Abstract group data - 1944.3477

Formats: - HTML - YAML - JSON - 2026-06-12T15:41:51.376736

• 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, 8, 8, 12], 'aut_gens': [[1, 8, 24, 72, 216, 648], [1321, 672, 16, 288, 360, 648], [1697, 40, 1360, 288, 360, 1296], [1033, 1336, 712, 216, 144, 1296], [1187, 32, 704, 288, 504, 648]], 'aut_group': None, 'aut_hash': 8814442550351613409, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 31104, 'aut_permdeg': 486, 'aut_perms': [15659963636196456244727214592768128636576405836175085039843423318414972602963999042429515652063685474443756807603654551579205838912219217249972932769739619775125988464898776756742516492547921097737892498682385986077317958967968516474694442774104137284987405136078805866655997023233758417375900301730017183582914294725811563816359970377240669207817006035335952100537159028015970190365948583847518193348691607695641167699623197004585335565853049971155523365522379855926737899049014130478279356472617431426163347068884143700766528588316894469784504572625020927508001576828283607721181546601714830034559894942173647315674524330800532346547772822122436268932967267059943395129025519748927476839544959493628598903119452231301996719939896487296699174713761107041816612119891412963032780988197230575429807361326423235990949751110854649931046859823209967952274031425326917716982911676484006384665172567086576734684727513455006777489278482064665133619095432897311011641393034110727891066081844047201102440229596971071027738762808568109633984268697219597000761722857556437125391202642612113072169069645991847, 19925716218787357275286069544350569994495636199943698855515240328082792172839842241275969917278296734815732168866425071120959180160168500249967522480808736954292752667105735933673383177061219353577558322943127907229976168106534926325038493958141206179565548086233040698201836734636786829416943302608086399893733624576745638574197589031947364757164713586952448361865175403671673395291683713735312201982594454263321127664553748176357835367382753966367425635899932399731419958944568078066939871835274864931143541077509948221152997604931199835941745173151494542576502698436358042951289408479656766095846427074895187520380843649573190458197167722098308277348054172447767424520028400851258515838999254181373852449127916357390680513954562314171952660732083143168751900256169961041170497380570164214238123830335123455287641718281045649719697973933869003275465145709109566630718582702066682813211353689803042170865494436987702420064833530731633031926384391785083098515806674572942589995143661492506131543252455164794124017799341806316890702049888595684702263761849960543570549446864445416613176295845080457, 23505292337256669200652631412224161513035733443990257959697156837379205566586866252797811697063405045293625741878810787837713402107672930956390249808854996415470088632395319175324480031043823448643541494820097030717981317150735889136585134954433920747124901966814760810447879675287586952502336005488062261675414171715326460449721474743978167341941902514520285406594411813410858931817865018500361051704441727427144260503192561837353047194357486425957831728392273176667848542752729459051300723474255689328172989876802824422484666505023569191038231055565309532484739361619353772818148021441012739284039425793901341335862602406916471007185770604040915821911023771716652953581557404972646136415344663780423222360959576477348636213676034735411198970624858025359716879642970466454809830899214177172742290297445852131607526009615520968952383462174312850725183155347821354018069849504060448641785251737682724898093169204546408936710380404791362571303590309956021519862499801011708117167903373647993145201207923441824372482296277501837813420256741675830551052779890627802993878754540068168195581769530517632, 13545458415839910536804797956524763776493282072494018820608305641775984684923017401877747634344455432202622739495750235985778505313283054094502467286705567517949007723007493886958079709536884351896935241561227107280996749718919194064609373364585639034372502242667533251955032967246775592727016862094494078544086782227507075885803871596961140110729039054230991718165893260034825118847922214274142988656467032698552322438386652256937931222760822039408258986409678648800073900192804645342941495190758549592659115980092578406049612911681271488355012270445686093956368236564007344215512734746302741672280748937394009424024382994333352145555189102980494715416256989329855338172611904738922193559471689609383410456242825424545928904479380108002718037588367037721159013996464939450827576110614528101949656751636750796751959334907104540486537867400891832451631707438141547606345950690510573939721969213360364232260479686629334674725707558288891339624286006318409822956371893178061006829128872744667152735759613416861635458639562218582893463921405802732073640120743467731409619260627231282718013998422687980], 'aut_phi_ratio': 48.0, '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, 1, 1], [3, 24, 8, 1], [4, 81, 2, 1], [6, 162, 1, 1], [8, 243, 2, 2], [12, 162, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_3^2\\times \\He_3).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': 8814442550351613409, 'autcentquo_nilpotent': False, 'autcentquo_order': 31104, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3.C_3^4:C_2^2.C_4:D_4', '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': '1944.3477', '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': 3477, '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': 72, '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': '648.712', 'hash': 3477, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 3, 3, 3, 3, 3], 'inner_gens': [[1, 704, 1328, 360, 576, 1296], [1321, 8, 672, 72, 216, 648], [1313, 1304, 24, 72, 216, 648], [577, 8, 24, 72, 216, 648], [505, 8, 24, 72, 216, 648], [1297, 8, 24, 72, 216, 648]], 'inner_hash': 3477, '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': '1944.3477', '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': 12, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 24, 'number_divisions': 18, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 200, 'number_subgroups': 5580, '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': 8, 'outer_gen_orders': [2, 8], 'outer_gen_pows': [4, 0], 'outer_gens': [[3, 1328, 704, 504, 576, 648], [1, 704, 1328, 72, 216, 1296]], 'outer_group': '16.8', 'outer_hash': 8, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [4599, 7266], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': '\\SD_{16}', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 2, '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': 188540410192601772639868559848555330214882233115193317271667487, 'gens': [1, 4, 5, 6, 7, 8], 'pres': [8, -2, -2, -2, -3, 3, -3, 3, -3, 16, 41, 22531, 395, 147, 53124, 332, 500, 3388, 17285, 5197, 1749, 32262, 4046, 6070, 82951]}, 'Perm': {'d': 36, 'gens': [949403469120753297805896421260449981463, 1251015361368102530782391725795569732191, 1554942506251808364074587480127602775616, 62188, 94309, 11897834803533411706244847575874502252800, 22534064794592521127431827361231176979200, 33095134739844806084113520201793561676800]}}, 'schur_multiplier': [3, 3], '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: 136993956
