Abstract group data - 1944.3475

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• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [24, 6, 12, 12], 'aut_gens': [[1, 8, 24, 72, 216, 648], [129, 656, 1320, 360, 72, 648], [1529, 1240, 768, 72, 216, 648], [587, 744, 584, 360, 288, 1296], [1611, 1040, 1136, 144, 360, 648]], 'aut_group': None, 'aut_hash': 8502039167705073060, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 279936, 'aut_permdeg': 486, 'aut_perms': [20358450723985363314197927465511648496392686308153511979601788513840398350799326654768857510903713833683597985876605336227886854401232976726837730058844484942577276248430566008602456992523670233404876774994941022273664529723123415227223397392978784430418543123252454118175391435073079956413487178426780603771402254632480771152279087086381162966952198606823149600667609770236718373987273698739416771948901718545569942084728810961073720194619199695322870091097186330184056527265968585940824358480116101544127893417292517824329487072966402444653765526908210003690273677249678211307973058421870201948466065400908899756284891251757861484781993908112599608159302753564023119146757129563531444022165435168281008306972985962748006283827981862930363019405951240842788500219235386510075980906762150951238501669194616202095760950063675664960246988269713764244380055432676620996008974756211906862869045735062300366951333713076538581916514983371871475418489069455383078304172514579439088845032763981120520822511869775020352558216743500772869713406609237017992808350235528509547034757359734154693960542000122469, 4853036155308889291175557155599520958473157441998524185271376860817042103235232314507297216028488279044025541071935667791729436964938238308695190450740200068510057584065081382611461153607098745294525235451622665212920454995905968231743252986072729716888624517850501699851606664893010203957862333802181939513312127483124365222646154560599391522128147692028195124087942803649756360752636869447901073207209106352541581081218116831694450097568605372306934892107856712476280512643624748183734302290812071474758259040323581468915934661855699349450296314888144880653912535391132143682540808819829850467999949790271721443458119700874983337551306297646904559830890751281773359121383546111455574810170504224376494243550451554894943729130910802931141668868394600105364102785450720083090865253801107938760609173209413954730552316584630616894150586861297091646121722535815890271222583879140946579639900758275008042687872581835383153698047927407841183060932776326604097622877113359968128832770414194617998650924354124966038591171928280327695619353873991849819541876117097353980638014932520819654462701349370061, 18425179906492659444586885374497647900520053480869876029362599688911093520168686918718109642718290534133202329093739368658119268615470028424758471215755478589244410618686112839007648212389048523747072475593577590013522952662743797737974303400418926862030025844367365610351301237696720666838264262631282395093375038501979803168843405992253639141056837668610024431444474723171644547225846884490856178107319160893249747053116652230108775748540597994977877263453458088487108131822747696033975578343489145923546180912874425920590635653329614950801109565207843540698692346229743339166991476712032232139839751173260659121920631806610681011329628401462061228238571959558898327956710174874045529618037194977393515231791664529758638854479439313984451287061141564839236586578641373196001540253188288516300148055271761577060593293247299601348992980931739680298479139208678584810586081386139204932262353369864173380144019625575273147819579588165855803704937798479661382517736675380105329247473860993006006009354467233857193166553029897902056626448006368124667956852939021220660391586836150420042030056830941471, 12446953105800490358918354510263461129686827457487945644958276280515554090344078076117436112876738341240558486639627978584803057568734552686444056162198372555940492164496339619101888546965020081442217504538053618979290429309823443989000395016015495952715399841806844510282114757031980387882437089571399533009983672899979464263464563898608911222243717131012872503954600149829642687959726951118345496349940887111406387554213864491439500006164502729678421046631244639429934077002120232162532513774869716065125981830641393132096891093343758862082395137576580642815536002781013101428645757822205609502037429880091611728165536155687869343412606745518259897878541083331999543638277979875207543705230565048750545626365049123249751738816575800875552407067301334398242410213795559260438997178684940803985026194324312459141199583746458432848418038167181942903516589542266434022569775489834175422019310540513814154687503712643710619732340493319276099057710598232319040491612646295519726786716530233415023611555352436579869121758949942928256907688294942724240973151663076818276882641856651948969221812679076109], 'aut_phi_ratio': 432.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 24, 9, 1], [4, 81, 2, 1], [6, 162, 1, 1], [8, 243, 2, 2], [12, 162, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.C_3^2.C_8^2.C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 8502039167705073060, 'autcentquo_nilpotent': False, 'autcentquo_order': 279936, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.C_3^4.C_8:Q_8.C_2', 'cc_stats': [[1, 1, 1], [2, 81, 1], [3, 2, 1], [3, 8, 3], [3, 24, 9], [4, 81, 2], [6, 162, 1], [8, 243, 4], [12, 162, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1944.3475', 'commutator_count': 1, 'commutator_label': '243.62', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3475, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 24, 1, 9], [4, 81, 2, 1], [6, 162, 1, 1], [8, 243, 4, 1], [12, 162, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 20160, 'exponent': 24, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '648.711', 'hash': 3475, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 3, 3, 3, 3, 3], 'inner_gens': [[1, 1328, 688, 360, 72, 1296], [697, 8, 1320, 72, 216, 648], [9, 656, 24, 72, 216, 648], [577, 8, 24, 72, 216, 648], [361, 8, 24, 72, 216, 648], [1297, 8, 24, 72, 216, 648]], 'inner_hash': 3475, 'inner_nilpotent': False, 'inner_order': 1944, 'inner_split': True, 'inner_tex': '\\He_3:F_9', 'inner_used': [1, 2, 4], 'irrC_degree': 24, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 48, 'irrep_stats': [[1, 8], [6, 4], [8, 10], [24, 2]], 'label': '1944.3475', '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': 