.Z', '5832.O', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [8617, -1, 8219, -1], 'generators': [10628380765426555680417407140491725418388, 526270820936528087786368491935891908, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CN', 'old_label': '1944.ck1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CN', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369296
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.ET', '648.EZ', '648.FD', '648.FE', '648.FH', '648.FU', '648.FX', '648.GC', '648.GD', '648.GH', '648.GJ', '648.GK', '648.GL', '648.GM', '648.GN', '648.GO', '648.GP', '648.GV'], 'contains': ['3888.BA', '5832.O', '5832.R', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [8931, -1, 8201, -1], 'generators': [526270820936528087786368491935891908, 10628380783109691887645727440258124522240, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CO', 'old_label': '1944.cl1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CO', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369297
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.FA', '648.FB', '648.FE', '648.FI', '648.FY', '648.GB', '648.GK', '648.GL', '648.GM', '648.GO', '648.GS', '648.GV'], 'contains': ['3888.BB', '5832.O', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [8843, -1, 8165, -1], 'generators': [20666295950456232701192776179245209770240, 10628380774572818238512873542280610432148, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CP', 'old_label': '1944.cm1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CP', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369298
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.CJ', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.H', '36.E'], 'contains': ['144.BE', '216.BG', '216.BH', '216.BI', '216.BJ', '216.BK', '216.BW', '216.BX'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4021, -1, 5563, -1], 'generators': [526279357810177215774797298686100004, 9147456921273669403019911296147, 10628380783109691887640861971087360640244, 20965322872091829840960829206593966365706, 9146650338356281619235829943283, 20666295950455813846817572388150028906384], 'label': '34992.gk.72.S', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.s1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.S', 'subgroup_fusion': None, 'weyl_group': '108.44'}
    • id: 202369299
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.FA', '648.FE', '648.FF', '648.FZ', '648.GA', '648.GJ', '648.GN', '648.GS', '648.GU'], 'contains': ['3888.BC', '5832.O', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [7862, -1, 7847, -1], 'generators': [10628380774572818238512873542280610432148, 9146650338356281619235829943283, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CQ', 'old_label': '1944.cm2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CQ', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369300
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.EU', '648.FE', '648.FI', '648.FX', '648.GD', '648.GF', '648.GG', '648.GH', '648.GI', '648.GT', '648.GV'], 'contains': ['3888.BD', '5832.O', '5832.T', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [9302, -1, 8147, -1], 'generators': [10628380774572818238512873542280610432148, 526279357810177213463205545328768000, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CR', 'old_label': '1944.cn1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CR', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369301
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DG', '648.FQ', '648.FR', '648.GP', '648.GQ', '648.GR', '648.GS', '648.GT', '972.F'], 'contains': ['3888.BJ', '5832.O', '5832.P'], 'core': '34992.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [3030, -1, 6917, -1], 'generators': [10628380783110079667891945245656009369843, 526270821324308338869643060584621507, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.W', 'old_label': '1944.co1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CS', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369302
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.DH', '648.FR', '648.GU', '648.GV', '972.G', '972.U', '972.V'], 'contains': ['3888.A', '5832.O'], 'core': '3888.A', 'coset_action_label': None, 'count': 243, 'diagramx': [9327, -1, 7677, -1], 'generators': [526270820936528087786368491935891908, 10628380783109691887640861971087360640244, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CT', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.A', 'old_label': '1944.cp1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CT', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369303
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.ET', '648.EU', '648.FJ', '648.GP', '648.GW', '648.GX', '648.GY', '648.GZ', '648.HC', '648.HD', '648.HQ', '972.M'], 'contains': ['3888.BL', '5832.P', '5832.Q', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [4170, -1, 7130, -1], 'generators': [526270820517725414304798352382054643, 10628380783110079667891945245656009369843, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CU', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.M', 'old_label': '1944.cq1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CU', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 202369304