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3477, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136993967
    {'aut_label': '2A', 'centralizer': '81.a1', 'counter': 2, 'group_counter': 3477, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 692, 'size': 81}
  • id: 136993973
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 3477, 'group_order': 1944, 'label': '3A', 'order': 3, 'powers': [3, 1], 'representative': 648, 'size': 2}
  • id: 136993974
    {'aut_label': '3B', 'centralizer': '8.a1', 'counter': 4, 'group_counter': 3477, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [4, 1], 'representative': 216, 'size': 8}
  • id: 136993975
    {'aut_label': '3C1', 'centralizer': '8.a1', 'counter': 5, 'group_counter': 3477, 'group_order': 1944, 'label': '3C1', 'order': 3, 'powers': [6, 1], 'representative': 864, 'size': 8}
  • id: 136993976
    {'aut_label': '3C1', 'centralizer': '8.a1', 'counter': 6, 'group_counter': 3477, 'group_order': 1944, 'label': '3C-1', 'order': 3, 'powers': [5, 1], 'representative': 1512, 'size': 8}
  • id: 136993977
    {'aut_label': '3D', 'centralizer': '24.c1', 'counter': 7, 'group_counter': 3477, 'group_order': 1944, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 24, 'size': 24}
  • id: 136993978
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 8, 'group_counter': 3477, 'group_order': 1944, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 240, 'size': 24}
  • id: 136993979
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 9, 'group_counter': 3477, 'group_order': 1944, 'label': '3F', 'order': 3, 'powers': [9, 1], 'representative': 96, 'size': 24}
  • id: 136993957
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 10, 'group_counter': 3477, 'group_order': 1944, 'label': '3G', 'order': 3, 'powers': [10, 1], 'representative': 224, 'size': 24}
  • id: 136993958
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 11, 'group_counter': 3477, 'group_order': 1944, 'label': '3H', 'order': 3, 'powers': [11, 1], 'representative': 456, 'size': 24}
  • id: 136993959
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 12, 'group_counter': 3477, 'group_order': 1944, 'label': '3I', 'order': 3, 'powers': [12, 1], 'representative': 312, 'size': 24}
  • id: 136993960
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 13, 'group_counter': 3477, 'group_order': 1944, 'label': '3J', 'order': 3, 'powers': [13, 1], 'representative': 296, 'size': 24}
  • id: 136993961
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 14, 'group_counter': 3477, 'group_order': 1944, 'label': '3K', 'order': 3, 'powers': [14, 1], 'representative': 528, 'size': 24}
  • id: 136993962
    {'aut_label': '3E', 'centralizer': '24.c1', 'counter': 15, 'group_counter': 3477, 'group_order': 1944, 'label': '3L', 'order': 3, 'powers': [15, 1], 'representative': 336, 'size': 24}
  • id: 136993963
    {'aut_label': '4A1', 'centralizer': '81.a1', 'counter': 16, 'group_counter': 3477, 'group_order': 1944, 'label': '4A1', 'order': 4, 'powers': [2, 17], 'representative': 1322, 'size': 81}
  • id: 136993964
    {'aut_label': '4A1', 'centralizer': '81.a1', 'counter': 17, 'group_counter': 3477, 'group_order': 1944, 'label': '4A-1', 'order': 4, 'powers': [2, 16], 'representative': 670, 'size': 81}
  • id: 136993965
    {'aut_label': '6A', 'centralizer': '162.a1', 'counter': 18, 'group_counter': 3477, 'group_order': 1944, 'label': '6A', 'order': 6, 'powers': [3, 2], 'representative': 932, 'size': 162}
  • id: 136993966
    {'aut_label': '8A1', 'centralizer': '243.a1', 'counter': 19, 'group_counter': 3477, 'group_order': 1944, 'label': '8A1', 'order': 8, 'powers': [16, 21], 'representative': 1329, 'size': 243}
  • id: 136993968
    {'aut_label': '8A-1', 'centralizer': '243.a1', 'counter': 20, 'group_counter': 3477, 'group_order': 1944, 'label': '8A-1', 'order': 8, 'powers': [17, 22], 'representative': 55, 'size': 243}
  • id: 136993969
    {'aut_label': '8A1', 'centralizer': '243.a1', 'counter': 21, 'group_counter': 3477, 'group_order': 1944, 'label': '8A3', 'order': 8, 'powers': [17, 19], 'representative': 67, 'size': 243}
  • id: 136993970
    {'aut_label': '8A-1', 'centralizer': '243.a1', 'counter': 22, 'group_counter': 3477, 'group_order': 1944, 'label': '8A-3', 'order': 8, 'powers': [16, 20], 'representative': 661, 'size': 243}
  • id: 136993971
    {'aut_label': '12A1', 'centralizer': '162.a1', 'counter': 23, 'group_counter': 3477, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [18, 16], 'representative': 1854, 'size': 162}
  • id: 136993972
    {'aut_label': '12A1', 'centralizer': '162.a1', 'counter': 24, 'group_counter': 3477, 'group_order': 1944, 'label': '12A-1', 'order': 12, 'powers': [18, 17], 'representative': 1242, '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: 12109367
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.1a', '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: 12109377
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.1b', '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: 12109378
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.1c', '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: 12109379
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.1d', '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: 12109380
    {'cdim': 6, 'counter': 5, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.6a', '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: 12109381
    {'cdim': 6, 'counter': 6, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.6b', '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: 12109383
    {'cdim': 8, 'counter': 8, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8a', '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: 12109384
    {'cdim': 8, 'counter': 9, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8b', '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: 12109368
    {'cdim': 8, 'counter': 10, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8c', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -4, -4, 2, 2, 2, -1, -1, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109369