'He3:F9', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 11, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 24, 'number_divisions': 18, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 220, 'number_subgroups': 5652, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 81], [3, 242], [4, 162], [6, 162], [8, 972], [12, 324]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [8, 2, 4, 2, 3, 3], 'outer_gen_pows': [0, 0, 0, 0, 1, 6], 'outer_gens': [[1, 440, 384, 360, 72, 648], [3, 1488, 952, 576, 216, 1296], [1, 584, 96, 576, 360, 648], [1, 376, 912, 72, 216, 648], [1, 848, 608, 432, 576, 1296], [1, 1488, 1880, 576, 360, 648]], 'outer_group': '144.182', 'outer_hash': 182, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 9, 'outer_perms': [330610, 1567, 249578, 130439, 256929, 350342], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'F_9:C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1], [6, 2], [8, 10], [12, 1], [48, 1]], 'representations': {'PC': {'code': 376789862987692141402359691416409524917849242751546891930829599, 'gens': [1, 4, 5, 6, 7, 8], 'pres': [8, -2, -2, -2, -3, 3, -3, 3, -3, 16, 41, 42499, 21515, 147, 27524, 26092, 6980, 6628, 17285, 13837, 1749, 4038, 10094, 6070, 82951]}, 'Perm': {'d': 36, 'gens': [949403469120753297805896421260449977117, 1251015361368102530782391725795569727053, 1554942506251808364074587480127602776460, 63797, 109652, 11897834803533411706244847575874502390245, 22534064794592521127431827361231177173925, 33095134739844806084113520201793561676800]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\He_3:F_9', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 136993932
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3475, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136993943
    {'aut_label': '2A', 'centralizer': '81.a1', 'counter': 2, 'group_counter': 3475, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1332, 'size': 81}
  • id: 136993949
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 3475, 'group_order': 1944, 'label': '3A', 'order': 3, 'powers': [3, 1], 'representative': 648, 'size': 2}
  • id: 136993950
    {'aut_label': '3B', 'centralizer': '8.a1', 'counter': 4, 'group_counter': 3475, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [4, 1], 'representative': 216, 'size': 8}
  • id: 136993951
    {'aut_label': '3C1', 'centralizer': '8.a1', 'counter': 5, 'group_counter': 3475, 'group_order': 1944, 'label': '3C1', 'order': 3, 'powers': [6, 1], 'representative': 864, 'size': 8}
  • id: 136993952
    {'aut_label': '3C1', 'centralizer': '8.a1', 'counter': 6, 'group_counter': 3475, 'group_order': 1944, 'label': '3C-1', 'order': 3, 'powers': [5, 1], 'representative': 720, 'size': 8}
  • id: 136993953
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 7, 'group_counter': 3475, 'group_order': 1944, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 24, 'size': 24}
  • id: 136993954
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 8, 'group_counter': 3475, 'group_order': 1944, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 240, 'size': 24}
  • id: 136993955
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 9, 'group_counter': 3475, 'group_order': 1944, 'label': '3F', 'order': 3, 'powers': [9, 1], 'representative': 96, 'size': 24}
  • id: 136993933
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 10, 'group_counter': 3475, 'group_order': 1944, 'label': '3G', 'order': 3, 'powers': [10, 1], 'representative': 224, 'size': 24}
  • id: 136993934
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 11, 'group_counter': 3475, 'group_order': 1944, 'label': '3H', 'order': 3, 'powers': [11, 1], 'representative': 80, 'size': 24}
  • id: 136993935
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 12, 'group_counter': 3475, 'group_order': 1944, 'label': '3I', 'order': 3, 'powers': [12, 1], 'representative': 456, 'size': 24}
  • id: 136993936
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 13, 'group_counter': 3475, 'group_order': 1944, 'label': '3J', 'order': 3, 'powers': [13, 1], 'representative': 168, 'size': 24}
  • id: 136993937
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 14, 'group_counter': 3475, 'group_order': 1944, 'label': '3K', 'order': 3, 'powers': [14, 1], 'representative': 440, 'size': 24}
  • id: 136993938
    {'aut_label': '3D', 'centralizer': '24.b1', 'counter': 15, 'group_counter': 3475, 'group_order': 1944, 'label': '3L', 'order': 3, 'powers': [15, 1], 'representative': 152, 'size': 24}
  • id: 136993939
    {'aut_label': '4A1', 'centralizer': '81.a1', 'counter': 16, 'group_counter': 3475, 'group_order': 1944, 'label': '4A1', 'order': 4, 'powers': [2, 17], 'representative': 26, 'size': 81}
  • id: 136993940
    {'aut_label': '4A1', 'centralizer': '81.a1', 'counter': 17, 'group_counter': 3475, 'group_order': 1944, 'label': '4A-1', 'order': 4, 'powers': [2, 16], 'representative': 662, 'size': 81}
  • id: 136993941
    {'aut_label': '6A', 'centralizer': '162.a1', 'counter': 18, 'group_counter': 3475, 'group_order': 1944, 'label': '6A', 'order': 6, 'powers': [3, 2], 'representative': 348, 'size': 162}
  • id: 136993942
    {'aut_label': '8A1', 'centralizer': '243.a1', 'counter': 19, 'group_counter': 3475, 'group_order': 1944, 'label': '8A1', 'order': 8, 'powers': [16, 21], 'representative': 689, 'size': 243}
  • id: 136993944
    {'aut_label': '8A-1', 'centralizer': '243.a1', 'counter': 20, 'group_counter': 3475, 'group_order': 1944, 'label': '8A-1', 'order': 8, 'powers': [17, 22], 'representative': 55, 'size': 243}
  • id: 136993945
    {'aut_label': '8A1', 'centralizer': '243.a1', 'counter': 21, 'group_counter': 3475, 'group_order': 1944, 'label': '8A3', 'order': 8, 'powers': [17, 19], 'representative': 59, 'size': 243}
  • id: 136993946
    {'aut_label': '8A-1', 'centralizer': '243.a1', 'counter': 22, 'group_counter': 3475, 'group_order': 1944, 'label': '8A-3', 'order': 8, 'powers': [16, 20], 'representative': 1317, 'size': 243}
  • id: 136993947
    {'aut_label': '12A1', 'centralizer': '162.a1', 'counter': 23, 'group_counter': 3475, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [18, 16], 'representative': 1206, 'size': 162}
  • id: 136993948
    {'aut_label': '12A1', 'centralizer': '162.a1', 'counter': 24, 'group_counter': 3475, 'group_order': 1944, 'label': '12A-1', 'order': 12, 'powers': [18, 17], 'representative': 1090, 'size': 162}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 12109349
