Abstract group data - 1296.1067

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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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 12, 12, 6, 6, 6], 'aut_gens': [[1, 6, 36, 216], [161, 390, 36, 1080], [245, 336, 1026, 1080], [293, 636, 738, 1080], [581, 294, 180, 1080], [145, 912, 954, 216], [1025, 336, 810, 1080]], 'aut_group': None, 'aut_hash': 2799146922247543772, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 40, 'aut_perms': [152030522768379967373104577999489699653687581199, 557382259095836618923315867785923678735990995380, 344298867087126865615646817294812049435188749745, 570725018021525247696910985468092068565123160520, 436309363478781070716095960395067359579637045698, 224214781908969226749757616596692491199107670259], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 9, 2, 1], [2, 18, 2, 1], [3, 1, 2, 1], [3, 3, 6, 1], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 4, 1], [6, 3, 6, 1], [6, 6, 1, 1], [6, 6, 12, 1], [6, 9, 4, 1], [6, 9, 12, 1], [6, 12, 2, 1], [6, 18, 1, 1], [6, 18, 4, 1], [6, 18, 12, 1], [6, 36, 2, 1], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 6, 1], [12, 12, 1, 1], [12, 18, 2, 1], [12, 18, 6, 1], [12, 36, 1, 1], [18, 18, 2, 1], [18, 36, 4, 1], [36, 36, 2, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times \\He_3).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '24.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '216.102', 'autcentquo_hash': 102, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_6.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 9, 2], [2, 18, 2], [3, 1, 2], [3, 3, 6], [3, 6, 1], [3, 18, 1], [4, 2, 1], [4, 18, 1], [6, 1, 2], [6, 2, 4], [6, 3, 6], [6, 6, 13], [6, 9, 16], [6, 12, 2], [6, 18, 17], [6, 36, 2], [9, 18, 2], [12, 2, 2], [12, 6, 6], [12, 12, 1], [12, 18, 8], [12, 36, 1], [18, 18, 2], [18, 36, 4], [36, 36, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '216.110', 'commutator_count': 1, 'commutator_label': '54.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1067, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['162.10', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [3, 1, 2, 1], [3, 3, 2, 3], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 2, 2], [6, 3, 2, 3], [6, 6, 1, 1], [6, 6, 2, 6], [6, 9, 2, 8], [6, 12, 1, 2], [6, 18, 1, 1], [6, 18, 2, 8], [6, 36, 1, 2], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 2, 3], [12, 12, 1, 1], [12, 18, 2, 4], [12, 36, 1, 1], [18, 18, 2, 1], [18, 36, 2, 2], [36, 36, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 117936, 'exponent': 36, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 12]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '72.48', 'hash': 1067, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 6, 6, 1], 'inner_gens': [[1, 966, 1044, 216], [1021, 6, 252, 216], [505, 1086, 36, 216], [1, 6, 36, 216]], 'inner_hash': 110, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_6^2:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 18], [3, 48], [4, 3], [6, 16], [12, 1]], 'label': '1296.1067', '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': True, 'name': 'C3wrS3*D4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 33, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 110, 'number_divisions': 65, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': 216, 'number_subgroup_classes': 448, 'number_subgroups': 2800, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 59], [3, 44], [4, 20], [6, 652], [9, 36], [12, 232], [18, 180], [36, 72]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [4, 0, 0], 'outer_gens': [[649, 78, 36, 216], [5, 78, 180, 1080], [13, 60, 1026, 216]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 7], [6, 28], [8, 1], [12, 7]], 'representations': {'PC': {'code': 512097290824814612035178249279607355395188684464543061, 'gens': [1, 3, 5, 7], 'pres': [8, -2, -3, -2, -3, -2, -3, -2, -3, 16, 23186, 946, 66, 5379, 9419, 41764, 1700, 1588, 116, 27653, 4053, 3773, 166]}, 'Perm': {'d': 13, 'gens': [123753607, 16, 1, 163790040, 7, 614367480, 1124973360, 1597166040]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\wr S_3\\times D_4', 'transitive_degree': 36, '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: 114367765
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1067, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 114367787
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1067, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 648, 'size': 1}
  • id: 114367798
    {'aut_label': '2B', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 1067, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 108, 'size': 2}
  • id: 114367809
    {'aut_label': '2B', 'centralizer': '2.a1', 'counter': 4, 'group_counter': 1067, 'group_order': 1296, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 18, 'size': 2}
  • id: 114367820
    {'aut_label': '2D', 'centralizer': '9.a1', 'counter': 5, 'group_counter': 1067, 'group_order': 1296, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 3, 'size': 9}
  • id: 114367831
    {'aut_label': '2D', 'centralizer': '9.a1', 'counter': 6, 'group_counter': 1067, 'group_order': 1296, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 651, 'size': 9}
  • id: 114367842
    {'aut_label': '2F', 'centralizer': '18.b1', 'counter': 7, 'group_counter': 1067, 'group_order': 1296, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 903, 'size': 18}
  • id: 114367853
    {'aut_label': '2F', 'centralizer': '18.b1', 'counter': 8, 'group_counter': 1067, 'group_order': 1296, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 153, 'size': 18}
  • id: 114367864
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 9, 'group_counter': 1067, 'group_order': 1296, 'label': '3A1', 'order': 3, 'powers': [10, 1], 'representative': 864, 'size': 1}
  • id: 114367766
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 10, 'group_counter': 1067, 'group_order': 1296, 'label': '3A-1', 'order': 3, 'powers': [9, 1], 'representative': 432, 'size': 1}
  • id: 114367777
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 11, 'group_counter': 1067, 'group_order': 1296, 'label': '3B1', 'order': 3, 'powers': [12, 1], 'representative': 76, 'size': 3}
  • id: 114367779
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 12, 'group_counter': 1067, 'group_order': 1296, 'label': '3B-1', 'order': 3, 'powers': [11, 1], 'representative': 146, 'size': 3}
  • id: 114367780
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 13, 'group_counter': 1067, 'group_order': 1296, 'label': '3C1', 'order': 3, 'powers': [14, 1], 'representative': 74, 'size': 3}
  • id: 114367781
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 14, 'group_counter': 1067, 'group_order': 1296, 'label': '3C-1', 'order': 3, 'powers': [13, 1], 'representative': 148, 'size': 3}
  • id: 114367782
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 15, 'group_counter': 1067, 'group_order': 1296, 'label': '3D1', 'order': 3, 'powers': [16, 1], 'representative': 508, 'size': 3}
  • id: 114367783
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 16, 'group_counter': 1067, 'group_order': 1296, 'label': '3D-1', 'order': 3, 'powers': [15, 1], 'representative': 1010, 'size': 3}
  • id: 114367784
    {'aut_label': '3E', 'centralizer': '6.c1', 'counter': 17, 'group_counter': 1067, 'group_order': 1296, 'label': '3E', 'order': 3, 'powers': [17, 1], 'representative': 72, 'size': 6}
  • id: 114367785
    {'aut_label': '3F', 'centralizer': '18.k1', 'counter': 18, 'group_counter': 1067, 'group_order': 1296, 'label': '3F', 'order': 3, 'powers': [18, 1], 'representative': 12, 'size': 18}
  • id: 114367786
    {'aut_label': '4A', 'centralizer': '2.d1', 'counter': 19, 'group_counter': 1067, 'group_order': 1296, 'label': '4A', 'order': 4, 'powers': [2, 19], 'representative': 774, 'size': 2}
  • id: 114367788
    {'aut_label': '4B', 'centralizer': '18.n1', 'counter': 20, 'group_counter': 1067, 'group_order': 1296, 'label': '4B', 'order': 4, 'powers': [2, 20], 'representative': 837, 'size': 18}
  • id: 114367789
    {'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 21, 'group_counter': 1067, 'group_order': 1296, 'label': '6A1', 'order': 6, 'powers': [10, 2], 'representative': 216, 'size': 1}
  • id: 114367790
    {'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 22, 'group_counter': 1067, 'group_order': 1296, 'label': '6A-1', 'order': 6, 'powers': [9, 2], 'representative': 1080, 'size': 1}
  • id: 114367791