    {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8d', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -4, 2, -4, 2, -1, 2, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109370
    {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8e', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, 2, 5, -1, 2, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109371
    {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8f', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, -1, 5, 2, -1, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109372
    {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8g', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, 2, -4, 2, -4, -1, 5, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109373
    {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8h', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, 2, -1, -1, 5, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109374
    {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8i', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, 2, 2, -4, -4, 5, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109375
    {'cdim': 8, 'counter': 17, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.8j', 'multiplicity': 1, 'nt': [12, 173], 'qdim': 8, 'qvalues': [8, 0, 8, -1, -1, -1, -1, 5, -1, -1, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109382
    {'cdim': 6, 'counter': 7, 'faithful': False, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.6c', '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: 12109376
    {'cdim': 24, 'counter': 18, 'faithful': True, 'group': '1944.3477', 'group_order': 1944, 'image': None, 'label': '1944.3477.24a', '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: 27675406
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1944, 'label': '1944.3477.1a', '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: 27675417
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.3477.1b', '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: 27675423
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3477.1c1', '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: 27675424
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3477.1c2', '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: 27675425
    {'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': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3477.1d1', '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: 27675426
    {'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': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3477.1d2', '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: 27675427
    {'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': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3477.1d3', '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: 27675428
    {'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': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3477.1d4', '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: 27675429
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 9, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3477.6a', '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: 27675407
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 10, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3477.6b', '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: 27675408
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 11, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3477.6c1', '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: 27675409
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 12, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '216.86', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3477.6c2', '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: 27675410
    {'center': '72.b1', 'center_index': 72, 'center_order': 27, 'counter': 13, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.3477.8a', '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: 27675411
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 14, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3477.8b', '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: 27675412
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 15, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8c', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675413
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8d', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675414
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 17, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8e', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675415
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 18, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8f', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675416
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8g', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675418
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 20, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8h', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675419
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 21, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8i', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675420
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '648.712', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3477.8j', 'nt': [12, 173], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27675421
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3477', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.3477.24a1', '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: 27675422
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3477', 'group_counter': 3477, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3477', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.3477.24a2', '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: 107635096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.1.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': '1944.3477', 'subgroup_hash': 3477, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 107635107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.2.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: 107635118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.4.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: 107635129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.8.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: 107635140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.9.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: 107635151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.9.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: 107635159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.12.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: 107635160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.18.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: 107635098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.18.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: 107635099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107635100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.24.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: 107635101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.24.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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635102