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.1a', '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], 'schur_index': 1}
  • id: 12109359
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.1b', '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], 'schur_index': 1}
  • id: 12109360
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, -2, -2], 'schur_index': 1}
  • id: 12109361
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.1d', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109362
    {'cdim': 6, 'counter': 5, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.6a', 'multiplicity': 1, 'nt': [27, 77], 'qdim': 6, 'qvalues': [6, -2, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 12109363
    {'cdim': 6, 'counter': 6, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.6b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 6, 'qvalues': [6, -2, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 1, 1], 'schur_index': 2}
  • id: 12109365
    {'cdim': 8, 'counter': 8, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8a', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109366
    {'cdim': 8, 'counter': 9, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8b', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109350
    {'cdim': 8, 'counter': 10, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8c', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109351
    {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8d', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109352
    {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8e', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109353
    {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8f', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109354
    {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8g', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109355
    {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8h', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109356
    {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8i', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109357
    {'cdim': 8, 'counter': 17, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.8j', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109364
    {'cdim': 6, 'counter': 7, 'faithful': False, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.6c', 'multiplicity': 2, 'nt': [27, 77], 'qdim': 12, 'qvalues': [12, 4, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109358
    {'cdim': 24, 'counter': 18, 'faithful': True, 'group': '1944.3475', 'group_order': 1944, 'image': None, 'label': '1944.3475.24a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 27675382
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1944, 'label': '1944.3475.1a', '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]]]}
  • id: 27675393
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.3475.1b', '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]]]}
  • id: 27675399
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3475.1c1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 27675400
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3475.1c2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 27675401
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 5, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3475.1d1', 'nt': [8, 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, 2]], [[1, 2]], [[-1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 2]], [[-1, 2]]]}
  • id: 27675402
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 6, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3475.1d2', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 2]], [[1, 2]]]}
  • id: 27675403
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 7, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3475.1d3', 'nt': [8, 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, 2]], [[1, 2]], [[-1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 2]], [[-1, 2]]]}
  • id: 27675404
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 8, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3475.1d4', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 2]], [[1, 2]]]}
  • id: 27675405
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 9, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3475.6a', 'nt': [27, 77], 'q_character': None, 'values': [[[6, 0]], [[-2, 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]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27675383
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 10, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3475.6b', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 27675384
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 11, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3475.6c1', 'nt': [27, 77], 'q_character': None, 'values': [[[6, 0]], [[2, 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]], [[-2, 1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 27675385
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 12, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3475.6c2', 'nt': [27, 2], 'q_character': None, 'values': [[[6, 0]], [[2, 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]], [[2, 1]], [[-2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 27675386
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 13, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8a', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 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]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675387
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 14, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8b', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675388
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 15, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8c', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675389
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8d', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675390
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 17, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8e', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675391
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 18, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8f', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675392
