Abstract group data - 1944.3518

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [3, 6, 6, 8], 'aut_gens': [[1, 2, 6, 36, 216, 648], [941, 2, 942, 900, 864, 648], [535, 28, 822, 468, 1080, 1296], [1597, 12, 1760, 1278, 792, 1296], [1017, 12, 1378, 558, 720, 648]], 'aut_group': None, 'aut_hash': 5764451359405996420, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 93312, 'aut_permdeg': 180, 'aut_perms': [146331816854368808743311090327869425707467718022471604441114970661850479528158740714559368265424835817639192441965216236650230858679719892250529376348468026765995733381358327782592745096906995020120726857890127786364569998459786573012388884562785082605652520804180791743946597717911601568300947115511309772112516056186529154966387, 67769555085987269869582502796147618912450297239930393146778330372958498525242134549511258143535640548247636218418856826412046640019737769294744244249225936473707382622666863423299898500670585243040544702583546286530806856845756153502424716869838450527294463007857159529981444445367800936951986229538546664475823132158560239485535, 29404262466976922698065173987303051882528582754551926997256479071590224083083712227548830534739156760384705124663030814490373561843941741582965555467175190391157717595424199782687503318872011254501210951370717486678375213253097173338731864563328624147369238900119222862940417872920778655243552669253537081077629630122375095214137, 58306967206690871433106504078128312205107456793044637451942037436021882249178366322844343712457754411435884415741024327138039615442898535924740475004230431195928001874350500491149619396545760130802430535512917978895445494135097459289524776809852224280911436123938171812752353334655391709790660735476762637544103719403819865721554], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 18, 1, 1], [2, 162, 1, 1], [3, 2, 1, 1], [3, 2, 4, 1], [3, 4, 4, 1], [3, 12, 1, 2], [3, 12, 8, 1], [3, 24, 4, 1], [4, 162, 1, 1], [6, 18, 1, 1], [6, 18, 4, 1], [6, 18, 8, 1], [6, 36, 1, 1], [6, 36, 4, 1], [6, 36, 8, 1], [6, 324, 1, 1], [12, 162, 1, 2]], 'aut_supersolvable': False, 'aut_tex': '(C_3:S_3\\times \\He_3).(D_4\\times S_4)', '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': 5764451359405996420, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_3:S_3\\times \\He_3).(D_4\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 18, 1], [2, 162, 1], [3, 2, 5], [3, 4, 4], [3, 12, 10], [3, 24, 4], [4, 162, 1], [6, 18, 13], [6, 36, 13], [6, 324, 1], [12, 162, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1944.3518', 'commutator_count': 1, 'commutator_label': '486.230', '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': 3518, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 18, 1, 1], [2, 162, 1, 1], [3, 2, 1, 5], [3, 4, 1, 4], [3, 12, 1, 2], [3, 12, 2, 4], [3, 24, 1, 4], [4, 162, 1, 1], [6, 18, 1, 5], [6, 18, 2, 4], [6, 36, 1, 5], [6, 36, 2, 4], [6, 324, 1, 1], [12, 162, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 30240, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '648.721', 'hash': 3518, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 6, 6, 3, 3], 'inner_gens': [[1, 4, 30, 1278, 1440, 1296], [5, 2, 6, 36, 216, 648], [13, 2, 6, 1260, 1080, 648], [19, 2, 942, 36, 1728, 1296], [937, 2, 1734, 1116, 216, 648], [1297, 2, 6, 1332, 216, 648]], 'inner_hash': 3518, 'inner_nilpotent': False, 'inner_order': 1944, 'inner_split': True, 'inner_tex': 'C_3^3.\\SOPlus(4,2)', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 17], [4, 20], [6, 4], [8, 4], [12, 8]], 'label': '1944.3518', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^3.SO+(4,2)', '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': 21, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 57, 'number_divisions': 44, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 182, 'number_subgroup_classes': 522, 'number_subgroups': 12936, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 189], [3, 242], [4, 162], [6, 1026], [12, 324]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [522, 108], 'outer_gens': [[523, 26, 822, 1926, 720, 648], [1171, 2, 874, 36, 432, 1296]], 'outer_group': '48.29', 'outer_hash': 29, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 8, 'outer_perms': [38459, 7087], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3)', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 9], [4, 8], [6, 2], [8, 12], [12, 9]], 'representations': {'PC': {'code': 193722217512330889099246932010128334595023603090708548785239, 'gens': [1, 2, 3, 5, 7, 8], 'pres': [8, 2, 3, 2, 3, 2, 3, 3, 3, 65, 722, 66, 771, 51124, 8420, 116, 51845, 11541, 80646, 10102, 2726, 1222, 82951, 2343]}, 'Perm': {'d': 21, 'gens': [6423386324101921, 2479612579204685160, 54465125132851944, 5528620255912001424, 8083048291053706104, 10641519967659519603, 3, 13038081705142262640]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3.\\SOPlus(4,2)', 'transitive_degree': 54, '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: 136997974
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3518, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136997985
    {'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 3518, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 18, 'size': 9}
  • id: 136997996
    {'aut_label': '2B', 'centralizer': '18.e1', 'counter': 3, 'group_counter': 3518, 'group_order': 1944, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 108, 'size': 18}
  • id: 136998007
    {'aut_label': '2C', 'centralizer': '162.i1', 'counter': 4, 'group_counter': 3518, 'group_order': 1944, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1171, 'size': 162}
  • id: 136998018
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 3518, 'group_order': 1944, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 12, 'size': 2}
  • id: 136998027
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 3518, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 16, 'size': 2}
  • id: 136998028
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 3518, 'group_order': 1944, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 14, 'size': 2}
  • id: 136998029
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 3518, 'group_order': 1944, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 4, 'size': 2}
  • id: 136998030
    {'aut_label': '3E', 'centralizer': '2.c1', 'counter': 9, 'group_counter': 3518, 'group_order': 1944, 'label': '3E', 'order': 3, 'powers': [9, 1], 'representative': 648, 'size': 2}
  • id: 136997975
    {'aut_label': '3F', 'centralizer': '4.a1', 'counter': 10, 'group_counter': 3518, 'group_order': 1944, 'label': '3F', 'order': 3, 'powers': [10, 1], 'representative': 1308, 'size': 4}
  • id: 136997976
    {'aut_label': '3F', 'centralizer': '4.a1', 'counter': 11, 'group_counter': 3518, 'group_order': 1944, 'label': '3G', 'order': 3, 'powers': [11, 1], 'representative': 1312, 'size': 4}
  • id: 136997977
    {'aut_label': '3F', 'centralizer': '4.a1', 'counter': 12, 'group_counter': 3518, 'group_order': 1944, 'label': '3H', 'order': 3, 'powers': [12, 1], 'representative': 1310, 'size': 4}
  • id: 136997978
    {'aut_label': '3F', 'centralizer': '4.a1', 'counter': 13, 'group_counter': 3518, 'group_order': 1944, 'label': '3I', 'order': 3, 'powers': [13, 1], 'representative': 1300, 'size': 4}
  • id: 136997979
    {'aut_label': '3J', 'centralizer': '12.d1', 'counter': 14, 'group_counter': 3518, 'group_order': 1944, 'label': '3J', 'order': 3, 'powers': [14, 1], 'representative': 72, 'size': 12}
  • id: 136997980
    {'aut_label': '3K', 'centralizer': '12.j1', 'counter': 15, 'group_counter': 3518, 'group_order': 1944, 'label': '3K', 'order': 3, 'powers': [15, 1], 'representative': 288, 'size': 12}
  • id: 136997981
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 16, 'group_counter': 3518, 'group_order': 1944, 'label': '3L1', 'order': 3, 'powers': [17, 1], 'representative': 96, 'size': 12}
  • id: 136997982
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 17, 'group_counter': 3518, 'group_order': 1944, 'label': '3L-1', 'order': 3, 'powers': [16, 1], 'representative': 156, 'size': 12}
  • id: 136997983
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 18, 'group_counter': 3518, 'group_order': 1944, 'label': '3M1', 'order': 3, 'powers': [19, 1], 'representative': 76, 'size': 12}
  • id: 136997984
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 19, 'group_counter': 3518, 'group_order': 1944, 'label': '3M-1', 'order': 3, 'powers': [18, 1], 'representative': 146, 'size': 12}
  • id: 136997986
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 20, 'group_counter': 3518, 'group_order': 1944, 'label': '3N1', 'order': 3, 'powers': [21, 1], 'representative': 100, 'size': 12}
  • id: 136997987
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 21, 'group_counter': 3518, 'group_order': 1944, 'label': '3N-1', 'order': 3, 'powers': [20, 1], 'representative': 158, 'size': 12}
  • id: 136997988
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 22, 'group_counter': 3518, 'group_order': 1944, 'label': '3O1', 'order': 3, 'powers': [23, 1], 'representative': 232, 'size': 12}
  • id: 136997989
    {'aut_label': '3L1', 'centralizer': '12.d1', 'counter': 23, 'group_counter': 3518, 'group_order': 1944, 'label': '3O-1', 'order': 3, 'powers': [22, 1], 'representative': 458, 'size': 12}
  • id: 136997990
    {'aut_label': '3P', 'centralizer': '24.e1', 'counter': 24, 'group_counter': 3518, 'group_order': 1944, 'label': '3P', 'order': 3, 'powers': [24, 1], 'representative': 300, 'size': 24}
  • id: 136997991
    {'aut_label': '3P', 'centralizer': '24.e1', 'counter': 25, 'group_counter': 3518, 'group_order': 1944, 'label': '3Q', 'order': 3, 'powers': [25, 1], 'representative': 290, 'size': 24}
  • id: 136997992
    {'aut_label': '3P', 'centralizer': '24.e1', 'counter': 26, 'group_counter': 3518, 'group_order': 1944, 'label': '3R', 'order': 3, 'powers': [26, 1], 'representative': 302, 'size': 24}
  • id: 136997993
    {'aut_label': '3P', 'centralizer': '24.e1', 'counter': 27, 'group_counter': 3518, 'group_order': 1944, 'label': '3S', 'order': 3, 'powers': [27, 1], 'representative': 314, 'size': 24}
  • id: 136997994
    {'aut_label': '4A', 'centralizer': '162.g1', 'counter': 28, 'group_counter': 3518, 'group_order': 1944, 'label': '4A', 'order': 4, 'powers': [2, 28], 'representative': 613, 'size': 162}
  • id: 136997995
    {'aut_label': '6A', 'centralizer': '18.b1', 'counter': 29, 'group_counter': 3518, 'group_order': 1944, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 6, 'size': 18}
  • id: 136997997
    {'aut_label': '6A', 'centralizer': '18.b1', 'counter': 30, 'group_counter': 3518, 'group_order': 1944, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 8, 'size': 18}
  • id: 136997998
    {'aut_label': '6A', 'centralizer': '18.b1', 'counter': 31, 'group_counter': 3518, 'group_order': 1944, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 10, 'size': 18}
  • id: 136997999
    {'aut_label': '6A', 'centralizer': '18.b1', 'counter': 32, 'group_counter': 3518, 'group_order': 1944, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 20, 'size': 18}
  • id: 136998000
    {'aut_label': '6E', 'centralizer': '18.d1', 'counter': 33, 'group_counter': 3518, 'group_order': 1944, 'label': '6E', 'order': 6, 'powers': [9, 2], 'representative': 1098, 'size': 18}
  • id: 136998001
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 34, 'group_counter': 3518, 'group_order': 1944, 'label': '6F1', 'order': 6, 'powers': [5, 3], 'representative': 120, 'size': 18}
  • id: 136998002
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 35, 'group_counter': 3518, 'group_order': 1944, 'label': '6F-1', 'order': 6, 'powers': [5, 3], 'representative': 132, 'size': 18}
  • id: 136998003
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 36, 'group_counter': 3518, 'group_order': 1944, 'label': '6G1', 'order': 6, 'powers': [8, 3], 'representative': 110, 'size': 18}
  • id: 136998004
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 37, 'group_counter': 3518, 'group_order': 1944, 'label': '6G-1', 'order': 6, 'powers': [8, 3], 'representative': 112, 'size': 18}
  • id: 136998005
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 38, 'group_counter': 3518, 'group_order': 1944, 'label': '6H1', 'order': 6, 'powers': [7, 3], 'representative': 122, 'size': 18}
  • id: 136998006
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 39, 'group_counter': 3518, 'group_order': 1944, 'label': '6H-1', 'order': 6, 'powers': [7, 3], 'representative': 136, 'size': 18}
  • id: 136998008
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 40, 'group_counter': 3518, 'group_order': 1944, 'label': '6I1', 'order': 6, 'powers': [6, 3], 'representative': 260, 'size': 18}
  • id: 136998009
    {'aut_label': '6F1', 'centralizer': '18.e1', 'counter': 41, 'group_counter': 3518, 'group_order': 1944, 'label': '6I-1', 'order': 6, 'powers': [6, 3], 'representative': 134, 'size': 18}
  • id: 136998010
    {'aut_label': '6J', 'centralizer': '36.i1', 'counter': 42, 'group_counter': 3518, 'group_order': 1944, 'label': '6J', 'order': 6, 'powers': [14, 3], 'representative': 36, 'size': 36}
  • id: 136998011
    {'aut_label': '6K', 'centralizer': '36.b1', 'counter': 43, 'group_counter': 3518, 'group_order': 1944, 'label': '6K', 'order': 6, 'powers': [10, 2], 'representative': 654, 'size': 36}
  • id: 136998012
    {'aut_label': '6K', 'centralizer': '36.b1', 'counter': 44, 'group_counter': 3518, 'group_order': 1944, 'label': '6L', 'order': 6, 'powers': [11, 2], 'representative': 656, 'size': 36}
  • id: 136998013
    {'aut_label': '6K', 'centralizer': '36.b1', 'counter': 45, 'group_counter': 3518, 'group_order': 1944, 'label': '6M', 'order': 6, 'powers': [12, 2], 'representative': 658, 'size': 36}
  • id: 136998014
    {'aut_label': '6K', 'centralizer': '36.b1', 'counter': 46, 'group_counter': 3518, 'group_order': 1944, 'label': '6N', 'order': 6, 'powers': [13, 2], 'representative': 668, 'size': 36}
  • id: 136998015
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 47, 'group_counter': 3518, 'group_order': 1944, 'label': '6O1', 'order': 6, 'powers': [16, 3], 'representative': 48, 'size': 36}
  • id: 136998016
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 48, 'group_counter': 3518, 'group_order': 1944, 'label': '6O-1', 'order': 6, 'powers': [17, 3], 'representative': 60, 'size': 36}
  • id: 136998017
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 49, 'group_counter': 3518, 'group_order': 1944, 'label': '6P1', 'order': 6, 'powers': [18, 3], 'representative': 38, 'size': 36}
  • id: 136998019
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 50, 'group_counter': 3518, 'group_order': 1944, 'label': '6P-1', 'order': 6, 'powers': [19, 3], 'representative': 40, 'size': 36}
  • id: 136998020
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 51, 'group_counter': 3518, 'group_order': 1944, 'label': '6Q1', 'order': 6, 'powers': [20, 3], 'representative': 50, 'size': 36}
  • id: 136998021
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 52, 'group_counter': 3518, 'group_order': 1944, 'label': '6Q-1', 'order': 6, 'powers': [21, 3], 'representative': 64, 'size': 36}
  • id: 136998022
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 53, 'group_counter': 3518, 'group_order': 1944, 'label': '6R1', 'order': 6, 'powers': [22, 3], 'representative': 44, 'size': 36}