    {'aut_label': '6B1', 'centralizer': '2.a1', 'counter': 23, 'group_counter': 1067, 'group_order': 1296, 'label': '6B1', 'order': 6, 'powers': [10, 4], 'representative': 882, 'size': 2}
  • id: 114367792
    {'aut_label': '6B1', 'centralizer': '2.a1', 'counter': 24, 'group_counter': 1067, 'group_order': 1296, 'label': '6B-1', 'order': 6, 'powers': [9, 4], 'representative': 450, 'size': 2}
  • id: 114367793
    {'aut_label': '6B1', 'centralizer': '2.a1', 'counter': 25, 'group_counter': 1067, 'group_order': 1296, 'label': '6C1', 'order': 6, 'powers': [10, 3], 'representative': 972, 'size': 2}
  • id: 114367794
    {'aut_label': '6B1', 'centralizer': '2.a1', 'counter': 26, 'group_counter': 1067, 'group_order': 1296, 'label': '6C-1', 'order': 6, 'powers': [9, 3], 'representative': 540, 'size': 2}
  • id: 114367795
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 27, 'group_counter': 1067, 'group_order': 1296, 'label': '6D1', 'order': 6, 'powers': [12, 2], 'representative': 724, 'size': 3}
  • id: 114367796
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 28, 'group_counter': 1067, 'group_order': 1296, 'label': '6D-1', 'order': 6, 'powers': [11, 2], 'representative': 794, 'size': 3}
  • id: 114367797
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 29, 'group_counter': 1067, 'group_order': 1296, 'label': '6E1', 'order': 6, 'powers': [14, 2], 'representative': 722, 'size': 3}
  • id: 114367799
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 30, 'group_counter': 1067, 'group_order': 1296, 'label': '6E-1', 'order': 6, 'powers': [13, 2], 'representative': 796, 'size': 3}
  • id: 114367800
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 31, 'group_counter': 1067, 'group_order': 1296, 'label': '6F1', 'order': 6, 'powers': [16, 2], 'representative': 1156, 'size': 3}
  • id: 114367801
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 32, 'group_counter': 1067, 'group_order': 1296, 'label': '6F-1', 'order': 6, 'powers': [15, 2], 'representative': 362, 'size': 3}
  • id: 114367802
    {'aut_label': '6G', 'centralizer': '6.c1', 'counter': 33, 'group_counter': 1067, 'group_order': 1296, 'label': '6G', 'order': 6, 'powers': [17, 2], 'representative': 720, 'size': 6}
  • id: 114367803
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 34, 'group_counter': 1067, 'group_order': 1296, 'label': '6H1', 'order': 6, 'powers': [11, 3], 'representative': 38, 'size': 6}
  • id: 114367804
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 35, 'group_counter': 1067, 'group_order': 1296, 'label': '6H-1', 'order': 6, 'powers': [12, 3], 'representative': 472, 'size': 6}
  • id: 114367805
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 36, 'group_counter': 1067, 'group_order': 1296, 'label': '6I1', 'order': 6, 'powers': [13, 3], 'representative': 40, 'size': 6}
  • id: 114367806
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 37, 'group_counter': 1067, 'group_order': 1296, 'label': '6I-1', 'order': 6, 'powers': [14, 3], 'representative': 470, 'size': 6}
  • id: 114367807
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 38, 'group_counter': 1067, 'group_order': 1296, 'label': '6J1', 'order': 6, 'powers': [15, 3], 'representative': 254, 'size': 6}
  • id: 114367808
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 39, 'group_counter': 1067, 'group_order': 1296, 'label': '6J-1', 'order': 6, 'powers': [16, 3], 'representative': 256, 'size': 6}
  • id: 114367810
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 40, 'group_counter': 1067, 'group_order': 1296, 'label': '6K1', 'order': 6, 'powers': [11, 4], 'representative': 20, 'size': 6}
  • id: 114367811
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 41, 'group_counter': 1067, 'group_order': 1296, 'label': '6K-1', 'order': 6, 'powers': [12, 4], 'representative': 22, 'size': 6}
  • id: 114367812
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 42, 'group_counter': 1067, 'group_order': 1296, 'label': '6L1', 'order': 6, 'powers': [14, 4], 'representative': 452, 'size': 6}
  • id: 114367813
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 43, 'group_counter': 1067, 'group_order': 1296, 'label': '6L-1', 'order': 6, 'powers': [13, 4], 'representative': 238, 'size': 6}
  • id: 114367814
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 44, 'group_counter': 1067, 'group_order': 1296, 'label': '6M1', 'order': 6, 'powers': [15, 4], 'representative': 236, 'size': 6}
  • id: 114367815
    {'aut_label': '6H1', 'centralizer': '6.g1', 'counter': 45, 'group_counter': 1067, 'group_order': 1296, 'label': '6M-1', 'order': 6, 'powers': [16, 4], 'representative': 454, 'size': 6}
  • id: 114367816
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 46, 'group_counter': 1067, 'group_order': 1296, 'label': '6N1', 'order': 6, 'powers': [12, 5], 'representative': 1, 'size': 9}
  • id: 114367817
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 47, 'group_counter': 1067, 'group_order': 1296, 'label': '6N-1', 'order': 6, 'powers': [11, 5], 'representative': 5, 'size': 9}
  • id: 114367818
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 48, 'group_counter': 1067, 'group_order': 1296, 'label': '6O1', 'order': 6, 'powers': [16, 5], 'representative': 433, 'size': 9}
  • id: 114367819
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 49, 'group_counter': 1067, 'group_order': 1296, 'label': '6O-1', 'order': 6, 'powers': [15, 5], 'representative': 77, 'size': 9}
  • id: 114367821
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 50, 'group_counter': 1067, 'group_order': 1296, 'label': '6P1', 'order': 6, 'powers': [13, 6], 'representative': 217, 'size': 9}
  • id: 114367822
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 51, 'group_counter': 1067, 'group_order': 1296, 'label': '6P-1', 'order': 6, 'powers': [14, 6], 'representative': 293, 'size': 9}
  • id: 114367823
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 52, 'group_counter': 1067, 'group_order': 1296, 'label': '6Q1', 'order': 6, 'powers': [13, 5], 'representative': 73, 'size': 9}
  • id: 114367824
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 53, 'group_counter': 1067, 'group_order': 1296, 'label': '6Q-1', 'order': 6, 'powers': [14, 5], 'representative': 437, 'size': 9}
  • id: 114367825
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 54, 'group_counter': 1067, 'group_order': 1296, 'label': '6R1', 'order': 6, 'powers': [12, 6], 'representative': 649, 'size': 9}
  • id: 114367826
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 55, 'group_counter': 1067, 'group_order': 1296, 'label': '6R-1', 'order': 6, 'powers': [11, 6], 'representative': 653, 'size': 9}
  • id: 114367827
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 56, 'group_counter': 1067, 'group_order': 1296, 'label': '6S1', 'order': 6, 'powers': [16, 6], 'representative': 289, 'size': 9}
  • id: 114367828
    {'aut_label': '6N1', 'centralizer': '9.a1', 'counter': 57, 'group_counter': 1067, 'group_order': 1296, 'label': '6S-1', 'order': 6, 'powers': [15, 6], 'representative': 221, 'size': 9}
  • id: 114367829
    {'aut_label': '6T1', 'centralizer': '9.a1', 'counter': 58, 'group_counter': 1067, 'group_order': 1296, 'label': '6T1', 'order': 6, 'powers': [9, 5], 'representative': 435, 'size': 9}
  • id: 114367830
    {'aut_label': '6T1', 'centralizer': '9.a1', 'counter': 59, 'group_counter': 1067, 'group_order': 1296, 'label': '6T-1', 'order': 6, 'powers': [10, 5], 'representative': 75, 'size': 9}
  • id: 114367832
    {'aut_label': '6T1', 'centralizer': '9.a1', 'counter': 60, 'group_counter': 1067, 'group_order': 1296, 'label': '6U1', 'order': 6, 'powers': [10, 6], 'representative': 219, 'size': 9}
  • id: 114367833
    {'aut_label': '6T1', 'centralizer': '9.a1', 'counter': 61, 'group_counter': 1067, 'group_order': 1296, 'label': '6U-1', 'order': 6, 'powers': [9, 6], 'representative': 291, 'size': 9}
  • id: 114367834
    {'aut_label': '6V', 'centralizer': '12.a1', 'counter': 62, 'group_counter': 1067, 'group_order': 1296, 'label': '6V', 'order': 6, 'powers': [17, 3], 'representative': 36, 'size': 12}
  • id: 114367835
    {'aut_label': '6V', 'centralizer': '12.a1', 'counter': 63, 'group_counter': 1067, 'group_order': 1296, 'label': '6W', 'order': 6, 'powers': [17, 4], 'representative': 90, 'size': 12}
  • id: 114367836
    {'aut_label': '6X', 'centralizer': '18.k1', 'counter': 64, 'group_counter': 1067, 'group_order': 1296, 'label': '6X', 'order': 6, 'powers': [18, 2], 'representative': 300, 'size': 18}
  • id: 114367837
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 65, 'group_counter': 1067, 'group_order': 1296, 'label': '6Y1', 'order': 6, 'powers': [16, 7], 'representative': 37, 'size': 18}
  • id: 114367838