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8g', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675394
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 20, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8h', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675395
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 21, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3475.8i', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675396
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3475.8j', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675397
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3475', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.3475.24a1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[6, 0], [9, 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]]]}
  • id: 27675398
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3475', 'group_counter': 3475, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3475', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.3475.24a2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[-3, 0], [-9, 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]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 107635048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.3475.1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3475', 'subgroup_hash': 3475, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 107635059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3475.2.a1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.775', 'subgroup_hash': 775, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107635070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 486, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3475.4.a1', '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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.248', 'subgroup_hash': 248, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 243, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1944.3475.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 107635091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, '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': '216.155', 'subgroup_hash': 155, 'subgroup_order': 216, 'subgroup_tex': 'C_3:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 107635092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.9.b1', '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': '216.86', 'subgroup_hash': 86, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 107635093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.12.b1', '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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.18.a1', '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 107635049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.18.b1', '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': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107635050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 107635052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 107635053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.36.a1', '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.36.b1', '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.36.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c2', '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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.36.d1', '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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.54.a1', '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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107635060
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3475.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.39', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3475.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.39', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635066
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 107635067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635072
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107635073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3475.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.86', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 86, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635078
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107635079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '1944.3475.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 2}
  • id: 107635080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635082
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635083
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3475.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635084
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107635085
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 3, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3475.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.711', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 711, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:F_9', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'D2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635086
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635087
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635088
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635089
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3475.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107635090
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3475', 'ambient_counter': 3475, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.3475.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1944.3475', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3475, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:F_9', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  
  • id: 107635048
    {'ambient': '1944.3475', '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': '1944.a1', 'complements': ['1944.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '9.a1', '9.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9013, 801, 8734, 2557], 'generators': [1, 24, 72, 2, 704, 648, 216, 4], 'label': '1944.3475.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '1944.3475', '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': '1944.3475'}