  • id: 136998023
    {'aut_label': '6O1', 'centralizer': '36.i1', 'counter': 54, 'group_counter': 3518, 'group_order': 1944, 'label': '6R-1', 'order': 6, 'powers': [23, 3], 'representative': 62, 'size': 36}
  • id: 136998024
    {'aut_label': '6S', 'centralizer': '324.k1', 'counter': 55, 'group_counter': 3518, 'group_order': 1944, 'label': '6S', 'order': 6, 'powers': [15, 4], 'representative': 1531, 'size': 324}
  • id: 136998025
    {'aut_label': '12A1', 'centralizer': '162.g1', 'counter': 56, 'group_counter': 3518, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [33, 28], 'representative': 1783, 'size': 162}
  • id: 136998026
    {'aut_label': '12A5', 'centralizer': '162.g1', 'counter': 57, 'group_counter': 3518, 'group_order': 1944, 'label': '12A5', 'order': 12, 'powers': [33, 28], 'representative': 487, '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: 12111040
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12111051
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12111062
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 12111073
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 12111079
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111080
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 0, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111081
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 0, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0], 'schur_index': 1}
  • id: 12111082
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 0, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111083
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111041
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, -1, -1, -1, 2, 2, 1, 1, -2, -2, 1, 1, 1, 1, -2, -1, -1, -1, 2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111042
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 0, -1, -1, 2, -1, 2, 1, 1, 1, 1, -2, -2, 1, 1, -2, -1, -1, 2, -1, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111043
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 0, -1, 2, -1, -1, 2, 1, 1, 1, 1, 1, 1, -2, -2, -2, -1, 2, -1, -1, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0], 'schur_index': 1}
  • id: 12111044
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 2, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 0, 2, -1, -1, -1, 2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 2, -1, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111045
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2j', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, 4, -2, -2, -2, 4, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, -2, 4, -2, -2, 0, 2, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111046
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2k', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, 4, -2, 4, -2, -2, 4, -2, 4, 4, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, -2, 0, 2, 2, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111047
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2l', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, 4, -2, -2, 4, -2, 4, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, 4, 0, 2, -4, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111048
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.2m', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, -2, -2, -2, 4, 4, -2, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, 0, -4, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111049
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 0, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 12111050
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111052
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4c', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111053
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, 0, -2, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], 'schur_index': 1}
  • id: 12111063
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.6a', 'multiplicity': 1, 'nt': [27, 76], 'qdim': 6, 'qvalues': [6, -2, 0, 0, 6, 6, 6, 6, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 12111064
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.6b', 'multiplicity': 1, 'nt': [36, 277], 'qdim': 6, 'qvalues': [6, -2, 0, 0, 6, 6, 6, 6, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 12111054
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4e', 'multiplicity': 2, 'nt': [12, 116], 'qdim': 8, 'qvalues': [8, 0, 4, 0, -4, -4, -4, 8, 8, -4, -4, -4, 8, 2, -4, -1, -1, 2, 2, -1, -1, -1, -1, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111055
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4f', 'multiplicity': 2, 'nt': [12, 116], 'qdim': 8, 'qvalues': [8, 0, 4, 0, -4, -4, 8, -4, 8, -4, -4, 8, -4, 2, -4, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, 4, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111056
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4g', 'multiplicity': 2, 'nt': [12, 116], 'qdim': 8, 'qvalues': [8, 0, 4, 0, -4, 8, -4, -4, 8, -4, 8, -4, -4, 2, -4, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0], 'schur_index': 1}
  • id: 12111057
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4h', 'multiplicity': 2, 'nt': [12, 116], 'qdim': 8, 'qvalues': [8, 0, 4, 0, 8, -4, -4, -4, 8, 8, -4, -4, -4, 2, -4, 2, 2, -1, -1, -1, -1, -1, -1, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 12111058
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4i', 'multiplicity': 2, 'nt': [24, 556], 'qdim': 8, 'qvalues': [8, 0, -4, 0, -4, -4, -4, 8, 8, -4, -4, -4, 8, 2, -4, -1, -1, 2, 2, -1, -1, -1, -1, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111059
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4j', 'multiplicity': 2, 'nt': [24, 556], 'qdim': 8, 'qvalues': [8, 0, -4, 0, -4, -4, 8, -4, 8, -4, -4, 8, -4, 2, -4, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -4, -4, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111060
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4k', 'multiplicity': 2, 'nt': [24, 556], 'qdim': 8, 'qvalues': [8, 0, -4, 0, -4, 8, -4, -4, 8, -4, 8, -4, -4, 2, -4, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0], 'schur_index': 1}
  • id: 12111061
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.4l', 'multiplicity': 2, 'nt': [24, 556], 'qdim': 8, 'qvalues': [8, 0, -4, 0, 8, -4, -4, -4, 8, 8, -4, -4, -4, 2, -4, 2, 2, -1, -1, -1, -1, -1, -1, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 12111066
    {'cdim': 8, 'counter': 33, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.8a', 'multiplicity': 1, 'nt': [12, 120], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, -4, 8, 8, -4, -4, -4, 8, -4, 2, 2, 2, -4, -4, 2, 2, 2, 2, -1, 2, -1, -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], 'schur_index': 1}
  • id: 12111067
    {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.8b', 'multiplicity': 1, 'nt': [12, 120], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, 8, -4, 8, -4, -4, 8, -4, -4, 2, 2, 2, 2, 2, -4, -4, 2, 2, -1, -1, 2, -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], 'schur_index': 1}
  • id: 12111068
    {'cdim': 8, 'counter': 35, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.8c', 'multiplicity': 1, 'nt': [12, 120], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, 8, -4, -4, 8, -4, 8, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, -4, -4, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111069
    {'cdim': 8, 'counter': 36, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.8d', 'multiplicity': 1, 'nt': [12, 120], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, -4, -4, -4, 8, 8, -4, -4, -4, -4, 2, -4, -4, 2, 2, 2, 2, 2, 2, 2, -1, -1, -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], 'schur_index': 1}
  • id: 12111065
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.6c', 'multiplicity': 2, 'nt': [18, 105], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 12, 12, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111070
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12a', 'multiplicity': 1, 'nt': [18, 215], 'qdim': 12, 'qvalues': [12, 4, 0, 0, -6, -6, -6, 12, -6, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111071
    {'cdim': 12, 'counter': 38, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12b', 'multiplicity': 1, 'nt': [18, 215], 'qdim': 12, 'qvalues': [12, 4, 0, 0, -6, -6, 12, -6, -6, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111072
    {'cdim': 12, 'counter': 39, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12c', 'multiplicity': 1, 'nt': [18, 215], 'qdim': 12, 'qvalues': [12, 4, 0, 0, -6, 12, -6, -6, -6, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111074
    {'cdim': 12, 'counter': 40, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12d', 'multiplicity': 1, 'nt': [18, 215], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, -6, -6, -6, -6, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111075
    {'cdim': 12, 'counter': 41, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12e', 'multiplicity': 1, 'nt': [36, 1116], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -6, -6, -6, 12, -6, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111076
    {'cdim': 12, 'counter': 42, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12f', 'multiplicity': 1, 'nt': [36, 1116], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -6, -6, 12, -6, -6, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111077
    {'cdim': 12, 'counter': 43, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12g', 'multiplicity': 1, 'nt': [36, 1116], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -6, 12, -6, -6, -6, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12111078
    {'cdim': 12, 'counter': 44, 'faithful': False, 'group': '1944.3518', 'group_order': 1944, 'image': None, 'label': '1944.3518.12h', 'multiplicity': 1, 'nt': [36, 1116], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, -6, -6, -6, -6, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 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: 27679424
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1944, 'label': '1944.3518.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 27679435
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.3518.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 27679446
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 972, 'label': '1944.3518.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27679457
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.3518.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27679468
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.3518.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679477
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.3518.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679478
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.3518.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679479
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.3518.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679480
    {'center': '4.a1', 'center_index': 4, 'center_order': 486, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 243, 'label': '1944.3518.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679425
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.3518.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679426
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.3518.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679427
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.3518.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679428
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.3518.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679429
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2j1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679430
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679431
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2k1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679432
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679433
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2l1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679434
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 19, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679436
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 20, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2m1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679437
    {'center': '12.a1', 'center_index': 12, 'center_order': 162, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 81, 'label': '1944.3518.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679438
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3518.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679439
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3518.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679440
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3518.4c', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679441
    {'center': '72.a1', 'center_index': 72, 'center_order': 27, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3518.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679442
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 26, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4e1', 'nt': [12, 116], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679443
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 27, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4e2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679444
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 28, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4f1', 'nt': [12, 116], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679445
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4f2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679447
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 30, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4g1', 'nt': [12, 116], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679448
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 31, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4g2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679449
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 32, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4h1', 'nt': [12, 116], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679450
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 33, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4h2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679451
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 34, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4i1', 'nt': [24, 556], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679452
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 35, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4i2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679453
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 36, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4j1', 'nt': [24, 556], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679454
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 37, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4j2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679455