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 107635103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.27.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: 107635104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.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: 107635105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.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: 107635106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107635108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f2', '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: 107635112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.f3', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f3', '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: 107635113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.54.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: 107635115
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3477.72.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: 107635116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3477.72.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: 107635117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.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: 107635119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f2', '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: 107635123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.f3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f3', '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: 107635124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107635126
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.81.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: 107635127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.108.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: 107635128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.108.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: 107635130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107635131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, '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': '1944.3477.108.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: 107635132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 107635133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 107635134
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.162.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: 107635135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3477.216.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: 107635136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.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: 107635137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.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: 107635138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.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: 107635139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.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: 107635141
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.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: 107635142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107635143
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107635144
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107635145
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '1944.3477.243.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: 107635146
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.324.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: 107635147
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.324.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: 107635148
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.324.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: 107635149
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3477.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 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: 107635150
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.486.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: 107635152
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 3, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3477.648.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': '648.712', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 712, '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: 107635153
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.648.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: 107635154
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.648.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: 107635155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.648.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: 107635156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 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: 107635157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3477.972.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: 107635158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3477', 'ambient_counter': 3477, 'ambient_order': 1944, 'ambient_tex': '\\He_3:F_9', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.3477.1944.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': '1944.3477', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3477, '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: 107635112
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.f3', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '18.c1'], 'contains': ['72.f3', '108.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2857, -1, 2901, -1], 'generators': [4, 992, 168, 648], 'label': '1944.3477.36.f3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.f3', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f3', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107635113