  • id: 107635049
    {'ambient': '1944.3475', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['2.a1', '9.b1'], 'contains': ['36.c2', '162.a1'], 'core': '72.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [8545, -1, 8165, -1], 'generators': [2, 648, 4, 1328, 1320], 'label': '1944.3475.18.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635050
    {'ambient': '1944.3475', 'aut_centralizer_order': 27, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 972, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['8.a1', '12.a1'], 'contains': ['72.b1', '72.c1', '72.d1'], 'core': '72.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5479, -1, 5240, -1], 'generators': [32, 1320, 288], 'label': '1944.3475.24.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635051
    {'ambient': '1944.3475', 'aut_centralizer_order': 81, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 324, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1'], 'contains': ['72.a1', '72.c1', '72.e1', '72.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1626, -1, 561, -1], 'generators': [1320, 288, 216, 648], 'label': '1944.3475.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635052
    {'ambient': '1944.3475', 'aut_centralizer_order': 72, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['54.a1', '243.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9154, -1, 9031, -1], 'generators': [1, 216, 2, 4, 72], 'label': '1944.3475.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635053
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '216.102', 'aut_weyl_index': 1296, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.a1', '12.b1'], 'contains': ['72.c1', '108.a1', '108.b1', '108.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5026, -1, 3798, -1], 'generators': [4, 648, 672, 288], 'label': '1944.3475.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '36.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635054
    {'ambient': '1944.3475', 'aut_centralizer_order': 108, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 972, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.a1'], 'contains': ['72.a1', '108.a1', '108.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3793, -1, 2468, -1], 'generators': [4, 648, 288, 216], 'label': '1944.3475.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635055
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['12.a1'], 'contains': ['72.d1', '108.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6622, -1, 6466, -1], 'generators': [4, 1328, 960, 648], 'label': '1944.3475.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '36.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635056
    {'ambient': '1944.3475', 'aut_centralizer_order': 24, 'aut_label': '36.c2', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['12.a1', '18.b1'], 'contains': ['72.b1', '108.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [7877, -1, 7364, -1], 'generators': [4, 1328, 672, 648], 'label': '1944.3475.36.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.c2', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c2', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635057
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 36, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1'], 'contains': ['72.f1', '108.c1', '108.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2754, -1, 1346, -1], 'generators': [4, 672, 288, 216], 'label': '1944.3475.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.d1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107635058
    {'ambient': '1944.3475', 'aut_centralizer_order': 216, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '27.a1'], 'contains': ['108.d1', '486.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7506, -1, 8302, -1], 'generators': [2, 4, 288, 216], 'label': '1944.3475.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635059
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '18.a1', '18.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7580, 801, 7380, 2557], 'generators': [2, 216, 288, 4, 648, 1328, 1320], 'label': '1944.3475.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '648.711'}
  • id: 107635060
    {'ambient': '1944.3475', 'aut_centralizer_order': 8748, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.40', 'aut_weyl_index': 8748, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.b1'], 'contains': ['216.a1', '216.b1', '216.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1032, 3531, 1571, 6203], 'generators': [288, 216, 648], 'label': '1944.3475.72.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['216.a1', '648.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '1944.3475', 'quotient_action_image': '8.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '8.1'}
  • id: 107635061
    {'ambient': '1944.3475', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '72.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 9, 'contained_in': ['24.a1', '36.c2'], 'contains': ['216.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6281, 9199, 5970, 9417], 'generators': [32, 1320], 'label': '1944.3475.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '1944.3475', 'quotient_action_image': '8.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635062
    {'ambient': '1944.3475', 'aut_centralizer_order': 81, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 3888, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.a1', '24.b1', '36.a1'], 'contains': ['216.b1', '216.c1', '216.e1', '216.f1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2442, -1, 2228, -1], 'generators': [1320, 288, 648], 'label': '1944.3475.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635063
    {'ambient': '1944.3475', 'aut_centralizer_order': 27, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['24.a1', '36.c1'], 'contains': ['216.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5746, -1, 5393, -1], 'generators': [32, 1608], 'label': '1944.3475.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.d1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635064
    {'ambient': '1944.3475', 'aut_centralizer_order': 81, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 7776, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1'], 'contains': ['216.d1', '216.e1', '216.f1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1640, -1, 256, -1], 'generators': [1320, 936, 216], 'label': '1944.3475.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '72.e1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635065