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 66, 'group_counter': 1067, 'group_order': 1296, 'label': '6Y-1', 'order': 6, 'powers': [15, 7], 'representative': 473, 'size': 18}
  • id: 114367839
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 67, 'group_counter': 1067, 'group_order': 1296, 'label': '6Z1', 'order': 6, 'powers': [13, 8], 'representative': 7, 'size': 18}
  • id: 114367840
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 68, 'group_counter': 1067, 'group_order': 1296, 'label': '6Z-1', 'order': 6, 'powers': [14, 8], 'representative': 11, 'size': 18}
  • id: 114367841
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 69, 'group_counter': 1067, 'group_order': 1296, 'label': '6AA1', 'order': 6, 'powers': [13, 7], 'representative': 469, 'size': 18}
  • id: 114367843
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 70, 'group_counter': 1067, 'group_order': 1296, 'label': '6AA-1', 'order': 6, 'powers': [14, 7], 'representative': 41, 'size': 18}
  • id: 114367844
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 71, 'group_counter': 1067, 'group_order': 1296, 'label': '6AB1', 'order': 6, 'powers': [12, 7], 'representative': 253, 'size': 18}
  • id: 114367845
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 72, 'group_counter': 1067, 'group_order': 1296, 'label': '6AB-1', 'order': 6, 'powers': [11, 7], 'representative': 257, 'size': 18}
  • id: 114367846
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 73, 'group_counter': 1067, 'group_order': 1296, 'label': '6AC1', 'order': 6, 'powers': [12, 8], 'representative': 439, 'size': 18}
  • id: 114367847
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 74, 'group_counter': 1067, 'group_order': 1296, 'label': '6AC-1', 'order': 6, 'powers': [11, 8], 'representative': 227, 'size': 18}
  • id: 114367848
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 75, 'group_counter': 1067, 'group_order': 1296, 'label': '6AD1', 'order': 6, 'powers': [16, 8], 'representative': 223, 'size': 18}
  • id: 114367849
    {'aut_label': '6Y1', 'centralizer': '18.b1', 'counter': 76, 'group_counter': 1067, 'group_order': 1296, 'label': '6AD-1', 'order': 6, 'powers': [15, 8], 'representative': 443, 'size': 18}
  • id: 114367850
    {'aut_label': '6AE1', 'centralizer': '18.b1', 'counter': 77, 'group_counter': 1067, 'group_order': 1296, 'label': '6AE1', 'order': 6, 'powers': [9, 7], 'representative': 39, 'size': 18}
  • id: 114367851
    {'aut_label': '6AE1', 'centralizer': '18.b1', 'counter': 78, 'group_counter': 1067, 'group_order': 1296, 'label': '6AE-1', 'order': 6, 'powers': [10, 7], 'representative': 471, 'size': 18}
  • id: 114367852
    {'aut_label': '6AE1', 'centralizer': '18.b1', 'counter': 79, 'group_counter': 1067, 'group_order': 1296, 'label': '6AF1', 'order': 6, 'powers': [9, 8], 'representative': 441, 'size': 18}
  • id: 114367854
    {'aut_label': '6AE1', 'centralizer': '18.b1', 'counter': 80, 'group_counter': 1067, 'group_order': 1296, 'label': '6AF-1', 'order': 6, 'powers': [10, 8], 'representative': 225, 'size': 18}
  • id: 114367855
    {'aut_label': '6AG', 'centralizer': '36.d1', 'counter': 81, 'group_counter': 1067, 'group_order': 1296, 'label': '6AG', 'order': 6, 'powers': [18, 4], 'representative': 6, 'size': 36}
  • id: 114367856
    {'aut_label': '6AG', 'centralizer': '36.d1', 'counter': 82, 'group_counter': 1067, 'group_order': 1296, 'label': '6AH', 'order': 6, 'powers': [18, 3], 'representative': 48, 'size': 36}
  • id: 114367857
    {'aut_label': '9A1', 'centralizer': '18.l1', 'counter': 83, 'group_counter': 1067, 'group_order': 1296, 'label': '9A1', 'order': 9, 'powers': [84, 10], 'representative': 520, 'size': 18}
  • id: 114367858
    {'aut_label': '9A1', 'centralizer': '18.l1', 'counter': 84, 'group_counter': 1067, 'group_order': 1296, 'label': '9A-1', 'order': 9, 'powers': [83, 9], 'representative': 458, 'size': 18}
  • id: 114367859
    {'aut_label': '12A1', 'centralizer': '2.d1', 'counter': 85, 'group_counter': 1067, 'group_order': 1296, 'label': '12A1', 'order': 12, 'powers': [22, 19], 'representative': 342, 'size': 2}
  • id: 114367860
    {'aut_label': '12A1', 'centralizer': '2.d1', 'counter': 86, 'group_counter': 1067, 'group_order': 1296, 'label': '12A-1', 'order': 12, 'powers': [21, 19], 'representative': 558, 'size': 2}
  • id: 114367861
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 87, 'group_counter': 1067, 'group_order': 1296, 'label': '12B1', 'order': 12, 'powers': [27, 19], 'representative': 56, 'size': 6}
  • id: 114367862
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 88, 'group_counter': 1067, 'group_order': 1296, 'label': '12B-1', 'order': 12, 'powers': [28, 19], 'representative': 490, 'size': 6}
  • id: 114367863
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 89, 'group_counter': 1067, 'group_order': 1296, 'label': '12C1', 'order': 12, 'powers': [29, 19], 'representative': 58, 'size': 6}
  • id: 114367865
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 90, 'group_counter': 1067, 'group_order': 1296, 'label': '12C-1', 'order': 12, 'powers': [30, 19], 'representative': 488, 'size': 6}
  • id: 114367866
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 91, 'group_counter': 1067, 'group_order': 1296, 'label': '12D1', 'order': 12, 'powers': [31, 19], 'representative': 272, 'size': 6}
  • id: 114367867
    {'aut_label': '12B1', 'centralizer': '6.j1', 'counter': 92, 'group_counter': 1067, 'group_order': 1296, 'label': '12D-1', 'order': 12, 'powers': [32, 19], 'representative': 274, 'size': 6}
  • id: 114367868
    {'aut_label': '12E', 'centralizer': '12.e1', 'counter': 93, 'group_counter': 1067, 'group_order': 1296, 'label': '12E', 'order': 12, 'powers': [33, 19], 'representative': 54, 'size': 12}
  • id: 114367869
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 94, 'group_counter': 1067, 'group_order': 1296, 'label': '12F1', 'order': 12, 'powers': [29, 20], 'representative': 43, 'size': 18}
  • id: 114367870
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 95, 'group_counter': 1067, 'group_order': 1296, 'label': '12F-1', 'order': 12, 'powers': [30, 20], 'representative': 47, 'size': 18}
  • id: 114367871
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 96, 'group_counter': 1067, 'group_order': 1296, 'label': '12G1', 'order': 12, 'powers': [28, 20], 'representative': 475, 'size': 18}
  • id: 114367872
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 97, 'group_counter': 1067, 'group_order': 1296, 'label': '12G-1', 'order': 12, 'powers': [27, 20], 'representative': 263, 'size': 18}
  • id: 114367873
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 98, 'group_counter': 1067, 'group_order': 1296, 'label': '12H1', 'order': 12, 'powers': [32, 20], 'representative': 259, 'size': 18}
  • id: 114367874
    {'aut_label': '12F1', 'centralizer': '18.n1', 'counter': 99, 'group_counter': 1067, 'group_order': 1296, 'label': '12H-1', 'order': 12, 'powers': [31, 20], 'representative': 479, 'size': 18}
  • id: 114367767
    {'aut_label': '12I1', 'centralizer': '18.n1', 'counter': 100, 'group_counter': 1067, 'group_order': 1296, 'label': '12I1', 'order': 12, 'powers': [21, 20], 'representative': 477, 'size': 18}
  • id: 114367768
    {'aut_label': '12I1', 'centralizer': '18.n1', 'counter': 101, 'group_counter': 1067, 'group_order': 1296, 'label': '12I-1', 'order': 12, 'powers': [22, 20], 'representative': 261, 'size': 18}
  • id: 114367769
    {'aut_label': '12J', 'centralizer': '36.r1', 'counter': 102, 'group_counter': 1067, 'group_order': 1296, 'label': '12J', 'order': 12, 'powers': [64, 19], 'representative': 42, 'size': 36}
  • id: 114367770
    {'aut_label': '18A1', 'centralizer': '18.l1', 'counter': 103, 'group_counter': 1067, 'group_order': 1296, 'label': '18A1', 'order': 18, 'powers': [84, 22], 'representative': 808, 'size': 18}
  • id: 114367771
    {'aut_label': '18A1', 'centralizer': '18.l1', 'counter': 104, 'group_counter': 1067, 'group_order': 1296, 'label': '18A-1', 'order': 18, 'powers': [83, 21], 'representative': 1250, 'size': 18}
  • id: 114367772
    {'aut_label': '18B1', 'centralizer': '36.e1', 'counter': 105, 'group_counter': 1067, 'group_order': 1296, 'label': '18B1', 'order': 18, 'powers': [83, 23], 'representative': 8, 'size': 36}
  • id: 114367773
    {'aut_label': '18B1', 'centralizer': '36.e1', 'counter': 106, 'group_counter': 1067, 'group_order': 1296, 'label': '18B-1', 'order': 18, 'powers': [84, 24], 'representative': 10, 'size': 36}
  • id: 114367774
    {'aut_label': '18B1', 'centralizer': '36.e1', 'counter': 107, 'group_counter': 1067, 'group_order': 1296, 'label': '18C1', 'order': 18, 'powers': [83, 25], 'representative': 50, 'size': 36}