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 36, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1'], 'contains': ['72.h1', '108.d1', '108.e1', '108.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7598, -1, 8447, -1], 'generators': [4, 24, 288, 216], 'label': '1944.3477.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '36.g1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107635114
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '27.a1'], 'contains': ['108.f1', '486.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5497, -1, 1112, -1], 'generators': [2, 4, 72, 216], 'label': '1944.3477.54.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': '1944.3477', '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: 107635096
    {'ambient': '1944.3477', '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': [640, 801, 944, 2557], 'generators': [1, 672, 72, 2, 1328, 648, 216, 4], 'label': '1944.3477.1.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': '1944.3477', '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': '1944.3477'}
  • id: 107635097
    {'ambient': '1944.3477', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 108, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.c1', '54.a1', '162.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5951, -1, 2854, -1], 'generators': [2, 216, 648, 4, 72], 'label': '1944.3477.18.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': '1944.3477', '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'}
  • id: 107635098
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '9.b1'], 'contains': ['36.e1', '162.a1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [347, -1, 1212, -1], 'generators': [2, 648, 4, 704, 1320], 'label': '1944.3477.18.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': '1944.3477', '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: 107635099
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['36.f3', '162.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1182, -1, 1962, -1], 'generators': [2, 648, 4, 992, 1464], 'label': '1944.3477.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '18.c1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107635100
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.a1', '12.a1'], 'contains': ['72.c1', '72.d1', '72.e1', '72.f1', '72.f2', '72.f3'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4725, -1, 6768, -1], 'generators': [1352, 1536, 288], 'label': '1944.3477.24.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': '1944.3477', '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: 107635101
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 108, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1'], 'contains': ['72.b1', '72.c1', '72.e1'], 'core': '72.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2532, -1, 3704, -1], 'generators': [1352, 1320, 288], 'label': '1944.3477.24.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': '1944.3477', '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': '18.4'}
  • id: 107635102
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.120', 'aut_weyl_index': 324, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.c1'], 'contains': ['72.a1', '72.c1', '72.d1', '72.g1', '72.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8883, -1, 9832, -1], 'generators': [1320, 288, 216, 648], 'label': '1944.3477.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.c1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635103
    {'ambient': '1944.3477', 'aut_centralizer_order': 8, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, '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': [3159, -1, 645, -1], 'generators': [1, 216, 2, 4, 72], 'label': '1944.3477.27.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': '1944.3477', '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: 107635104
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '72.46', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.b1', '12.c1'], 'contains': ['72.c1', '108.a1', '108.b1', '108.c1', '108.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5918, -1, 5824, -1], 'generators': [4, 648, 24, 288], 'label': '1944.3477.36.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': '1944.3477', '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: 107635105
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1', '12.c1'], 'contains': ['72.d1', '108.a1', '108.c1', '108.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6956, -1, 7713, -1], 'generators': [4, 648, 240, 288], 'label': '1944.3477.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '36.b1', 'projective_image': '1944.3477', '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': '18.4'}
  • id: 107635106
    {'ambient': '1944.3477', 'aut_centralizer_order': 12, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 108, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.a1'], 'contains': ['72.a1', '108.a1', '108.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8415, -1, 9182, -1], 'generators': [4, 648, 288, 216], 'label': '1944.3477.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.c1', 'projective_image': '1944.3477', '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': '72.39'}
  • id: 107635107
    {'ambient': '1944.3477', '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', '18.c1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1315, 801, 1962, 2557], 'generators': [2, 216, 72, 4, 648, 704, 1320], 'label': '1944.3477.2.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': '1944.3477', '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': '648.712'}
  • id: 107635108
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1', '12.b1'], 'contains': ['72.e1', '108.b1', '108.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1994, -1, 2314, -1], 'generators': [4, 704, 312, 648], 'label': '1944.3477.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '36.d1', 'projective_image': '1944.3477', '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': '18.4'}
  • id: 107635109
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.b1'], 'contains': ['72.b1', '108.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1131, -1, 1726, -1], 'generators': [4, 704, 24, 648], 'label': '1944.3477.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.e1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635110