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DI', '648.EV', '648.FK', '648.GQ', '648.HA', '648.HB', '648.HD', '648.HQ', '972.N'], 'contains': ['3888.BM', '5832.P', '5832.Q'], 'core': '34992.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [3146, -1, 6953, -1], 'generators': [526279357810177215774797298686100004, 17684330570406523300984971344644, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CV', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BC', 'old_label': '1944.cr1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CV', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 202369305
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DJ', '648.EV', '648.EX', '648.EY', '648.EZ', '648.FM', '648.GS', '648.GW', '648.GZ', '648.HG', '648.HI', '648.HM', '648.HN', '648.HR'], 'contains': ['3888.BO', '5832.P', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [3818, -1, 7166, -1], 'generators': [17683523987484270089888159927043, 526279357810177215774797298686100004, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.DJ', 'old_label': '1944.cs1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CW', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369306
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.ET', '648.EW', '648.FA', '648.FL', '648.GR', '648.GW', '648.GZ', '648.HA', '648.HE', '648.HF', '648.HH', '648.HI', '648.HJ', '648.HK', '648.HM', '648.HN', '648.HR'], 'contains': ['3888.BN', '5832.P', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [6950, -1, 7522, -1], 'generators': [20666822194446963881024789604221679750963, 295241030720035824849169818559470203785, 271353676394454375238866221064237508], 'label': '34992.gk.1944.CX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CX', 'old_label': '1944.cs2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CX', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369307
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.EW', '648.FA', '648.FJ', '648.GP', '648.GX', '648.GY', '648.HB', '648.HG', '648.HI', '648.HL', '648.HM', '648.HN', '648.HR'], 'contains': ['3888.BP', '5832.P', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [4476, -1, 7459, -1], 'generators': [806582927119726662377552788, 20666822194446963881024789604221679750963, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CY', 'old_label': '1944.cs3', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CY', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369308
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.EU', '648.EW', '648.FL', '648.GR', '648.GW', '648.HA', '648.HE', '648.HF', '648.HG', '648.HH', '648.HI', '648.HO', '648.HP', '648.HS'], 'contains': ['3888.BQ', '5832.P', '5832.S', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [7047, -1, 7491, -1], 'generators': [20666822194446963881024789604221679750963, 526279357810177213463205545328768000, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.CZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.CZ', 'old_label': '1944.ct1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.CZ', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369309
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '36.J'], 'contains': ['144.B', '216.BN', '216.CA'], 'core': '144.B', 'coset_action_label': None, 'count': 9, 'diagramx': [2004, -1, 3275, -1], 'generators': [526279357810177215774797298686100004, 10628380783110079667891945245656009369843, 17684330570406523300984971344644, 20666295941918940197689585005482773098240, 265924700963405912844766770636866454609984, 20965322872091829840960829206593966365706], 'label': '34992.gk.72.T', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.B', 'old_label': '72.t1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.T', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 202369310
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DK', '648.EX', '648.FN', '648.GQ', '648.GX', '648.HH', '648.HJ', '648.HP', '648.HS'], 'contains': ['3888.BR', '5832.P', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [4199, -1, 7025, -1], 'generators': [526279357810177215774797298686100004, 20666295941919359052064787708592879786480, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.DK', 'old_label': '1944.cu1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DA', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369311
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.DL', '648.EY', '648.FK', '648.FN', '648.GT', '648.GY', '648.HF', '648.HK', '648.HO', '648.HS'], 'contains': ['3888.BS', '5832.P', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [3364, -1, 7044, -1], 'generators': [526279357810177215774797298686100004, 4866515565566135187, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.DL', 'old_label': '1944.cv1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DB', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369312
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DM', '648.EZ', '648.FN', '648.GT', '648.HC', '648.HE', '648.HL', '648.HQ'], 'contains': ['3888.BT', '5832.P', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [3050, -1, 6990, -1], 'generators': [526279357810177215774797298686100004, 10628380774572818238517738969605794538480, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.DM', 'old_label': '1944.cw1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DC', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202369313