  • id: 114367775
    {'aut_label': '18B1', 'centralizer': '36.e1', 'counter': 108, 'group_counter': 1067, 'group_order': 1296, 'label': '18C-1', 'order': 18, 'powers': [84, 26], 'representative': 52, 'size': 36}
  • id: 114367776
    {'aut_label': '36A1', 'centralizer': '36.t1', 'counter': 109, 'group_counter': 1067, 'group_order': 1296, 'label': '36A1', 'order': 36, 'powers': [103, 85], 'representative': 44, 'size': 36}
  • id: 114367778
    {'aut_label': '36A1', 'centralizer': '36.t1', 'counter': 110, 'group_counter': 1067, 'group_order': 1296, 'label': '36A-1', 'order': 36, 'powers': [104, 86], 'representative': 46, 'size': 36}
• 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: 5312581
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5312592
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 5312603
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 5312614
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 5312625
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 5312636
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 5312643
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 5312644
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5312645
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5312582
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, -2, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -2, -2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 1, 1, 1, 1, -2, 1, 1, -2, 2, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 5312583
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 2, -2, 1, -2, -2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 5312584
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, -2, 2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 2, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, 2, -1, -1, -1, 1, 1, -2, -1, -1, 1, 2, 1, 1, 1, 2, 2, -2, -1, 2, -2, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, -2, -1, -1, -1, -1, 2, -1, -1, 2, -2, -1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 5312585
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 2, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -2, 2, 1, 1, 1, -1, -1, 2, 1, 1, -1, -2, -1, -1, -1, -2, 2, 2, 1, 2, -2, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, -1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 5312586
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, -2, 2, -2, 1, 1, 1, -1, -1, 2, 1, 1, -1, -2, -1, -1, -1, -2, 2, 2, 1, -2, 2, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, -2, -1, -1, -1, -1, 2, -1, -1, 2, -2, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 5312587
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -2, -1, -1, -1, 1, 1, -2, -1, -1, 1, 2, 1, 1, 1, 2, 2, -2, -1, -2, 2, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 5312588
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, -2, 2, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 2, -2, 1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 1, 1, 1, 1, -2, 1, 1, -2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5312589
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5312590
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, -2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312591
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312593
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 0, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 5312594
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -2, 0, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 5312595
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -2, 0, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 5312596
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 4, 0, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 1, 1, 4, 4, -2, -2, -2, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5312597
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2h', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -4, 4, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, -4, 4, 2, 2, -2, -2, 2, -4, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312598
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2i', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, -4, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, 4, -4, -2, -2, 2, 2, -2, 4, -2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312599
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2j', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 4, 0, 4, 4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 1, 1, 4, 4, -2, -2, -2, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 5312600
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2k', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -4, 0, 4, 4, 4, 4, -4, -4, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 4, -2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 1, 1, -4, -4, 2, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 5312601
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.2l', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -4, 0, 4, 4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 4, 2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 1, 1, -4, -4, 2, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 5312629
    {'cdim': 4, 'counter': 53, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312602
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3a', 'multiplicity': 2, 'nt': [9, 20], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 2, 2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, 6, 2, -3, -3, -3, -3, -3, -3, 3, -3, 0, -3, 3, 0, 3, 3, -3, -3, -3, 0, 3, 0, 0, 0, -3, 3, 0, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 0, -1, 2, 0, 0, 0, 0, -3, -3, 3, 3, 0, -3, -3, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312604
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3b', 'multiplicity': 2, 'nt': [9, 20], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 2, 2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, 6, 2, -3, -3, -3, -3, -3, -3, -3, 0, 3, 0, -3, 3, -3, -3, 0, 0, 0, 0, -3, 3, 3, 3, 0, -3, 3, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, -3, -3, 3, 0, 0, 3, 0, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312605
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3c', 'multiplicity': 2, 'nt': [9, 20], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 2, 2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, 6, 2, -3, -3, -3, -3, -3, -3, 0, 3, -3, 3, 0, -3, 0, 0, 3, 3, 3, 0, 0, -3, -3, -3, 3, 0, -3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, 0, 0, -3, 3, 3, -3, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312606
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3d', 'multiplicity': 2, 'nt': [18, 86], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, 6, -2, -3, -3, -3, -3, -3, -3, 3, -3, 0, -3, 3, 0, 3, 3, -3, -3, -3, 0, 3, 0, 0, 0, -3, 3, 0, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 0, 0, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 0, 1, -2, 0, 0, 0, 0, -3, -3, 3, 3, 0, -3, -3, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312607
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3e', 'multiplicity': 2, 'nt': [18, 86], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, 6, -2, -3, -3, -3, -3, -3, -3, -3, 0, 3, 0, -3, 3, -3, -3, 0, 0, 0, 0, -3, 3, 3, 3, 0, -3, 3, 1, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 1, -2, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, -3, -3, 3, 0, 0, 3, 0, 1, 1, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312608
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3f', 'multiplicity': 2, 'nt': [18, 86], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, 6, -2, -3, -3, -3, -3, -3, -3, 0, 3, -3, 3, 0, -3, 0, 0, 3, 3, 3, 0, 0, -3, -3, -3, 3, 0, -3, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 1, 1, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, 0, 0, -3, 3, 3, -3, 0, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312609
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3g', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, 2, 2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, 6, -2, -3, -3, 3, 3, 3, 3, 3, -3, 0, -3, 3, 0, -3, -3, 3, 3, 3, 0, -3, 0, 0, 0, 3, -3, 0, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 0, -1, 2, 0, 0, 0, 0, -3, -3, 3, 3, 0, -3, -3, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312610