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '36.9', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1'], 'contains': ['72.f1', '108.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4059, -1, 5094, -1], 'generators': [4, 992, 240, 648], 'label': '1944.3477.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '36.f1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635111
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '36.f2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1'], 'contains': ['72.f2', '108.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3545, -1, 4507, -1], 'generators': [4, 992, 456, 648], 'label': '1944.3477.36.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f2', 'old_label': '36.f2', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635115
    {'ambient': '1944.3477', 'aut_centralizer_order': 972, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.40', 'aut_weyl_index': 972, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.c1'], 'contains': ['216.a1', '216.b1', '216.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9773, 3531, 9796, 6203], 'generators': [288, 216, 648], 'label': '1944.3477.72.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': '1944.3477', '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: 107635116
    {'ambient': '1944.3477', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.e1'], 'contains': ['216.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1618, 9199, 3290, 9417], 'generators': [1352, 1320], 'label': '1944.3477.72.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': '1944.3477', '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: 107635117
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1296, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.b1', '24.c1', '36.a1'], 'contains': ['216.b1', '216.c1', '216.d1', '216.f1', '216.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5404, -1, 7109, -1], 'generators': [1320, 288, 648], 'label': '1944.3477.72.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': '1944.3477', '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: 107635118
    {'ambient': '1944.3477', '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', '12.c1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4110, 801, 5094, 2557], 'generators': [4, 648, 216, 704, 24, 288], 'label': '1944.3477.4.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': '1944.3477', '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': '648.712'}
  • id: 107635119
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.c1', '36.b1'], 'contains': ['216.b1', '216.d1', '216.g1', '216.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [8305, -1, 8022, -1], 'generators': [1536, 288, 648], 'label': '1944.3477.72.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': '1944.3477', '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': '6.1'}
  • id: 107635120
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '36.d1'], 'contains': ['216.c1', '216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2687, -1, 3667, -1], 'generators': [1352, 1608], 'label': '1944.3477.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.e1', 'projective_image': '1944.3477', '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': '18.4'}
  • id: 107635121
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.9', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '36.f1'], 'contains': ['216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4354, -1, 5514, -1], 'generators': [1640, 1536], 'label': '1944.3477.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.f1', 'projective_image': '1944.3477', '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': '18.4'}
  • id: 107635122
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '72.f2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.f2'], 'contains': ['216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4023, -1, 5136, -1], 'generators': [1640, 1752], 'label': '1944.3477.72.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.f2', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635123
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '72.f3', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '36.f3'], 'contains': ['216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3693, -1, 4759, -1], 'generators': [1640, 1464], 'label': '1944.3477.72.f3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.f3', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f3', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107635124
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1'], 'contains': ['216.e1', '216.f1', '216.g1', '216.h1', '216.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9021, -1, 9365, -1], 'generators': [1320, 936, 216], 'label': '1944.3477.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '72.g1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635125
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.40', 'aut_weyl_index': 972, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.g1'], 'contains': ['216.a1', '216.f1', '216.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9397, -1, 8935, -1], 'generators': [1320, 288, 216], 'label': '1944.3477.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '72.h1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635126
    {'ambient': '1944.3477', 'aut_centralizer_order': 32, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, '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': [470, -1, 215, -1], 'generators': [1, 2, 4, 648], 'label': '1944.3477.81.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '1944.3477', '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: 107635127
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.c1'], 'contains': ['216.b1', '324.a1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6561, -1, 6537, -1], 'generators': [4, 648, 288], 'label': '1944.3477.108.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': '1944.3477', '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: 107635128
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.d1', '36.e1'], 'contains': ['216.c1', '324.a1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2444, -1, 2744, -1], 'generators': [4, 648, 24], 'label': '1944.3477.108.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': '1944.3477', '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: 107635129
    {'ambient': '1944.3477', 'aut_centralizer_order': 27, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1152.16441', 'aut_weyl_index': 27, 'centralizer': '72.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.a1', '24.b1', '24.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4693, 801, 6527, 2557], 'generators': [1352, 1320, 288, 216], 'label': '1944.3477.8.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': '1944.3477', '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: 107635130