    {'ambient': '1944.3475', 'aut_centralizer_order': 81, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 972, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.d1'], 'contains': ['216.a1', '216.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [423, -1, 913, -1], 'generators': [1320, 288, 216], 'label': '1944.3475.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.f1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635066
    {'ambient': '1944.3475', 'aut_centralizer_order': 288, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['162.a1', '243.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9762, -1, 9688, -1], 'generators': [1, 2, 4, 648], 'label': '1944.3475.81.a1', 'mobius_quo': None, 'mobius_sub': 9, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635067
    {'ambient': '1944.3475', 'aut_centralizer_order': 216, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1'], 'contains': ['216.b1', '324.a1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5012, -1, 4559, -1], 'generators': [4, 648, 288], 'label': '1944.3475.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '108.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635068
    {'ambient': '1944.3475', 'aut_centralizer_order': 24, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 972, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['36.a1', '36.c1', '36.c2'], 'contains': ['216.c1', '324.a1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [6734, -1, 6803, -1], 'generators': [4, 648, 672], 'label': '1944.3475.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '108.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635069
    {'ambient': '1944.3475', 'aut_centralizer_order': 6, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '108.17', 'aut_weyl_index': 2592, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.a1', '36.d1'], 'contains': ['216.e1', '324.b1', '324.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3882, -1, 3654, -1], 'generators': [4, 672, 288], 'label': '1944.3475.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635070
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.a1', '12.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5427, 801, 4888, 2557], 'generators': [4, 648, 216, 1328, 672, 288], 'label': '1944.3475.4.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '648.711'}
  • id: 107635071
    {'ambient': '1944.3475', 'aut_centralizer_order': 216, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 1944, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.d1', '54.a1'], 'contains': ['216.a1', '324.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3207, -1, 2925, -1], 'generators': [4, 288, 216], 'label': '1944.3475.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.d1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635072
    {'ambient': '1944.3475', 'aut_centralizer_order': 864, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 69984, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '81.a1'], 'contains': ['324.a1', '486.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8620, -1, 9143, -1], 'generators': [2, 648, 4], 'label': '1944.3475.162.a1', 'mobius_quo': None, 'mobius_sub': -9, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635073
    {'ambient': '1944.3475', 'aut_centralizer_order': 17496, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 17496, 'centralizer': '8.a1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.f1', '108.d1'], 'contains': ['648.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [943, 3531, 2885, 6203], 'generators': [288, 216], 'label': '1944.3475.216.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '1944.3475', 'quotient_action_image': '8.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '8.1'}
  • id: 107635074
    {'ambient': '1944.3475', 'aut_centralizer_order': 17496, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 69984, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.c1', '108.a1'], 'contains': ['648.a1', '648.b1', '648.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2301, -1, 3542, -1], 'generators': [288, 648], 'label': '1944.3475.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635075
    {'ambient': '1944.3475', 'aut_centralizer_order': 648, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.b1', '72.c1', '72.d1', '108.b1'], 'contains': ['648.a1', '648.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5598, -1, 4776, -1], 'generators': [1320, 648], 'label': '1944.3475.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635076
    {'ambient': '1944.3475', 'aut_centralizer_order': 8748, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 69984, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.e1'], 'contains': ['648.b1', '648.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [238, -1, 913, -1], 'generators': [936, 216], 'label': '1944.3475.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.d1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635077
    {'ambient': '1944.3475', 'aut_centralizer_order': 162, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.c1', '72.e1', '72.f1', '108.c1'], 'contains': ['648.b1', '648.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1596, -1, 2228, -1], 'generators': [1320, 288], 'label': '1944.3475.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.e1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635078
    {'ambient': '1944.3475', 'aut_centralizer_order': 81, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 23328, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.c1', '72.e1'], 'contains': ['648.c1', '648.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3007, -1, 1571, -1], 'generators': [1320, 936], 'label': '1944.3475.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '216.f1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635079
    {'ambient': '1944.3475', 'aut_centralizer_order': 576, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '81.a1'], 'contains': ['486.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [9280, -1, 9784, -1], 'generators': [1], 'label': '1944.3475.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635080