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 38, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4k1', 'nt': [24, 556], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679456
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 39, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4k2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679458
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 40, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4l1', 'nt': [24, 556], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679459
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.4l2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679460
    {'center': '216.b1', 'center_index': 216, 'center_order': 9, 'counter': 42, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3518.6a', 'nt': [27, 76], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27679461
    {'center': '216.b1', 'center_index': 216, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3518.6b', 'nt': [36, 277], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 27679462
    {'center': '216.b1', 'center_index': 216, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3518.6c1', 'nt': [18, 105], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 27679463
    {'center': '216.b1', 'center_index': 216, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3518.6c2', 'nt': [18, 105], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 27679464
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.8a', 'nt': [12, 120], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679465
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.8b', 'nt': [12, 120], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679466
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 48, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.8c', 'nt': [12, 120], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27679467
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 49, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '216.158', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3518.8d', 'nt': [12, 120], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679469
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 50, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12a', 'nt': [18, 215], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[1, 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]], [[0, 0]], [[0, 0]]]}
  • id: 27679470
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 51, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12b', 'nt': [18, 215], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679471
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 52, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12c', 'nt': [18, 215], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679472
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 53, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12d', 'nt': [18, 215], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679473
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 54, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12e', 'nt': [36, 1116], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[-1, 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]], [[0, 0]], [[0, 0]]]}
  • id: 27679474
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12f', 'nt': [36, 1116], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679475
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 56, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12g', 'nt': [36, 1116], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27679476
    {'center': '648.a1', 'center_index': 648, 'center_order': 3, 'counter': 57, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1944.3518', 'group_counter': 3518, 'group_order': 1944, 'image': None, 'image_isoclass': '648.545', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.3518.12h', 'nt': [36, 1116], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 107643914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.3518.1.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': '1944.3518', 'subgroup_hash': 3518, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 107644008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.781', 'subgroup_hash': 781, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 972, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107644041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.545', 'subgroup_hash': 545, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 107644052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 486, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.4.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.222', 'subgroup_hash': 222, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.242', 'subgroup_hash': 242, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107643959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 243, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1944.3518.8.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': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L2', '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: 107643970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.9.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': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107643981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.9.b1', 'maximal': False, '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': '216.87', 'subgroup_hash': 87, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 107643992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107644013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107644016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 108, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107644022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107644029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, '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: 107644031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.24.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: 107644032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.24.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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 107644034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 107644035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.27.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107644036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107644037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 54, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 107644038
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', '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: 107644058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107644060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', '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: 107644061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', '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: 107644062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', '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: 107644064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', '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: 107644065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', '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: 107644066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107644072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107644073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107644079
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 27, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.72.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': '72.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 107644080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.72.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': '72.35', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], '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: 107644081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.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: 107644082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.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: 107644083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.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: 107644087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.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: 107644088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107644090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107644093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107644094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107644095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107643919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107643920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107643921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 107643922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 107643923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 107643924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', '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: 107643935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1', '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: 107643936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.u1', '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: 107643938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1', '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: 107643939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.w1', '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: 107643940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.x1', '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: 107643941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1', '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: 107643942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1', '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: 107643943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1', '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: 107643944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1', '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: 107643945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1', '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: 107643946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643952
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107643953
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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: 107643954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.162.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 9, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.158', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 158, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 9, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3518.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.87', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 87, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:D_4', '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: 107643958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.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: 107643966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.3518.243.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
  • id: 107643974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.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: 107643975
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 154, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107643977
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.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: 107643978
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 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: 107643979
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 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: 107643980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 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: 107643982
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 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: 107643983
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 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: 107643984
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643986
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643987
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643988
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643989
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643990
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.324.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 107643991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.486.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3518.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107643994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 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: 107643995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3518.648.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': '648.545', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 545, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2.\\SOPlus(4,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107643996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 3, 'counter': 173, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3518.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.721', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 721, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:D_4', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'D3', 'C6'], '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: 107643997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.648.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: 107643998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.648.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: 107643999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.648.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: 107644000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 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: 107644001
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 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: 107644002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.972.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: 107644004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 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: 107644005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3518.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 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: 107644006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3518', 'ambient_counter': 3518, 'ambient_order': 1944, 'ambient_tex': 'C_3^3.\\SOPlus(4,2)', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 182, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.3518.1944.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': '1944.3518', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3518, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3.\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C7'], '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: 107643922