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.a1', '36.b1', '36.d1', '36.f1', '36.f2', '36.f3'], 'contains': ['216.d1', '324.a1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [3440, -1, 4213, -1], 'generators': [4, 648, 312], 'label': '1944.3477.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '108.c1', 'projective_image': '1944.3477', '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': '6.1'}
  • id: 107635131
    {'ambient': '1944.3477', 'aut_centralizer_order': 6, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.g1'], 'contains': ['216.f1', '324.b1', '324.c1', '324.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5863, -1, 5944, -1], 'generators': [4, 24, 288], 'label': '1944.3477.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.d1', 'projective_image': '1944.3477', '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': '18.4'}
  • id: 107635132
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '36.10', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.b1', '36.g1'], 'contains': ['216.g1', '324.b1', '324.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [7259, -1, 7566, -1], 'generators': [4, 240, 288], 'label': '1944.3477.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.e1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107635133
    {'ambient': '1944.3477', 'aut_centralizer_order': 24, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.g1', '54.a1'], 'contains': ['216.a1', '324.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7676, -1, 8478, -1], 'generators': [4, 288, 216], 'label': '1944.3477.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.f1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 107635134
    {'ambient': '1944.3477', 'aut_centralizer_order': 96, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.c1', '81.a1'], 'contains': ['324.a1', '486.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [438, -1, 561, -1], 'generators': [2, 648, 4], 'label': '1944.3477.162.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '1944.3477', '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: 107635135
    {'ambient': '1944.3477', 'aut_centralizer_order': 1944, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1944, 'centralizer': '8.a1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.h1', '108.f1'], 'contains': ['648.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9833, 3531, 8909, 6203], 'generators': [288, 216], 'label': '1944.3477.216.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': '1944.3477', '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: 107635136
    {'ambient': '1944.3477', 'aut_centralizer_order': 1944, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.c1', '72.d1', '108.a1'], 'contains': ['648.a1', '648.b1', '648.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7975, -1, 7162, -1], 'generators': [288, 648], 'label': '1944.3477.216.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': '1944.3477', '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: 107635137
    {'ambient': '1944.3477', 'aut_centralizer_order': 648, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.b1'], 'contains': ['648.a1', '648.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2567, -1, 5100, -1], 'generators': [1320, 648], 'label': '1944.3477.216.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': '1944.3477', '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: 107635138
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.d1', '72.e1', '72.f1', '72.f2', '72.f3', '108.c1'], 'contains': ['648.a1', '648.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4395, -1, 5530, -1], 'generators': [1608, 648], 'label': '1944.3477.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.d1', 'projective_image': '1944.3477', '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': '6.1'}
  • id: 107635139
    {'ambient': '1944.3477', 'aut_centralizer_order': 972, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.g1'], 'contains': ['648.b1', '648.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9342, -1, 9350, -1], 'generators': [936, 216], 'label': '1944.3477.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.e1', 'projective_image': '1944.3477', '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': '1.1'}
  • id: 107635140
    {'ambient': '1944.3477', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 36, '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': [2870, -1, 944, -1], 'generators': [1, 648, 216, 2, 4, 72], 'label': '1944.3477.9.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': '1944.3477', '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: 107635141
    {'ambient': '1944.3477', 'aut_centralizer_order': 162, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.g1', '72.h1', '108.d1'], 'contains': ['648.b1', '648.d1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7598, -1, 6731, -1], 'generators': [1320, 288], 'label': '1944.3477.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '216.f1', 'projective_image': '1944.3477', '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': '2.1'}
  • id: 107635142
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.g1', '72.h1', '108.e1'], 'contains': ['648.b1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8846, -1, 8022, -1], 'generators': [1536, 288], 'label': '1944.3477.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '216.g1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635143
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 7776, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.g1'], 'contains': ['648.c1', '648.d1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6130, -1, 7592, -1], 'generators': [1320, 936], 'label': '1944.3477.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '216.h1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635144
    {'ambient': '1944.3477', 'aut_centralizer_order': 81, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.g1'], 'contains': ['648.c1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [8410, -1, 8452, -1], 'generators': [1536, 936], 'label': '1944.3477.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '216.i1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107635145
    {'ambient': '1944.3477', 'aut_centralizer_order': 64, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, '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': [2123, -1, 142, -1], 'generators': [1], 'label': '1944.3477.243.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': '1944.3477', '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: 107635146