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3h', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, 2, 2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, 6, -2, -3, -3, 3, 3, 3, 3, -3, 0, 3, 0, -3, 3, 3, 3, 0, 0, 0, 0, 3, -3, -3, -3, 0, 3, -3, 1, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, -3, -3, 3, 0, 0, 3, 0, 1, 1, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312611
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3i', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, 2, 2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, 6, -2, -3, -3, 3, 3, 3, 3, 0, 3, -3, 3, 0, -3, 0, 0, -3, -3, -3, 0, 0, 3, 3, 3, -3, 0, 3, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, 0, 0, -3, 3, 3, -3, 0, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312612
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3j', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 2, 2, -2, -2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, 6, 2, -3, -3, 3, 3, 3, 3, 3, -3, 0, -3, 3, 0, -3, -3, 3, 3, 3, 0, -3, 0, 0, 0, 3, -3, 0, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 0, 1, -2, 0, 0, 0, 0, -3, -3, 3, 3, 0, -3, -3, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312613
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3k', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 2, 2, -2, -2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, 6, 2, -3, -3, 3, 3, 3, 3, -3, 0, 3, 0, -3, 3, 3, 3, 0, 0, 0, 0, 3, -3, -3, -3, 0, 3, -3, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 1, -2, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, -3, -3, 3, 0, 0, 3, 0, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312615
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3l', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 2, 2, -2, -2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, 6, 2, -3, -3, 3, 3, 3, 3, 0, 3, -3, 3, 0, -3, 0, 0, -3, -3, -3, 0, 0, 3, 3, 3, -3, 0, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, 1, 1, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, 0, 0, -3, 3, 3, -3, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312616
    {'cdim': 3, 'counter': 41, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3m', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -2, -2, 2, -2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, -6, 2, -3, -3, -3, -3, 3, 3, 3, -3, 0, -3, 3, 0, -3, -3, 3, -3, -3, 0, 3, 0, 0, 0, 3, 3, 0, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 0, 0, 2, -1, -1, -2, 1, 1, -1, -1, 1, -1, -2, 1, 1, -1, 0, 1, 2, 0, 0, 0, 0, 3, 3, -3, -3, 0, 3, 3, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312617
    {'cdim': 3, 'counter': 42, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3n', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -2, -2, 2, -2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, -6, 2, -3, -3, -3, -3, 3, 3, -3, 0, 3, 0, -3, 3, 3, 3, 0, 0, 0, 0, -3, -3, -3, 3, 0, -3, 3, 1, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, -1, 2, -1, 1, -2, 1, 2, -1, 1, -1, 1, -2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 3, 3, 3, 3, -3, 0, 0, -3, 0, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312618
    {'cdim': 3, 'counter': 43, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3o', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -2, -2, 2, -2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, -6, 2, -3, -3, -3, -3, 3, 3, 0, 3, -3, 3, 0, -3, 0, 0, -3, 3, 3, 0, 0, 3, 3, -3, -3, 0, -3, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, -1, -1, 2, 1, 1, 1, -1, 2, -2, -1, 1, 1, -2, -1, 0, 1, -1, 0, 0, 0, 0, 3, 3, 0, 0, 3, -3, -3, 3, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312619
    {'cdim': 3, 'counter': 44, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3p', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 2, 2, -2, 2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, -6, -2, -3, -3, -3, -3, 3, 3, 3, -3, 0, -3, 3, 0, -3, -3, 3, -3, -3, 0, 3, 0, 0, 0, 3, 3, 0, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, -2, 1, 1, 2, -1, -1, 1, 1, -1, 1, 2, -1, -1, 1, 0, -1, -2, 0, 0, 0, 0, 3, 3, -3, -3, 0, 3, 3, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312620
    {'cdim': 3, 'counter': 45, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3q', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 2, 2, -2, 2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, -6, -2, -3, -3, -3, -3, 3, 3, -3, 0, 3, 0, -3, 3, 3, 3, 0, 0, 0, 0, -3, -3, -3, 3, 0, -3, 3, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 1, -2, 1, -1, 2, -1, -2, 1, -1, 1, -1, 2, -1, 1, 0, -1, 1, 0, 0, 0, 0, 3, 3, 3, 3, -3, 0, 0, -3, 0, 1, 1, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312621
    {'cdim': 3, 'counter': 46, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3r', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 2, 2, -2, 2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, -6, -2, -3, -3, -3, -3, 3, 3, 0, 3, -3, 3, 0, -3, 0, 0, -3, 3, 3, 0, 0, 3, 3, -3, -3, 0, -3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, 1, 1, -2, -1, -1, -1, 1, -2, 2, 1, -1, -1, 2, 1, 0, -1, 1, 0, 0, 0, 0, 3, 3, 0, 0, 3, -3, -3, 3, 0, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312622
    {'cdim': 3, 'counter': 47, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3s', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -2, -2, -2, 2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, -6, 2, -3, -3, 3, 3, -3, -3, 3, -3, 0, -3, 3, 0, 3, 3, -3, 3, 3, 0, -3, 0, 0, 0, -3, -3, 0, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 0, 0, -2, 1, 1, 2, -1, -1, 1, 1, -1, 1, 2, -1, -1, 1, 0, -1, -2, 0, 0, 0, 0, 3, 3, -3, -3, 0, 3, 3, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312623
    {'cdim': 3, 'counter': 48, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3t', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -2, -2, -2, 2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, -6, 2, -3, -3, 3, 3, -3, -3, -3, 0, 3, 0, -3, 3, -3, -3, 0, 0, 0, 0, 3, 3, 3, -3, 0, 3, -3, 1, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 1, -2, 1, -1, 2, -1, -2, 1, -1, 1, -1, 2, -1, 1, 0, -1, 1, 0, 0, 0, 0, 3, 3, 3, 3, -3, 0, 0, -3, 0, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312624
    {'cdim': 3, 'counter': 49, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3u', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -2, -2, -2, 2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, -6, 2, -3, -3, 3, 3, -3, -3, 0, 3, -3, 3, 0, -3, 0, 0, 3, -3, -3, 0, 0, -3, -3, 3, 3, 0, 3, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 1, 1, -2, -1, -1, -1, 1, -2, 2, 1, -1, -1, 2, 1, 0, -1, 1, 0, 0, 0, 0, 3, 3, 0, 0, 3, -3, -3, 3, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312626
    {'cdim': 3, 'counter': 50, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3v', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 2, 2, 2, -2, -3, -3, -3, 3, 0, 0, -3, 3, 0, 0, -6, -2, -3, -3, 3, 3, -3, -3, 3, -3, 0, -3, 3, 0, 3, 3, -3, 3, 3, 0, -3, 0, 0, 0, -3, -3, 0, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, 2, -1, -1, -2, 1, 1, -1, -1, 1, -1, -2, 1, 1, -1, 0, 1, 2, 0, 0, 0, 0, 3, 3, -3, -3, 0, 3, 3, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312627
    {'cdim': 3, 'counter': 51, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3w', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 2, 2, 2, -2, -3, -3, 0, -3, 3, 3, 0, -3, 0, 0, -6, -2, -3, -3, 3, 3, -3, -3, -3, 0, 3, 0, -3, 3, -3, -3, 0, 0, 0, 0, 3, 3, 3, -3, 0, 3, -3, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, 2, -1, 1, -2, 1, 2, -1, 1, -1, 1, -2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 3, 3, 3, 3, -3, 0, 0, -3, 0, 1, 1, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312628
    {'cdim': 3, 'counter': 52, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.3x', 'multiplicity': 2, 'nt': [18, 119], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 2, 2, 2, -2, -3, -3, 3, 0, -3, -3, 3, 0, 0, 0, -6, -2, -3, -3, 3, 3, -3, -3, 0, 3, -3, 3, 0, -3, 0, 0, 3, -3, -3, 0, 0, -3, -3, 3, 3, 0, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, -1, -1, 2, 1, 1, 1, -1, 2, -2, -1, 1, 1, -2, -1, 0, 1, -1, 0, 0, 0, 0, 3, 3, 0, 0, 3, -3, -3, 3, 0, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312631
    {'cdim': 6, 'counter': 55, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6a', 'multiplicity': 1, 'nt': [9, 11], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312632
    {'cdim': 6, 'counter': 56, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6b', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 6, 6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312633