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.e1'], 'contains': ['216.l1', '324.c1', '324.d1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6837, -1, 6818, -1], 'generators': [522, 660, 1512], 'label': '1944.3518.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644027
    {'ambient': '1944.3518', 'aut_centralizer_order': 48, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.87', 'aut_weyl_index': 432, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.b1'], 'contains': ['36.a1', '36.t1', '54.k1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4359, -1, 4037, -1], 'generators': [1, 648, 522, 288, 1512], 'label': '1944.3518.18.j1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 107644028
    {'ambient': '1944.3518', 'aut_centralizer_order': 144, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1296, 'centralizer': '648.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.b1'], 'contains': ['36.a1', '162.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5582, -1, 5087, -1], 'generators': [757, 648, 522, 1368, 216], 'label': '1944.3518.18.k1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 107644090
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.b1', '36.o1'], 'contains': ['216.h1', '216.j1', '216.k1'], 'core': '648.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [7441, -1, 6060, -1], 'generators': [300, 1512], 'label': '1944.3518.72.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '72.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107644091
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.c1', '36.u1'], 'contains': ['216.i1', '216.j1', '216.k1'], 'core': '648.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4827, -1, 4576, -1], 'generators': [1092, 1152], 'label': '1944.3518.72.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107644092
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1296, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.b1', '24.c1'], 'contains': ['216.j1', '216.k1'], 'core': '648.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [6367, -1, 5701, -1], 'generators': [1514, 300], 'label': '1944.3518.72.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.m1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107643921
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.d1', '54.k1'], 'contains': ['216.i1', '324.b1', '324.e1'], 'core': '648.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4554, -1, 4403, -1], 'generators': [522, 648, 504], 'label': '1944.3518.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '108.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643914
    {'ambient': '1944.3518', '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', '2.b1', '2.c1', '3.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5002, 5224, 4898, 5389], 'generators': [1, 12, 288, 108, 2, 648, 216, 522], 'label': '1944.3518.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '1944.3518', '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': '1944.3518'}
  • id: 107643915
    {'ambient': '1944.3518', 'aut_centralizer_order': 9, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1728.46336', 'aut_weyl_index': 54, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['12.b1', '12.d1', '12.g1', '18.b1', '18.e1', '18.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7970, -1, 7797, -1], 'generators': [108, 648, 1512, 522, 2, 12], 'label': '1944.3518.6.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '6.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107643916
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '36.e1', '36.f1', '54.d1'], 'contains': ['216.c1', '324.a1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4008, -1, 4178, -1], 'generators': [522, 2, 660], 'label': '1944.3518.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.b1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643917
    {'ambient': '1944.3518', 'aut_centralizer_order': 216, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1944, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.g1', '36.h1', '54.a1', '54.e1', '54.g1'], 'contains': ['216.b1', '324.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5508, -1, 5529, -1], 'generators': [522, 2, 12], 'label': '1944.3518.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.c1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643918
    {'ambient': '1944.3518', 'aut_centralizer_order': 324, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '36.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.e1', '36.g1', '54.h1'], 'contains': ['216.d1', '324.a1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7155, -1, 7316, -1], 'generators': [522, 12, 1512], 'label': '1944.3518.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.d1', 'projective_image': '1944.3518', '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': '6.1'}
  • id: 107643919
    {'ambient': '1944.3518', 'aut_centralizer_order': 324, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1', '36.f1', '36.h1', '54.j1'], 'contains': ['216.e1', '324.a1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2059, -1, 3441, -1], 'generators': [522, 12, 504], 'label': '1944.3518.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '108.e1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107643920
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.c1', '54.i1'], 'contains': ['216.h1', '324.b1', '324.d1'], 'core': '648.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6315, -1, 6594, -1], 'generators': [522, 648, 1512], 'label': '1944.3518.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.f1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107643923
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.d1', '36.f1', '54.l1'], 'contains': ['216.m1', '324.c1', '324.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1627, -1, 3217, -1], 'generators': [522, 660, 504], 'label': '1944.3518.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '108.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643924
    {'ambient': '1944.3518', 'aut_centralizer_order': 324, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1', '36.j1', '54.h1'], 'contains': ['216.d1', '324.f1', '324.g1', '324.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9946, -1, 9073, -1], 'generators': [108, 12, 72], 'label': '1944.3518.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '108.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643925
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1', '36.k1'], 'contains': ['216.f1', '324.f1', '324.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [8880, -1, 9299, -1], 'generators': [108, 2, 156], 'label': '1944.3518.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '108.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643926
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '15552.lj', 'aut_weyl_index': 6, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['12.c1', '12.j1', '12.k1', '18.c1', '18.g1', '18.h1', '18.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2935, -1, 2412, -1], 'generators': [1, 648, 504, 522, 2, 12], 'label': '1944.3518.6.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '6.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '324.168'}
  • id: 107643927
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1944, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '36.l1', '36.m1', '54.a1'], 'contains': ['216.b1', '324.f1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6576, -1, 8486, -1], 'generators': [108, 2, 12], 'label': '1944.3518.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '108.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643928
    {'ambient': '1944.3518', 'aut_centralizer_order': 324, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.j1', '36.k1', '36.l1', '36.n1', '54.b1'], 'contains': ['216.a1', '324.f1', '324.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7651, -1, 7915, -1], 'generators': [108, 12, 648], 'label': '1944.3518.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.m1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643929
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.m1', '36.n1', '54.h1'], 'contains': ['216.d1', '324.f1', '324.j1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9742, -1, 8848, -1], 'generators': [108, 12, 1512], 'label': '1944.3518.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '108.n1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643930
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.p1', '54.i1'], 'contains': ['216.h1', '324.g1', '324.i1'], 'core': '648.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9141, -1, 7691, -1], 'generators': [108, 720, 648], 'label': '1944.3518.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.o1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643931
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.j1', '36.k1', '36.o1'], 'contains': ['216.j1', '324.h1', '324.i1'], 'core': '648.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9539, -1, 8260, -1], 'generators': [108, 1452, 648], 'label': '1944.3518.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '108.p1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643932
    {'ambient': '1944.3518', 'aut_centralizer_order': 432, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.o1', '36.p1', '54.i1'], 'contains': ['216.h1', '324.i1', '324.j1'], 'core': '648.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9311, -1, 7503, -1], 'generators': [108, 1512, 648], 'label': '1944.3518.108.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '108.q1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107643933
    {'ambient': '1944.3518', 'aut_centralizer_order': 36, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.q1', '36.r1', '36.s1', '54.j1'], 'contains': ['216.e1', '324.k1', '324.l1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [854, -1, 1649, -1], 'generators': [1, 504, 12], 'label': '1944.3518.108.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.r1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643934
    {'ambient': '1944.3518', 'aut_centralizer_order': 144, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.t1', '36.u1', '54.k1'], 'contains': ['216.i1', '324.k1', '324.m1'], 'core': '648.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [3244, -1, 2993, -1], 'generators': [1, 1152, 648], 'label': '1944.3518.108.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '108.s1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643935
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.q1', '36.r1', '54.l1'], 'contains': ['216.m1', '324.k1', '324.n1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [498, -1, 1425, -1], 'generators': [1, 504, 660], 'label': '1944.3518.108.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '108.t1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643936
    {'ambient': '1944.3518', 'aut_centralizer_order': 36, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.q1', '36.v1', '36.w1', '36.y1', '54.c1'], 'contains': ['216.a1', '324.l1', '324.m1', '324.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2401, -1, 2533, -1], 'generators': [1, 12, 648], 'label': '1944.3518.108.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '108.u1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107643937
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1296.2909', 'aut_weyl_index': 72, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.h1', '18.g1', '18.j1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4301, -1, 4037, -1], 'generators': [1, 648, 1512, 522, 12, 288], 'label': '1944.3518.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '648.545'}
  • id: 107643938
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.r1', '36.x1', '36.y1', '54.d1'], 'contains': ['216.c1', '324.l1', '324.n1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1458, -1, 1237, -1], 'generators': [1, 2, 660], 'label': '1944.3518.108.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '108.v1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107643939
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.v1', '36.x1', '36.z1', '54.j1'], 'contains': ['216.e1', '324.l1', '324.o1', '324.p1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [191, -1, 1086, -1], 'generators': [1, 12, 288], 'label': '1944.3518.108.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.w1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107643940
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.w1', '36.x1', '36.z1'], 'contains': ['216.g1', '324.l1', '324.p1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1321, -1, 935, -1], 'generators': [1, 2, 300], 'label': '1944.3518.108.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.x1', 'old_label': '108.x1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107643941
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '432.734', 'aut_weyl_index': 216, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.y1', '36.z1', '54.e1'], 'contains': ['216.b1', '324.l1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [3665, -1, 2093, -1], 'generators': [1, 2, 12], 'label': '1944.3518.108.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.y1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107643942
    {'ambient': '1944.3518', 'aut_centralizer_order': 48, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.v1', '54.k1'], 'contains': ['216.i1', '324.m1', '324.o1'], 'core': '648.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [3414, -1, 2805, -1], 'generators': [1, 288, 648], 'label': '1944.3518.108.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.z1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107643943
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.u1', '36.v1', '36.w1'], 'contains': ['216.k1', '324.m1', '324.p1'], 'core': '648.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [2645, -1, 2382, -1], 'generators': [1, 300, 648], 'label': '1944.3518.108.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.u1', 'old_label': '108.ba1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 107643944
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.v1', '36.x1', '54.l1'], 'contains': ['216.m1', '324.n1', '324.o1', '324.p1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [54, -1, 784, -1], 'generators': [1, 660, 288], 'label': '1944.3518.108.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '108.bb1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107643945
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.w1', '36.x1'], 'contains': ['216.o1', '324.n1', '324.p1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [328, -1, 633, -1], 'generators': [1, 650, 1596], 'label': '1944.3518.108.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bc1', 'old_label': '108.bc1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107643946