    {'ambient': '1944.3477', 'aut_centralizer_order': 192, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.c1', '162.a1'], 'contains': ['648.a1', '972.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3000, -1, 4266, -1], 'generators': [4, 648], 'label': '1944.3477.324.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': '1944.3477', '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: 107635147
    {'ambient': '1944.3477', 'aut_centralizer_order': 48, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.d1', '108.e1', '108.f1'], 'contains': ['648.b1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6584, -1, 6327, -1], 'generators': [4, 288], 'label': '1944.3477.324.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': '1944.3477', '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: 107635148
    {'ambient': '1944.3477', 'aut_centralizer_order': 48, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '108.d1'], 'contains': ['648.d1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5097, -1, 4696, -1], 'generators': [4, 24], 'label': '1944.3477.324.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': '1944.3477', '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: 107635149
    {'ambient': '1944.3477', 'aut_centralizer_order': 6, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.c1', '108.d1', '108.e1'], 'contains': ['648.e1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [5532, -1, 5944, -1], 'generators': [4, 312], 'label': '1944.3477.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '324.d1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107635150
    {'ambient': '1944.3477', 'aut_centralizer_order': 192, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, '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': [3485, -1, 834, -1], 'generators': [2], 'label': '1944.3477.486.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': '1944.3477', '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: 107635151
    {'ambient': '1944.3477', 'aut_centralizer_order': 8, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.520', 'aut_weyl_index': 72, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.b1', '81.a1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [167, -1, 467, -1], 'generators': [1, 648, 672, 2, 4, 1328], 'label': '1944.3477.9.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': '1944.3477', '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: 107635152
    {'ambient': '1944.3477', 'aut_centralizer_order': 15552, 'aut_label': '648.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.c1', '216.d1', '324.a1'], 'contains': ['1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2986, 3858, 5530, 7864], 'generators': [648], 'label': '1944.3477.648.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': '1944.3477', '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: 107635153
    {'ambient': '1944.3477', 'aut_centralizer_order': 3888, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '216.e1', '216.f1', '216.g1', '324.b1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8149, -1, 7162, -1], 'generators': [288], 'label': '1944.3477.648.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': '1944.3477', '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: 107635154
    {'ambient': '1944.3477', 'aut_centralizer_order': 1944, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.e1', '216.h1', '216.i1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7625, -1, 7592, -1], 'generators': [936], 'label': '1944.3477.648.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': '1944.3477', '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: 107635155
    {'ambient': '1944.3477', 'aut_centralizer_order': 1296, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.f1', '216.h1', '324.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6019, -1, 6380, -1], 'generators': [1320], 'label': '1944.3477.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.d1', 'projective_image': '1944.3477', '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: 107635156
    {'ambient': '1944.3477', 'aut_centralizer_order': 162, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.d1', '216.f1', '216.g1', '216.h1', '216.i1', '324.d1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6621, -1, 6758, -1], 'generators': [1608], 'label': '1944.3477.648.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '648.e1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107635157
    {'ambient': '1944.3477', 'aut_centralizer_order': 384, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '324.d1', '486.a1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5336, -1, 4927, -1], 'generators': [4], 'label': '1944.3477.972.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': '1944.3477', '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: 107635158
    {'ambient': '1944.3477', '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', '648.e1', '972.a1'], 'contains': [], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6171, 3858, 6569, 7864], 'generators': [], 'label': '1944.3477.1944.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': '1944.3477', '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: 107635159
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '108.39', 'aut_weyl_index': 288, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.a1'], 'contains': ['24.a1', '36.a1', '36.b1', '36.d1', '36.f1', '36.f2', '36.f3'], 'core': '648.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4110, -1, 5094, -1], 'generators': [4, 648, 704, 240, 288], 'label': '1944.3477.12.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': '1944.3477', '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: 107635160
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 36, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.b1', '36.a1', '36.d1', '36.e1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2532, -1, 3704, -1], 'generators': [4, 648, 704, 24, 288], 'label': '1944.3477.12.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': '1944.3477', '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: 107635161
    {'ambient': '1944.3477', 'aut_centralizer_order': 3, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 36, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.c1', '36.a1', '36.b1', '36.c1', '36.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7282, -1, 7949, -1], 'generators': [4, 216, 648, 24, 288], 'label': '1944.3477.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '12.c1', 'projective_image': '1944.3477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}