    {'cdim': 6, 'counter': 57, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6c', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, 6, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312634
    {'cdim': 6, 'counter': 58, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6d', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, 6, 6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312630
    {'cdim': 4, 'counter': 54, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.4b', 'multiplicity': 2, 'nt': [24, 208], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 0, 0, -8, -8, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312635
    {'cdim': 6, 'counter': 59, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6e', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -4, 4, 0, 0, -6, -6, -6, 6, 0, 0, -6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, -6, 6, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 2, -2, 4, 2, -2, -4, 2, -2, -2, 2, 2, -4, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312637
    {'cdim': 6, 'counter': 60, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6f', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -4, 4, 0, 0, -6, -6, 0, -6, 6, 6, 0, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 6, 0, -6, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -4, 4, -2, 2, -2, 2, -4, 4, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312638
    {'cdim': 6, 'counter': 61, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6g', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -4, 4, 0, 0, -6, -6, 6, 0, -6, -6, 6, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, -6, 6, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, -2, -2, 2, -2, 2, 2, -2, 4, -4, 2, 2, -4, -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], 'schur_index': 1}
  • id: 5312639
    {'cdim': 6, 'counter': 62, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6h', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 4, -4, 0, 0, -6, -6, -6, 6, 0, 0, -6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, -6, 6, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -2, 2, -4, -2, 2, 4, -2, 2, 2, -2, -2, 4, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312640
    {'cdim': 6, 'counter': 63, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6i', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 4, -4, 0, 0, -6, -6, 0, -6, 6, 6, 0, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 6, 0, -6, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, -4, 2, -2, 2, -2, 4, -4, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5312641
    {'cdim': 6, 'counter': 64, 'faithful': True, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.6j', 'multiplicity': 2, 'nt': [36, 1982], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 4, -4, 0, 0, -6, -6, 6, 0, -6, -6, 6, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, -6, 6, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -2, 2, 2, -2, 2, -2, -2, 2, -4, 4, -2, -2, 4, 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], 'schur_index': 1}
  • id: 5312642
    {'cdim': 12, 'counter': 65, 'faithful': False, 'group': '1296.1067', 'group_order': 1296, 'image': None, 'label': '1296.1067.12a', 'multiplicity': 1, 'nt': [36, 582], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 10319787
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1296, 'label': '1296.1067.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10319809
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 648, 'label': '1296.1067.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10319820
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 648, 'label': '1296.1067.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10319831
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 648, 'label': '1296.1067.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10319842
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 648, 'label': '1296.1067.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10319853
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 648, 'label': '1296.1067.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10319864
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 648, 'label': '1296.1067.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10319875
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 648, 'label': '1296.1067.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10319886
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 432, 'label': '1296.1067.1i1', 'nt': [3, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319788
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 432, 'label': '1296.1067.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319799
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.f1', 'kernel_order': 216, 'label': '1296.1067.1j1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319801
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.f1', 'kernel_order': 216, 'label': '1296.1067.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319802
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 216, 'label': '1296.1067.1k1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319803
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 216, 'label': '1296.1067.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319804
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 216, 'label': '1296.1067.1l1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319805
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 216, 'label': '1296.1067.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319806
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.1067.1m1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319807
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.1067.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319808
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 216, 'label': '1296.1067.1n1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319810
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 216, 'label': '1296.1067.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319811
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.1067.1o1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319812
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.1067.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319813
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 216, 'label': '1296.1067.1p1', 'nt': [6, 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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319814
    {'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 216, 'label': '1296.1067.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319815
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1', 'kernel_order': 216, 'label': '1296.1067.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 10319816
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 162, 'label': '1296.1067.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319817
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 162, 'label': '1296.1067.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319818
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1', 'kernel_order': 108, 'label': '1296.1067.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 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]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 10319819
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 29, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.1067.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 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]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 10319821
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 30, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.1067.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 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]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 10319822
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 72, 'label': '1296.1067.2g1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319823
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 72, 'label': '1296.1067.2g2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319824
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 54, 'label': '1296.1067.2h1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[2, -1]], [[2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -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, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319825