    {'ambient': '1944.3518', 'aut_centralizer_order': 216, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.a1', '54.b1', '54.h1', '81.a1'], 'contains': ['324.a1', '324.f1', '486.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6915, -1, 6232, -1], 'generators': [108, 522, 12], 'label': '1944.3518.162.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.a1', 'projective_image': '1944.3518', '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: 107643947
    {'ambient': '1944.3518', 'aut_centralizer_order': 864, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1', '54.i1', '81.b1'], 'contains': ['324.b1', '324.i1', '486.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7072, -1, 5940, -1], 'generators': [108, 522, 648], 'label': '1944.3518.162.b1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643948
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 216, 'centralizer': '648.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '18.k1', '54.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5415, -1, 5238, -1], 'generators': [757, 648, 216, 522, 12, 1368], 'label': '1944.3518.6.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 107643949
    {'ambient': '1944.3518', 'aut_centralizer_order': 24, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.c1', '54.d1', '54.e1', '54.j1', '81.a1'], 'contains': ['324.a1', '324.l1', '486.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [3162, -1, 3614, -1], 'generators': [1, 522, 12], 'label': '1944.3518.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643950
    {'ambient': '1944.3518', 'aut_centralizer_order': 96, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.k1', '81.b1'], 'contains': ['324.b1', '324.m1', '486.b1'], 'core': '648.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [3654, -1, 4005, -1], 'generators': [1, 522, 648], 'label': '1944.3518.162.d1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643951
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.c1', '54.d1', '54.l1'], 'contains': ['324.c1', '324.n1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [2262, -1, 2669, -1], 'generators': [1, 522, 660], 'label': '1944.3518.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '162.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643952
    {'ambient': '1944.3518', 'aut_centralizer_order': 72, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.f1', '54.g1', '81.a1'], 'contains': ['324.a1', '486.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5239, -1, 4978, -1], 'generators': [1063, 522, 12], 'label': '1944.3518.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107643953
    {'ambient': '1944.3518', 'aut_centralizer_order': 576, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '162.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '54.f1', '81.b1'], 'contains': ['324.b1', '486.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [5373, -1, 4828, -1], 'generators': [757, 648, 522], 'label': '1944.3518.162.g1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643954
    {'ambient': '1944.3518', 'aut_centralizer_order': 864, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1', '54.i1'], 'contains': ['324.d1', '324.g1', '324.j1', '486.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9061, -1, 8088, -1], 'generators': [108, 522, 1512], 'label': '1944.3518.162.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '162.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643955
    {'ambient': '1944.3518', 'aut_centralizer_order': 96, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1', '54.k1', '54.l1'], 'contains': ['324.e1', '324.k1', '324.o1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1044, -1, 1821, -1], 'generators': [1, 522, 504], 'label': '1944.3518.162.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.i1', 'old_label': '162.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643956
    {'ambient': '1944.3518', 'aut_centralizer_order': 5832, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.c1', '72.d1', '72.e1', '72.f1', '108.a1', '108.m1', '108.u1'], 'contains': ['648.a1', '648.b1', '648.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6323, 8069, 5057, 8895], 'generators': [12, 648], 'label': '1944.3518.216.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['24.a1', '72.a1'], 'normal_contains': ['648.a1', '648.b1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '1944.3518', 'quotient_action_image': '4.2', 'quotient_action_kernel': '54.13', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107643957
    {'ambient': '1944.3518', 'aut_centralizer_order': 1944, 'aut_label': '216.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1944, 'centralizer': '2.a1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.i1', '72.j1', '108.c1', '108.l1', '108.y1'], 'contains': ['648.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5810, 6984, 5348, 7776], 'generators': [2, 12], 'label': '1944.3518.216.b1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '216.b1', 'normal_contained_in': ['72.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '216.b1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.17', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643958
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.g1', '72.h1', '108.b1', '108.v1'], 'contains': ['648.a1', '648.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3968, -1, 4184, -1], 'generators': [2, 660], 'label': '1944.3518.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.c1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643959
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3456.kh', 'aut_weyl_index': 27, 'centralizer': '72.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['24.a1', '24.b1', '24.c1', '24.d1', '24.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5877, 5145, 6070, 4584], 'generators': [2, 12, 288, 1512], 'label': '1944.3518.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['24.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1944.3518', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 107643960
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.g1', '72.i1', '108.d1', '108.j1', '108.n1'], 'contains': ['648.a1', '648.d1', '648.f1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8851, -1, 7323, -1], 'generators': [12, 1512], 'label': '1944.3518.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '216.d1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643961
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.h1', '72.j1', '108.e1', '108.r1', '108.w1'], 'contains': ['648.a1', '648.e1', '648.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1741, -1, 2502, -1], 'generators': [12, 1152], 'label': '1944.3518.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '216.e1', 'projective_image': '1944.3518', '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': '4.2'}
  • id: 107643962
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.g1', '72.i1', '108.k1'], 'contains': ['648.a1', '648.f1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8305, -1, 7186, -1], 'generators': [2, 1524], 'label': '1944.3518.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '216.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643963
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.f1', '72.h1', '72.j1', '108.x1'], 'contains': ['648.a1', '648.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2548, -1, 2638, -1], 'generators': [2, 300], 'label': '1944.3518.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '216.g1', 'projective_image': '1944.3518', '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: 107643964
    {'ambient': '1944.3518', 'aut_centralizer_order': 3888, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.c1', '72.k1', '108.f1', '108.o1', '108.q1'], 'contains': ['648.b1', '648.d1'], 'core': '648.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7817, -1, 6670, -1], 'generators': [1512, 648], 'label': '1944.3518.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.h1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107643965
    {'ambient': '1944.3518', 'aut_centralizer_order': 3888, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.d1', '72.l1', '108.g1', '108.s1', '108.z1'], 'contains': ['648.b1', '648.e1'], 'core': '648.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4528, -1, 4321, -1], 'generators': [1152, 648], 'label': '1944.3518.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.i1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107643966
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.e1', '72.k1', '72.l1', '72.m1', '108.p1'], 'contains': ['648.b1', '648.f1'], 'core': '648.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [8180, -1, 6368, -1], 'generators': [1524, 648], 'label': '1944.3518.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '216.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643967
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.f1', '72.k1', '72.l1', '72.m1', '108.ba1'], 'contains': ['648.b1', '648.g1'], 'core': '648.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4709, -1, 4576, -1], 'generators': [300, 648], 'label': '1944.3518.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '216.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107643968
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.c1', '72.g1', '108.h1'], 'contains': ['648.c1', '648.d1', '648.f1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7964, -1, 6811, -1], 'generators': [660, 1512], 'label': '1944.3518.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643969
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.h1', '108.i1', '108.t1', '108.bb1'], 'contains': ['648.c1', '648.e1', '648.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1411, -1, 2230, -1], 'generators': [660, 1152], 'label': '1944.3518.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '216.m1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107643970
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 18, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.b1', '18.c1', '18.d1', '27.a1', '27.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5002, -1, 4898, -1], 'generators': [1, 648, 12, 108, 522, 2], 'label': '1944.3518.9.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': '1944.3518', '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': '108.39'}
  • id: 107643971
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.g1'], 'contains': ['648.c1', '648.f1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7690, -1, 6524, -1], 'generators': [650, 1524], 'label': '1944.3518.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1', 'old_label': '216.n1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643972
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.f1', '72.h1', '108.bc1'], 'contains': ['648.c1', '648.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1288, -1, 2366, -1], 'generators': [650, 300], 'label': '1944.3518.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '216.o1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643973
    {'ambient': '1944.3518', 'aut_centralizer_order': 96, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1'], 'contains': ['486.a1', '486.b1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [4798, -1, 4696, -1], 'generators': [1297, 108], 'label': '1944.3518.243.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': '1944.3518', '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': '4.2'}
  • id: 107643974
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '108.e1', '162.a1', '162.c1', '162.f1'], 'contains': ['648.a1', '972.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5707, -1, 4930, -1], 'generators': [522, 12], 'label': '1944.3518.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.a1', 'projective_image': '1944.3518', '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: 107643975
    {'ambient': '1944.3518', 'aut_centralizer_order': 5184, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '18.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.f1', '108.g1', '162.b1', '162.d1', '162.g1'], 'contains': ['648.b1', '972.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6072, -1, 5185, -1], 'generators': [522, 648], 'label': '1944.3518.324.b1', 'mobius_quo': None, 'mobius_sub': -54, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.b1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643976
    {'ambient': '1944.3518', 'aut_centralizer_order': 648, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.b1', '108.h1', '108.i1', '162.e1'], 'contains': ['648.c1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3974, -1, 4448, -1], 'generators': [522, 660], 'label': '1944.3518.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '324.c1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643977
    {'ambient': '1944.3518', 'aut_centralizer_order': 2592, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '36.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1', '108.f1', '108.h1', '162.h1'], 'contains': ['648.d1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6745, -1, 6939, -1], 'generators': [522, 1512], 'label': '1944.3518.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '324.d1', 'projective_image': '1944.3518', '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: 107643978
    {'ambient': '1944.3518', 'aut_centralizer_order': 2592, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '36.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1', '108.g1', '108.i1', '162.i1'], 'contains': ['648.e1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2242, -1, 3328, -1], 'generators': [522, 504], 'label': '1944.3518.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '324.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643979
    {'ambient': '1944.3518', 'aut_centralizer_order': 648, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.j1', '108.k1', '108.l1', '108.m1', '108.n1', '162.a1'], 'contains': ['648.a1', '972.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7413, -1, 8028, -1], 'generators': [108, 12], 'label': '1944.3518.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '324.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643980
    {'ambient': '1944.3518', 'aut_centralizer_order': 2592, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1', '108.o1', '162.h1'], 'contains': ['648.d1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9141, -1, 7691, -1], 'generators': [108, 72], 'label': '1944.3518.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '324.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643981
    {'ambient': '1944.3518', 'aut_centralizer_order': 48, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.87', 'aut_weyl_index': 432, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.j1', '18.k1', '81.b1'], 'core': '18.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4478, -1, 4599, -1], 'generators': [1, 648, 216, 108, 522, 288], 'label': '1944.3518.9.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '1944.3518', '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': '216.87'}
  • id: 107643982
    {'ambient': '1944.3518', 'aut_centralizer_order': 324, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.j1', '108.k1', '108.p1'], 'contains': ['648.f1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9428, -1, 8260, -1], 'generators': [108, 156], 'label': '1944.3518.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '324.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107643983