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DN', '648.FQ', '648.HQ', '648.HR', '648.HS', '972.H', '972.W', '972.X'], 'contains': ['3888.B', '5832.P'], 'core': '3888.B', 'coset_action_label': None, 'count': 81, 'diagramx': [3622, -1, 6935, -1], 'generators': [526279357810177215774797298686100004, 10628380783110079667891945245656009369843, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DD', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.B', 'old_label': '1944.cx1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DD', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369314
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DO', '648.DP', '648.DQ', '648.DT', '648.DU', '648.DV', '648.DZ', '648.FV', '648.FW', '648.FY', '648.FZ', '648.GC', '648.GE', '648.GW', '648.GX', '648.HA'], 'contains': ['3888.CD', '5832.Q', '5832.R', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [7348, -1, 8027, -1], 'generators': [20666822203593614167669861395963898521603, 10628907044783559274703750619374676633600, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DE', 'old_label': '1944.cy1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DE', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369315
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DO', '648.DP', '648.DQ', '648.DS', '648.DT', '648.DU', '648.DW', '648.DX', '648.DY', '648.DZ', '648.EA', '648.EB', '648.FT', '648.FV', '648.FX', '648.FY', '648.GA', '648.GB', '648.GD', '648.GW', '648.GY', '648.HA'], 'contains': ['3888.CE', '5832.Q', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [7831, -1, 8111, -1], 'generators': [20666295950456620481443859453801404458244, 20666822203593614167669861395963898521603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DF', 'old_label': '1944.cz1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DF', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369316
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['648.DR', '648.DU', '648.DV', '648.DW', '648.DY', '648.EA', '648.EB', '648.FY', '648.GA', '648.GC', '648.GZ', '648.HB'], 'contains': ['3888.CF', '5832.Q', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [7613, -1, 8093, -1], 'generators': [17684330570406523300984971344644, 20666822203593614167669861395963898521603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DG', 'old_label': '1944.da1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DG', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369317
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.DT', '648.DX', '648.EA', '648.FU', '648.FZ', '648.GB', '648.GE', '648.GZ', '648.HB'], 'contains': ['3888.CG', '5832.Q', '5832.R'], 'core': '34992.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [7593, -1, 7923, -1], 'generators': [526270820517725414304798352382054643, 20666295950456232649488742324945953488788, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DH', 'old_label': '1944.da2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DH', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369318
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.DO', '648.DR', '648.FU', '648.FX', '648.HC', '648.HD'], 'contains': ['3888.CH', '5832.Q', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [8289, -1, 7713, -1], 'generators': [10628907027100423067475430319608277529748, 20666295941918940197689585005482773098240, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DI', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DI', 'old_label': '1944.db1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DI', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369319
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.DZ', '648.EA', '648.GC', '648.GD', '648.HC', '648.HD', '972.Y'], 'contains': ['3888.CI', '5832.Q', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [7975, -1, 7695, -1], 'generators': [526270820517725414304798352382054643, 20666295941918940197689585005482773098240, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.Y', 'old_label': '1944.dc1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DJ', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 202369320
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '72.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '24.G'], 'contains': ['144.BU', '216.BN', '216.CB', '216.CC'], 'core': '432.B', 'coset_action_label': None, 'count': 72, 'diagramx': [2605, -1, 3161, -1], 'generators': [526279357810177215774797298686100004, 10628380783110079667891945245656009369843, 265924700981089824612497257486013004984243, 17684330570406523300984971344644, 20666295941918940197689585005482773098240, 20965322872091829840960829206593966365706], 'label': '34992.gk.72.U', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.U', 'old_label': '72.u1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.U', 'subgroup_fusion': None, 'weyl_group': '486.103'}
    • id: 202369321
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.EB', '648.GE', '648.HD', '972.R', '972.Z', '972.BA'], 'contains': ['3888.CJ', '5832.Q'], 'core': '34992.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [7311, -1, 7258, -1], 'generators': [17684330570406523300984971344644, 20666295941918940197689585005482773098240, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.C', 'old_label': '1944.dd1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DK', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 202369322