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 54, 'label': '1296.1067.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 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, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319826
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 54, 'label': '1296.1067.2i1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, -1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -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, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319827
    {'center': '4.b1', 'center_index': 4, 'center_order': 324, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 54, 'label': '1296.1067.2i2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[-2, -1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 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, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319828
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 37, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 36, 'label': '1296.1067.2j1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10319829
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 36, 'label': '1296.1067.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10319830
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 36, 'label': '1296.1067.2k1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[-2, 1]], [[2, 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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319832
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 36, 'label': '1296.1067.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[-2, -1]], [[2, -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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319833
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 36, 'label': '1296.1067.2l1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[2, 1]], [[-2, 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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 10319834
    {'center': '6.c1', 'center_index': 6, 'center_order': 216, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 36, 'label': '1296.1067.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[2, -1]], [[-2, -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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 10319835
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 43, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3a1', 'nt': [9, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319836
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 44, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3a2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319837
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 45, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3b1', 'nt': [9, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319838
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 46, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3b2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319839
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 47, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3c1', 'nt': [9, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319840
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 48, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3c2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319841
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 49, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3d1', 'nt': [18, 86], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319843
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 50, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3d2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319844
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 51, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3e1', 'nt': [18, 86], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319845
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 52, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3e2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319846
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 53, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3f1', 'nt': [18, 86], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319847
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 54, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '162.10', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1', 'kernel_order': 8, 'label': '1296.1067.3f2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319848
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 55, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3g1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319849
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 56, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3g2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319850
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 57, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3h1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319851
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 58, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3h2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319852
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 59, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3i1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319854
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 60, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3i2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319855
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 61, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3j1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319856
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 62, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3j2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319857
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 63, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3k1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319858
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 64, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3k2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319859
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 65, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3l1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319860
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 66, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.b1', 'kernel_order': 4, 'label': '1296.1067.3l2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319861
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 67, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3m1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319862
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 68, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3m2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319863
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 69, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3n1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319865
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 70, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3n2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319866
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 71, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3o1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319867
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 72, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3o2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319868
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 73, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3p1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319869
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 74, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3p2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319870
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 75, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3q1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319871
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 76, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3q2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319872