    {'ambient': '1944.3518', 'aut_centralizer_order': 2592, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1', '108.o1', '108.p1', '108.q1', '162.b1'], 'contains': ['648.b1', '972.b1'], 'core': '648.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8148, -1, 7059, -1], 'generators': [108, 648], 'label': '1944.3518.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '324.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643984
    {'ambient': '1944.3518', 'aut_centralizer_order': 864, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.n1', '108.q1', '162.h1'], 'contains': ['648.d1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9249, -1, 7537, -1], 'generators': [108, 1512], 'label': '1944.3518.324.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '324.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643985
    {'ambient': '1944.3518', 'aut_centralizer_order': 288, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '324.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.r1', '108.s1', '108.t1', '162.i1'], 'contains': ['648.e1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [970, -1, 2060, -1], 'generators': [1, 504], 'label': '1944.3518.324.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.i1', 'old_label': '324.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643986
    {'ambient': '1944.3518', 'aut_centralizer_order': 72, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.r1', '108.u1', '108.v1', '108.w1', '108.x1', '108.y1', '162.c1'], 'contains': ['648.a1', '972.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2053, -1, 1941, -1], 'generators': [1, 12], 'label': '1944.3518.324.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '324.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643987
    {'ambient': '1944.3518', 'aut_centralizer_order': 288, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.s1', '108.u1', '108.z1', '108.ba1', '162.d1'], 'contains': ['648.b1', '972.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [3226, -1, 2805, -1], 'generators': [1, 648], 'label': '1944.3518.324.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '324.m1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643988
    {'ambient': '1944.3518', 'aut_centralizer_order': 36, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.t1', '108.u1', '108.v1', '108.bb1', '108.bc1', '162.e1'], 'contains': ['648.c1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1099, -1, 1562, -1], 'generators': [1, 660], 'label': '1944.3518.324.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '324.n1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643989
    {'ambient': '1944.3518', 'aut_centralizer_order': 96, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.w1', '108.z1', '108.bb1', '162.i1'], 'contains': ['648.e1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [692, -1, 1821, -1], 'generators': [1, 288], 'label': '1944.3518.324.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.i1', 'old_label': '324.o1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643990
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '324.p1', 'aut_quo_index': None, 'aut_stab_index': 1296, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.w1', '108.x1', '108.ba1', '108.bb1', '108.bc1'], 'contains': ['648.g1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [391, -1, 1086, -1], 'generators': [1, 300], 'label': '1944.3518.324.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.p1', 'old_label': '324.p1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107643991
    {'ambient': '1944.3518', 'aut_centralizer_order': 1728, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.b1', '162.h1', '243.a1'], 'contains': ['972.a1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6893, -1, 6086, -1], 'generators': [108, 522], 'label': '1944.3518.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '486.a1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643992
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '144.186', 'aut_weyl_index': 648, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.a1', '6.d1', '6.e1'], 'contains': ['24.a1', '36.a1', '36.c1', '36.d1'], 'core': '12.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5668, 6812, 5738, 7312], 'generators': [522, 648, 12, 288, 1512], 'label': '1944.3518.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '1944.3518', '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': '72.40'}
  • id: 107643993
    {'ambient': '1944.3518', 'aut_centralizer_order': 192, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.c1', '162.d1', '162.e1', '162.i1', '243.a1'], 'contains': ['972.a1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [2752, -1, 3614, -1], 'generators': [1, 522], 'label': '1944.3518.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643994
    {'ambient': '1944.3518', 'aut_centralizer_order': 576, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '162.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.f1', '162.g1', '243.a1'], 'contains': ['972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5109, -1, 4810, -1], 'generators': [1063], 'label': '1944.3518.486.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '486.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643995
    {'ambient': '1944.3518', 'aut_centralizer_order': 11664, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '2.a1', 'complements': ['3.a1'], 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.b1', '216.c1', '216.d1', '216.e1', '216.f1', '216.g1', '324.a1', '324.f1', '324.l1'], 'contains': ['1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5915, 7116, 4933, 7912], 'generators': [12], 'label': '1944.3518.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '216.b1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.117', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643996
    {'ambient': '1944.3518', 'aut_centralizer_order': 46656, 'aut_label': '648.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.h1', '216.i1', '216.j1', '216.k1', '324.b1', '324.i1', '324.m1'], 'contains': ['1944.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6436, 8069, 5057, 8895], 'generators': [648], 'label': '1944.3518.648.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1', 'normal_contained_in': ['72.b1', '216.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.b1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.163', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107643997
    {'ambient': '1944.3518', 'aut_centralizer_order': 5832, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.c1', '216.l1', '216.m1', '216.n1', '216.o1', '324.c1', '324.n1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3948, -1, 4448, -1], 'generators': [660], 'label': '1944.3518.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '648.c1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107643998
    {'ambient': '1944.3518', 'aut_centralizer_order': 7776, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1', '216.h1', '216.l1', '324.d1', '324.g1', '324.j1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7997, -1, 6939, -1], 'generators': [1512], 'label': '1944.3518.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '648.d1', 'projective_image': '1944.3518', '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: 107643999
    {'ambient': '1944.3518', 'aut_centralizer_order': 7776, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '12.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1', '216.i1', '216.m1', '324.e1', '324.k1', '324.o1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1629, -1, 2442, -1], 'generators': [1152], 'label': '1944.3518.648.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '648.e1', 'projective_image': '1944.3518', '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: 107644000
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.d1', '216.f1', '216.j1', '216.l1', '216.n1', '324.h1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8736, -1, 6811, -1], 'generators': [1524], 'label': '1944.3518.648.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '648.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107644001
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '216.g1', '216.k1', '216.m1', '216.o1', '324.p1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1521, -1, 2561, -1], 'generators': [300], 'label': '1944.3518.648.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '648.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107644002
    {'ambient': '1944.3518', 'aut_centralizer_order': 10368, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 93312, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '324.d1', '324.e1', '486.a1', '486.b1', '486.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5832, -1, 4813, -1], 'generators': [522], 'label': '1944.3518.972.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '972.a1', 'projective_image': '1944.3518', '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: 107644003
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1'], 'contains': ['24.d1', '36.b1', '36.c1', '36.e1', '36.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7105, -1, 6906, -1], 'generators': [522, 1512, 2, 12, 648], 'label': '1944.3518.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.b1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644004
    {'ambient': '1944.3518', 'aut_centralizer_order': 5184, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 93312, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.f1', '324.g1', '324.h1', '324.i1', '324.j1', '486.a1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8079, -1, 7537, -1], 'generators': [108], 'label': '1944.3518.972.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '972.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107644005
    {'ambient': '1944.3518', 'aut_centralizer_order': 576, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '1.1', 'aut_weyl_index': 93312, 'centralizer': '162.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.k1', '324.l1', '324.m1', '324.n1', '324.o1', '324.p1', '486.b1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1233, -1, 2001, -1], 'generators': [1], 'label': '1944.3518.972.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.i1', 'old_label': '972.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107644006
    {'ambient': '1944.3518', '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', '648.f1', '648.g1', '972.a1', '972.b1', '972.c1'], 'contains': [], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5873, 7592, 4873, 8403], 'generators': [], 'label': '1944.3518.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['648.a1', '648.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '1944.3518', '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: 107644007
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.c1'], 'contains': ['24.e1', '36.b1', '36.d1', '36.f1', '36.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3632, -1, 3562, -1], 'generators': [522, 504, 2, 12, 648], 'label': '1944.3518.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.c1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644008
    {'ambient': '1944.3518', 'aut_centralizer_order': 9, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '216.b1', 'complements': ['972.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1', '6.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7970, 8294, 7088, 8553], 'generators': [108, 216, 288, 522, 648, 2, 12], 'label': '1944.3518.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 107644009
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.b1'], 'contains': ['24.d1', '36.i1', '36.j1', '36.k1', '36.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8393, -1, 8665, -1], 'generators': [108, 648, 2, 12, 720], 'label': '1944.3518.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644010
    {'ambient': '1944.3518', 'aut_centralizer_order': 9, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '648.555', 'aut_weyl_index': 144, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1'], 'contains': ['24.b1', '36.k1', '36.n1', '36.o1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8735, -1, 8038, -1], 'generators': [108, 648, 2, 300, 216], 'label': '1944.3518.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '12.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 107644011
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '216.102', 'aut_weyl_index': 432, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.a1', '36.j1', '36.n1', '36.o1', '36.p1'], 'core': '24.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9432, -1, 7407, -1], 'generators': [108, 648, 12, 288, 216], 'label': '1944.3518.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644012
    {'ambient': '1944.3518', 'aut_centralizer_order': 9, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.b1'], 'contains': ['24.d1', '36.l1', '36.m1', '36.n1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8135, -1, 8380, -1], 'generators': [108, 648, 2, 12, 1512], 'label': '1944.3518.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644013
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '648.555', 'aut_weyl_index': 144, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.d1'], 'contains': ['24.a1', '36.q1', '36.t1', '36.u1', '36.v1'], 'core': '24.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4076, -1, 2943, -1], 'generators': [1, 648, 1512, 12, 288], 'label': '1944.3518.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
  • id: 107644014
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1944.2342', 'aut_weyl_index': 48, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1'], 'contains': ['24.c1', '36.q1', '36.u1', '36.w1'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2795, -1, 2757, -1], 'generators': [1, 648, 1152, 2, 948], 'label': '1944.3518.12.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '12.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '162.40'}
  • id: 107644015
    {'ambient': '1944.3518', 'aut_centralizer_order': 3, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 18, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.c1'], 'contains': ['24.e1', '36.q1', '36.r1', '36.s1', '36.y1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2569, -1, 1876, -1], 'generators': [1, 648, 1152, 2, 12], 'label': '1944.3518.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '108.44'}
  • id: 107644016
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.c1'], 'contains': ['24.e1', '36.v1', '36.w1', '36.x1', '36.y1', '36.z1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2312, -1, 1577, -1], 'generators': [1, 648, 2, 12, 288], 'label': '1944.3518.12.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '972.816'}
  • id: 107644017
    {'ambient': '1944.3518', 'aut_centralizer_order': 432, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.87', 'aut_weyl_index': 432, 'centralizer': '216.b1', 'complements': ['108.y1', '108.v1', '108.x1', '108.bc1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.b1'], 'contains': ['36.a1', '36.p1', '54.i1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8890, 8081, 7128, 9358], 'generators': [108, 648, 522, 288, 216], 'label': '1944.3518.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['36.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 107644018