    {'ambient': '1944.3475', 'aut_centralizer_order': 1728, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '162.a1'], 'contains': ['648.a1', '972.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6489, -1, 5970, -1], 'generators': [4, 648], 'label': '1944.3475.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635081
    {'ambient': '1944.3475', 'aut_centralizer_order': 27, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 27, 'centralizer': '72.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.a1', '24.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4150, 801, 4255, 2557], 'generators': [32, 1320, 288, 216], 'label': '1944.3475.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1944.3475', 'quotient_action_image': '8.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635082
    {'ambient': '1944.3475', 'aut_centralizer_order': 432, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 46656, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.c1', '108.d1'], 'contains': ['648.b1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3853, -1, 4159, -1], 'generators': [4, 288], 'label': '1944.3475.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635083
    {'ambient': '1944.3475', 'aut_centralizer_order': 48, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 972, 'aut_weyl_group': '6.1', 'aut_weyl_index': 46656, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['108.b1', '108.c1'], 'contains': ['648.d1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [5954, -1, 5393, -1], 'generators': [4, 672], 'label': '1944.3475.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635084
    {'ambient': '1944.3475', 'aut_centralizer_order': 1728, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '162.a1', '243.a1'], 'contains': ['972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8300, -1, 8718, -1], 'generators': [2], 'label': '1944.3475.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635085
    {'ambient': '1944.3475', 'aut_centralizer_order': 139968, 'aut_label': '648.a1', 'aut_quo_index': 10, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.c1', '324.a1'], 'contains': ['1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5471, 3858, 4407, 7864], 'generators': [648], 'label': '1944.3475.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['72.a1', '72.b1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '1944.3475', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.164', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635086
    {'ambient': '1944.3475', 'aut_centralizer_order': 34992, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '216.d1', '216.e1', '324.b1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1596, -1, 2973, -1], 'generators': [288], 'label': '1944.3475.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635087
    {'ambient': '1944.3475', 'aut_centralizer_order': 17496, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.d1', '216.f1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2494, -1, 2027, -1], 'generators': [936], 'label': '1944.3475.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.c1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635088
    {'ambient': '1944.3475', 'aut_centralizer_order': 1296, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 139968, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['216.c1', '216.e1', '216.f1', '324.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4306, -1, 3646, -1], 'generators': [1320], 'label': '1944.3475.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.d1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635089
    {'ambient': '1944.3475', 'aut_centralizer_order': 3456, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 279936, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '486.a1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6110, -1, 5393, -1], 'generators': [4], 'label': '1944.3475.972.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635090
    {'ambient': '1944.3475', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.b1', '648.c1', '648.d1', '972.a1'], 'contains': [], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4306, 3858, 3646, 7864], 'generators': [], 'label': '1944.3475.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['216.a1', '648.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635091
    {'ambient': '1944.3475', 'aut_centralizer_order': 36, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 324, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.a1', '27.a1', '81.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9013, -1, 8734, -1], 'generators': [1, 648, 216, 2, 4, 72], 'label': '1944.3475.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '216.155'}
  • id: 107635092
    {'ambient': '1944.3475', 'aut_centralizer_order': 8, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '432.520', 'aut_weyl_index': 648, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['1.a1'], 'contains': ['18.b1', '81.a1'], 'core': '72.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [9688, -1, 9463, -1], 'generators': [1, 648, 24, 2, 4, 704], 'label': '1944.3475.9.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '216.86'}
  • id: 107635093
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 324, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['4.a1'], 'contains': ['24.a1', '36.a1', '36.c1', '36.c2'], 'core': '72.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [5888, -1, 5521, -1], 'generators': [4, 648, 1328, 672, 288], 'label': '1944.3475.12.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '12.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107635094
    {'ambient': '1944.3475', 'aut_centralizer_order': 3, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 36, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.b1', '36.a1', '36.b1', '36.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3771, -1, 2468, -1], 'generators': [4, 216, 648, 672, 288], 'label': '1944.3475.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '12.b1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107635095
    {'ambient': '1944.3475', 'aut_centralizer_order': 108, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 972, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.b1', '54.a1', '162.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6993, -1, 6803, -1], 'generators': [2, 216, 648, 4, 288], 'label': '1944.3475.18.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '1944.3475', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}