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DP', '648.DQ', '648.DT', '648.DU', '648.ED', '648.EG', '648.EH', '648.EI', '648.EJ', '648.EK', '648.EL', '648.EM', '648.EN', '648.FT', '648.FV', '648.FY', '648.GF', '648.GG', '648.GJ', '648.GK', '648.HF', '648.HG', '648.HH'], 'contains': ['3888.CK', '5832.R', '5832.S', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [7925, -1, 8309, -1], 'generators': [20666822203593614167669861395963898521603, 271353675587871452985655124252819907, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DL', 'old_label': '1944.de1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DL', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369323
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DO', '648.DZ', '648.EC', '648.EG', '648.EH', '648.EI', '648.EJ', '648.EK', '648.EL', '648.EM', '648.EN', '648.EO', '648.FU', '648.GC', '648.GF', '648.GG', '648.GJ', '648.GK', '648.GL', '648.GW', '648.GX', '648.HE'], 'contains': ['3888.CL', '5832.R', '5832.S', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [8280, -1, 8328, -1], 'generators': [10628380765425749097495153929394914000787, 20666822203593614167669861395963898521603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DM', 'old_label': '1944.df1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DM', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369324
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DV', '648.EH', '648.EI', '648.EO', '648.FV', '648.FW', '648.FZ', '648.GL', '648.HG', '648.HH', '972.BB'], 'contains': ['3888.CM', '5832.R', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 8748, 'diagramx': [7525, -1, 8237, -1], 'generators': [271362823044819702672148022253702963, 295241030720035824849169818559470203785, 20666295941919746832315870983149074474484], 'label': '34992.gk.1944.DN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.BB', 'old_label': '1944.dg1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DN', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 202369325
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DO', '648.DR', '648.EA', '648.EC', '648.ED', '648.EF', '648.EG', '648.EH', '648.EM', '648.EN', '648.EP', '648.ER', '648.ES', '648.GD', '648.GG', '648.GH', '648.GI', '648.GJ', '648.GM', '648.GO', '648.GW', '648.GY', '648.HE'], 'contains': ['3888.CN', '5832.R', '5832.T', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [9137, -1, 8642, -1], 'generators': [20666822203593614167669861395963898521603, 20666822203592807636451640951168815168243, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DO', 'old_label': '1944.dh1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DO', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369326
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DR', '648.DZ', '648.EA', '648.EC', '648.ED', '648.EE', '648.EG', '648.EI', '648.EK', '648.EL', '648.EP', '648.EQ', '648.ER', '648.FX', '648.GF', '648.GH', '648.GI', '648.GK', '648.GM', '648.GN', '648.GW', '648.GY', '648.HE'], 'contains': ['3888.CO', '5832.R', '5832.T', '5832.U'], 'core': '34992.a1', 'coset_action_label': None, 'count': 34992, 'diagramx': [9234, -1, 8594, -1], 'generators': [20666822203593614167669861395963898521603, 20666567286448296585161491744481302663104, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DP', 'old_label': '1944.dh2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DP', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369327
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.DP', '648.DS', '648.DX', '648.DY', '648.EE', '648.EG', '648.EP', '648.ER', '648.GA', '648.GG', '648.GI', '648.GM', '648.HF', '648.HG', '972.BC'], 'contains': ['3888.CP', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [8948, -1, 8550, -1], 'generators': [526279357810204189480295678726208148, 295241030720035824849169818559470203785, 526279358197957464546480101523456004], 'label': '34992.gk.1944.DQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.BC', 'old_label': '1944.di1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DQ', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 202369328
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['648.DQ', '648.DS', '648.DW', '648.EF', '648.EG', '648.EQ', '648.ES', '648.GB', '648.GF', '648.GI', '648.GN', '648.GO', '648.HF', '648.HG'], 'contains': ['3888.CQ', '5832.R', '5832.T'], 'core': '34992.a1', 'coset_action_label': None, 'count': 17496, 'diagramx': [8852, -1, 8514, -1], 'generators': [17683942790155440026428776656640, 20666822203593614167669861395963898521603, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DR', 'old_label': '1944.di2', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DR', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 202369329
      {'ambient': '34992.gk', 'aut_centralizer_order': None, 'aut_label': '1944.DS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.DT', '648.DV', '648.EE', '648.EF', '648.EG', '648.EJ', '648.EK', '648.EL', '648.EM', '648.EO', '648.FV', '648.FY', '648.GJ', '648.GL', '648.HI', '648.HJ'], 'contains': ['3888.CR', '5832.R', '5832.S'], 'core': '34992.a1', 'coset_action_label': None, 'count': 23328, 'diagramx': [7759, -1, 8346, -1], 'generators': [20666822203593614167669861395963898521603, 20666822194446157298100225847498551360147, 295241030720035824849169818559470203785], 'label': '34992.gk.1944.DS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.DS', 'old_label': '1944.dj1', 'projective_image': '34992.gk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.DS', 'subgroup_fusion': None, 'weyl_group': '18.4'}