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.b1', '36.l1', '54.a1', '54.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6292, -1, 6594, -1], 'generators': [108, 648, 522, 2, 12], 'label': '1944.3518.18.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644019
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '1944.a1', 'complements': ['972.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.c1', '6.d1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4301, 1706, 4037, 1760], 'generators': [1, 1512, 288, 522, 648, 2, 12], 'label': '1944.3518.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '1944.3518'}
  • id: 107644020
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 18, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.b1', '36.y1', '54.c1', '54.d1', '54.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3462, -1, 3277, -1], 'generators': [1, 648, 522, 2, 12], 'label': '1944.3518.18.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '1944.3518', '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': '108.39'}
  • id: 107644021
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '9.a1'], 'contains': ['36.b1', '54.f1', '54.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5333, -1, 5426, -1], 'generators': [757, 12, 648, 522, 2], 'label': '1944.3518.18.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644022
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['36.g1', '36.i1', '36.m1', '54.a1', '54.h1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8249, -1, 9045, -1], 'generators': [108, 1512, 522, 2, 12], 'label': '1944.3518.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '18.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644023
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '6.b1'], 'contains': ['36.c1', '36.j1', '36.n1', '54.b1', '54.h1', '54.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9230, -1, 7722, -1], 'generators': [108, 648, 522, 12, 1512], 'label': '1944.3518.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '18.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644024
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '216.162', 'aut_weyl_index': 432, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '6.d1'], 'contains': ['36.d1', '36.q1', '36.v1', '54.c1', '54.j1', '54.k1', '54.l1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2854, -1, 2444, -1], 'generators': [1, 648, 522, 12, 504], 'label': '1944.3518.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '18.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107644025
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '648.555', 'aut_weyl_index': 144, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.c1'], 'contains': ['36.f1', '36.r1', '36.x1', '54.d1', '54.j1', '54.l1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [956, -1, 1304, -1], 'generators': [1, 504, 522, 2, 660], 'label': '1944.3518.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '18.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107644026
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 36, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1'], 'contains': ['36.h1', '36.s1', '36.z1', '54.e1', '54.j1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [2453, -1, 2170, -1], 'generators': [1, 504, 522, 2, 12], 'label': '1944.3518.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '18.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107644029
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '144.186', 'aut_weyl_index': 648, 'centralizer': '72.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.a1', '12.f1', '12.h1'], 'contains': ['72.b1', '72.c1', '72.d1', '72.k1', '72.l1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5949, 5450, 5992, 6248], 'generators': [12, 288, 1512], 'label': '1944.3518.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['72.b1', '216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '1944.3518', 'quotient_action_image': '8.3', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 107644030
    {'ambient': '1944.3518', 'aut_centralizer_order': 3, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '31104.mm', 'aut_weyl_index': 3, 'centralizer': '648.b1', 'complements': ['972.b1', '972.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.e1', '18.d1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5319, 5224, 5351, 5389], 'generators': [757, 216, 1368, 522, 648, 2, 12], 'label': '1944.3518.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '648.721'}
  • id: 107644031
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.162', 'aut_weyl_index': 432, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.e1'], 'contains': ['72.c1', '72.e1', '72.f1', '72.k1', '72.m1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7655, -1, 6312, -1], 'generators': [2, 300, 1512], 'label': '1944.3518.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '24.b1', 'projective_image': '1944.3518', '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': '18.3'}
  • id: 107644032
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.162', 'aut_weyl_index': 432, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.i1'], 'contains': ['72.d1', '72.e1', '72.f1', '72.l1', '72.m1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4876, -1, 4395, -1], 'generators': [2, 1092, 1152], 'label': '1944.3518.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '24.c1', 'projective_image': '1944.3518', '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': '18.3'}
  • id: 107644033
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.d1', '12.g1'], 'contains': ['72.a1', '72.c1', '72.e1', '72.g1', '72.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7985, -1, 7419, -1], 'generators': [2, 12, 1512, 648], 'label': '1944.3518.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644034
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 162, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.c1', '12.j1', '12.k1'], 'contains': ['72.a1', '72.d1', '72.f1', '72.h1', '72.j1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3481, -1, 2624, -1], 'generators': [2, 12, 1152, 648], 'label': '1944.3518.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644035
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '1728.47845', 'aut_weyl_index': 54, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['54.a1', '54.e1', '54.g1', '81.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [4992, -1, 4875, -1], 'generators': [1297, 12, 108, 522, 2], 'label': '1944.3518.27.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': '1944.3518', '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': '36.13'}
  • id: 107644036
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '9.a1'], 'contains': ['54.b1', '54.c1', '54.f1', '81.a1', '81.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4703, -1, 4687, -1], 'generators': [1, 648, 108, 522, 12], 'label': '1944.3518.27.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644037
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1296, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.a1', '18.j1', '18.k1'], 'contains': ['72.b1', '108.f1', '108.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5954, 6984, 5738, 8335], 'generators': [522, 288, 1512, 648], 'label': '1944.3518.36.a1', 'mobius_quo': 0, 'mobius_sub': 54, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '18.a1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '1944.3518', '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': '72.40'}
  • id: 107644038
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.c1', '18.b1', '18.c1', '18.d1'], 'contains': ['72.a1', '108.a1', '108.b1', '108.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5637, -1, 5326, -1], 'generators': [522, 2, 12, 648], 'label': '1944.3518.36.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.b1', 'projective_image': '1944.3518', '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': '4.2'}
  • id: 107644039
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.b1', '18.f1'], 'contains': ['72.c1', '108.a1', '108.d1', '108.f1', '108.h1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6756, -1, 6962, -1], 'generators': [522, 12, 648, 1512], 'label': '1944.3518.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.c1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644040
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.c1', '18.g1'], 'contains': ['72.d1', '108.a1', '108.e1', '108.g1', '108.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3948, -1, 4105, -1], 'generators': [522, 12, 648, 504], 'label': '1944.3518.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.d1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644041
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1296.2909', 'aut_weyl_index': 72, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.d1', '6.e1', '9.b1', '27.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4720, -1, 4636, -1], 'generators': [1, 216, 288, 108, 648, 522, 12], 'label': '1944.3518.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '648.545'}
  • id: 107644042
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1'], 'contains': ['72.g1', '108.b1', '108.d1', '108.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6991, -1, 7221, -1], 'generators': [522, 2, 660, 1512], 'label': '1944.3518.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.e1', 'projective_image': '1944.3518', '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': '6.1'}
  • id: 107644043
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.c1', '18.h1'], 'contains': ['72.h1', '108.b1', '108.e1', '108.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1370, -1, 2427, -1], 'generators': [522, 2, 660, 504], 'label': '1944.3518.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.f1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644044
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '36.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.e1'], 'contains': ['72.i1', '108.c1', '108.d1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7510, -1, 8622, -1], 'generators': [522, 2, 12, 1512], 'label': '1944.3518.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.g1', 'projective_image': '1944.3518', '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': '6.1'}
  • id: 107644045
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.i1'], 'contains': ['72.j1', '108.c1', '108.e1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2670, -1, 3126, -1], 'generators': [522, 2, 12, 504], 'label': '1944.3518.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644046
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.i1', '108.j1', '108.k1', '108.l1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8537, -1, 9885, -1], 'generators': [108, 2, 12, 72], 'label': '1944.3518.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107644047
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.f1', '18.f1'], 'contains': ['72.c1', '108.j1', '108.m1', '108.o1', '108.p1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9637, -1, 8881, -1], 'generators': [108, 12, 720, 648], 'label': '1944.3518.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644048
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.e1'], 'contains': ['72.e1', '108.k1', '108.m1', '108.p1'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8772, -1, 9365, -1], 'generators': [108, 2, 1452, 648], 'label': '1944.3518.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '36.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644049
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.g1', '18.b1'], 'contains': ['72.a1', '108.l1', '108.m1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6351, -1, 8363, -1], 'generators': [108, 2, 12, 648], 'label': '1944.3518.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644050
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.e1'], 'contains': ['72.i1', '108.l1', '108.n1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8301, -1, 9624, -1], 'generators': [108, 2, 12, 1512], 'label': '1944.3518.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.m1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644051
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '216.102', 'aut_weyl_index': 432, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.f1', '12.g1', '18.f1'], 'contains': ['72.c1', '108.m1', '108.n1', '108.q1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9338, -1, 8096, -1], 'generators': [108, 12, 1512, 648], 'label': '1944.3518.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.n1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644052
    {'ambient': '1944.3518', 'aut_centralizer_order': 27, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '3456.kh', 'aut_weyl_index': 27, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.c1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5619, 5224, 5738, 5389], 'generators': [522, 648, 1512, 2, 12, 288], 'label': '1944.3518.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '1944.3518', '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': '72.40'}
  • id: 107644053
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.f1'], 'contains': ['72.k1', '108.p1', '108.q1'], 'core': '648.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [9830, -1, 7873, -1], 'generators': [108, 300, 216, 648], 'label': '1944.3518.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '36.o1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 107644054
    {'ambient': '1944.3518', 'aut_centralizer_order': 432, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.a1'], 'contains': ['72.b1', '108.o1', '108.q1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 7571, -1], 'generators': [108, 288, 216, 648], 'label': '1944.3518.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.p1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644055
    {'ambient': '1944.3518', 'aut_centralizer_order': 18, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '12.i1', '12.j1', '18.g1'], 'contains': ['72.d1', '108.r1', '108.s1', '108.t1', '108.u1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2008, -1, 1884, -1], 'generators': [1, 1152, 12, 648], 'label': '1944.3518.36.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '36.q1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644056
    {'ambient': '1944.3518', 'aut_centralizer_order': 3, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '216.102', 'aut_weyl_index': 432, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.j1', '18.h1'], 'contains': ['72.h1', '108.r1', '108.t1', '108.v1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [956, -1, 311, -1], 'generators': [1, 504, 2, 660], 'label': '1944.3518.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '36.r1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644057
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.i1'], 'contains': ['72.j1', '108.r1', '108.y1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [2429, -1, 910, -1], 'generators': [1, 504, 2, 12], 'label': '1944.3518.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.s1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644058
    {'ambient': '1944.3518', 'aut_centralizer_order': 48, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '18.j1'], 'contains': ['72.b1', '108.s1', '108.z1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [4370, -1, 3891, -1], 'generators': [1, 1512, 288, 648], 'label': '1944.3518.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.t1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644059
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '12.i1'], 'contains': ['72.l1', '108.s1', '108.ba1'], 'core': '648.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3377, -1, 2912, -1], 'generators': [1, 1152, 948, 648], 'label': '1944.3518.36.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.u1', 'old_label': '36.u1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 107644060
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '648.555', 'aut_weyl_index': 144, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '12.k1', '18.g1'], 'contains': ['72.d1', '108.u1', '108.w1', '108.z1', '108.ba1', '108.bb1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2218, -1, 1465, -1], 'generators': [1, 12, 288, 648], 'label': '1944.3518.36.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '36.v1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '324.124'}
  • id: 107644061
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1944.2342', 'aut_weyl_index': 48, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.i1', '12.k1'], 'contains': ['72.f1', '108.u1', '108.x1', '108.ba1', '108.bc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1629, -1, 1143, -1], 'generators': [1, 2, 300, 648], 'label': '1944.3518.36.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '36.w1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '162.40'}
  • id: 107644062
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '648.555', 'aut_weyl_index': 144, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.k1', '18.h1'], 'contains': ['72.h1', '108.v1', '108.w1', '108.x1', '108.bb1', '108.bc1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [302, -1, 79, -1], 'generators': [1, 2, 660, 288], 'label': '1944.3518.36.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '36.x1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107644063
    {'ambient': '1944.3518', 'aut_centralizer_order': 9, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.d1', '12.e1', '12.f1', '12.g1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8389, -1, 7447, -1], 'generators': [108, 648, 216, 2, 12, 288], 'label': '1944.3518.4.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107644064
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 36, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.k1', '18.c1'], 'contains': ['72.a1', '108.u1', '108.v1', '108.y1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2873, -1, 1652, -1], 'generators': [1, 2, 12, 648], 'label': '1944.3518.36.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.y1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107644065
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 36, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.i1'], 'contains': ['72.j1', '108.w1', '108.x1', '108.y1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [1798, -1, 543, -1], 'generators': [1, 2, 12, 288], 'label': '1944.3518.36.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.z1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107644066
    {'ambient': '1944.3518', 'aut_centralizer_order': 36, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.e1', '27.a1'], 'contains': ['108.c1', '108.l1', '162.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [6239, -1, 6765, -1], 'generators': [108, 522, 2, 12], 'label': '1944.3518.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.a1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107644067
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.b1', '18.f1', '27.b1'], 'contains': ['108.a1', '108.m1', '162.a1', '162.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7144, -1, 6584, -1], 'generators': [108, 522, 12, 648], 'label': '1944.3518.54.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644068
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '18.g1', '27.b1'], 'contains': ['108.a1', '108.u1', '162.c1', '162.d1', '162.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2981, -1, 3668, -1], 'generators': [1, 522, 12, 648], 'label': '1944.3518.54.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644069
    {'ambient': '1944.3518', 'aut_centralizer_order': 2, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '216.102', 'aut_weyl_index': 432, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '18.h1'], 'contains': ['108.b1', '108.v1', '162.c1', '162.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1876, -1, 2160, -1], 'generators': [1, 522, 2, 660], 'label': '1944.3518.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '54.d1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107644070
    {'ambient': '1944.3518', 'aut_centralizer_order': 4, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '18.i1', '27.a1'], 'contains': ['108.c1', '108.y1', '162.c1'], 'core': '216.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [4093, -1, 3393, -1], 'generators': [1, 522, 2, 12], 'label': '1944.3518.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.e1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644071
    {'ambient': '1944.3518', 'aut_centralizer_order': 72, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1', '18.d1', '27.b1'], 'contains': ['108.a1', '162.f1', '162.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5426, -1, 5057, -1], 'generators': [757, 648, 522, 12], 'label': '1944.3518.54.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.f1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644072
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '27.a1'], 'contains': ['108.c1', '162.f1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5102, -1, 5550, -1], 'generators': [1063, 522, 2, 12], 'label': '1944.3518.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.g1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107644073
    {'ambient': '1944.3518', 'aut_centralizer_order': 108, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.e1', '18.f1'], 'contains': ['108.d1', '108.j1', '108.n1', '162.a1', '162.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9491, -1, 9123, -1], 'generators': [108, 522, 12, 1512], 'label': '1944.3518.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '54.h1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107644074
    {'ambient': '1944.3518', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.a1', '12.h1', '12.i1', '12.j1', '12.k1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3151, -1, 2827, -1], 'generators': [1, 648, 288, 1512, 2, 12], 'label': '1944.3518.4.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.c1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '972.816'}
  • id: 107644075
    {'ambient': '1944.3518', 'aut_centralizer_order': 432, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.f1'], 'contains': ['108.f1', '108.o1', '108.q1', '162.b1', '162.h1'], 'core': '648.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8929, -1, 7722, -1], 'generators': [108, 522, 1512, 648], 'label': '1944.3518.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '54.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644076
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.g1', '18.h1', '18.i1'], 'contains': ['108.e1', '108.r1', '108.w1', '162.c1', '162.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [778, -1, 1304, -1], 'generators': [1, 522, 12, 504], 'label': '1944.3518.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '54.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644077
    {'ambient': '1944.3518', 'aut_centralizer_order': 48, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.j1'], 'contains': ['108.g1', '108.s1', '108.z1', '162.d1', '162.i1'], 'core': '648.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [3394, -1, 2761, -1], 'generators': [1, 522, 504, 648], 'label': '1944.3518.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '54.k1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644078
    {'ambient': '1944.3518', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2592, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['18.g1', '18.h1'], 'contains': ['108.i1', '108.t1', '108.bb1', '162.e1', '162.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [597, -1, 704, -1], 'generators': [1, 522, 660, 504], 'label': '1944.3518.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '54.l1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107644079
    {'ambient': '1944.3518', 'aut_centralizer_order': 972, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.e1', '36.b1', '36.l1', '36.y1'], 'contains': ['216.a1', '216.b1', '216.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5824, 7527, 5348, 8335], 'generators': [2, 12, 648], 'label': '1944.3518.72.a1', 'mobius_quo': -3, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['216.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '1944.3518', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107644080
    {'ambient': '1944.3518', 'aut_centralizer_order': 1296, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1296, 'centralizer': '72.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.a1', '36.p1', '36.t1'], 'contains': ['216.h1', '216.i1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6125, 6217, 5821, 7285], 'generators': [288, 1512], 'label': '1944.3518.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['24.a1', '36.a1'], 'normal_contains': ['648.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '1944.3518', 'quotient_action_image': '8.3', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 107644081
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.b1', '24.d1', '36.c1', '36.j1', '36.n1'], 'contains': ['216.a1', '216.d1', '216.h1', '216.j1', '216.l1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8435, -1, 6999, -1], 'generators': [12, 1512, 648], 'label': '1944.3518.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.c1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644082
    {'ambient': '1944.3518', 'aut_centralizer_order': 486, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.c1', '24.e1', '36.d1', '36.q1', '36.v1'], 'contains': ['216.a1', '216.e1', '216.i1', '216.k1', '216.m1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4304, -1, 3741, -1], 'generators': [12, 1152, 648], 'label': '1944.3518.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.d1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644083
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.c1', '24.d1', '36.k1'], 'contains': ['216.a1', '216.f1', '216.j1', '216.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7670, -1, 6413, -1], 'generators': [2, 1524, 648], 'label': '1944.3518.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '72.e1', 'projective_image': '1944.3518', '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': '6.1'}
  • id: 107644084
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '72.46', 'aut_weyl_index': 1296, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.c1', '24.e1', '36.w1'], 'contains': ['216.a1', '216.g1', '216.k1', '216.o1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3280, -1, 3877, -1], 'generators': [2, 300, 648], 'label': '1944.3518.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.f1', 'projective_image': '1944.3518', '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': '6.2'}
  • id: 107644085
    {'ambient': '1944.3518', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '432.530', 'aut_weyl_index': 216, 'centralizer': '216.b1', 'complements': ['324.l1', '324.n1', '324.p1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.f1', '18.a1', '18.f1'], 'core': '6.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8897, 8294, 7088, 8553], 'generators': [108, 648, 216, 522, 12, 288], 'label': '1944.3518.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '1944.3518', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 107644086
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '36.e1'], 'contains': ['216.c1', '216.d1', '216.f1', '216.l1', '216.n1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8189, -1, 7135, -1], 'generators': [2, 660, 1512], 'label': '1944.3518.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.g1', 'projective_image': '1944.3518', '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': '2.1'}
  • id: 107644087
    {'ambient': '1944.3518', 'aut_centralizer_order': 81, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.e1', '36.f1', '36.r1', '36.x1'], 'contains': ['216.c1', '216.e1', '216.g1', '216.m1', '216.o1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1293, -1, 1949, -1], 'generators': [2, 660, 1152], 'label': '1944.3518.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '72.h1', 'projective_image': '1944.3518', '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': '4.2'}
  • id: 107644088
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '36.g1', '36.i1', '36.m1'], 'contains': ['216.b1', '216.d1', '216.f1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8559, -1, 8667, -1], 'generators': [2, 12, 1512], 'label': '1944.3518.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.i1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107644089
    {'ambient': '1944.3518', 'aut_centralizer_order': 162, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.189', 'aut_weyl_index': 972, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.h1', '36.s1', '36.z1'], 'contains': ['216.b1', '216.e1', '216.g1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2491, -1, 2238, -1], 'generators': [2, 12, 1152], 'label': '1944.3518.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '72.j1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107644093
    {'ambient': '1944.3518', 'aut_centralizer_order': 12, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['27.a1', '27.b1'], 'contains': ['162.a1', '162.c1', '162.f1', '243.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [4923, -1, 4780, -1], 'generators': [1297, 108, 522, 12], 'label': '1944.3518.81.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '1944.3518', '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': '12.4'}
  • id: 107644094
    {'ambient': '1944.3518', 'aut_centralizer_order': 96, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '27.b1'], 'contains': ['162.b1', '162.d1', '162.g1', '243.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [4786, -1, 4629, -1], 'generators': [1, 108, 522, 648], 'label': '1944.3518.81.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': '1944.3518', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107644095
    {'ambient': '1944.3518', 'aut_centralizer_order': 648, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '36.c1', '36.d1', '54.b1', '54.c1', '54.f1'], 'contains': ['216.a1', '324.a1', '324.b1', '324.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5940, -1, 5167, -1], 'generators': [522, 12, 648], 'label': '1944.3518.108.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.a1', 'projective_image': '1944.3518', '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': '4.2'}