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 77, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3r1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319873
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 78, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3r2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319874
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 79, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3s1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319876
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 80, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3s2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319877
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 81, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3t1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319878
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 82, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3t2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319879
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 83, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3u1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[0, 0]], [[1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319880
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 84, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3u2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319881
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 85, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3v1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319882
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 86, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3v2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319883
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 87, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3w1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319884
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 88, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3w2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319885
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 89, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3x1', 'nt': [18, 119], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[0, 0]], [[-1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319887
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 90, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '324.68', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 4, 'label': '1296.1067.3x2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319888
    {'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 91, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 27, 'label': '1296.1067.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319889
    {'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 92, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '144.162', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 9, 'label': '1296.1067.4b1', 'nt': [24, 208], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, 1]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319890
    {'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 93, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '144.162', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 9, 'label': '1296.1067.4b2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, -1]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319891
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 94, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '54.5', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 24, 'label': '1296.1067.6a', 'nt': [9, 11], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319892
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 95, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1', 'kernel_order': 12, 'label': '1296.1067.6b', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319893
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 96, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 12, 'label': '1296.1067.6c', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319894
    {'center': '54.a1', 'center_index': 54, 'center_order': 24, 'counter': 97, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 12, 'label': '1296.1067.6d', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10319895
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 98, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6e1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[4, 0], [2, 1]], [[-2, 0], [2, 1]], [[2, 0], [4, 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]], [[2, 1]], [[2, 0]], [[-2, -1]], [[2, -1]], [[2, 0]], [[-2, -1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319896
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 99, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[2, 0], [-2, 1]], [[-4, 0], [-2, 1]], [[-2, 0], [-4, 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]], [[2, -1]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 0]], [[-2, 1]], [[2, -1]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319789
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 100, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6f1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[-2, 0], [-4, 1]], [[4, 0], [2, 1]], [[-4, 0], [-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]], [[2, -1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, -1]], [[2, 1]], [[-2, -1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319790
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 101, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6f2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[2, 0], [4, 1]], [[2, 0], [-2, 1]], [[-2, 0], [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]], [[2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[2, -1]], [[-2, 1]], [[2, -1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319791
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 102, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6g1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[-2, 0], [2, 1]], [[-2, 0], [-4, 1]], [[2, 0], [-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]], [[2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319792
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 103, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6g2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[-4, 0], [-2, 1]], [[2, 0], [4, 1]], [[4, 0], [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]], [[2, 0]], [[2, -1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319793
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 104, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6h1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[4, 0], [2, 1]], [[-2, 0], [2, 1]], [[2, 0], [4, 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]], [[-2, 1]], [[-2, 0]], [[2, -1]], [[-2, -1]], [[-2, 0]], [[2, -1]], [[-2, 1]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319794
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 105, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6h2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[2, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[2, 0], [-2, 1]], [[-4, 0], [-2, 1]], [[-2, 0], [-4, 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]], [[-2, -1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, -1]], [[2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319795
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 106, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6i1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[2, 0], [-2, 1]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[-2, 0], [-4, 1]], [[4, 0], [2, 1]], [[-4, 0], [-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]], [[-2, -1]], [[-2, -1]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, -1]], [[-2, 1]], [[2, -1]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319796
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 107, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6i2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[4, 0], [2, 1]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[2, 0], [4, 1]], [[2, 0], [-2, 1]], [[-2, 0], [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]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[2, 1]], [[-2, -1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319797
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 108, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6j1', 'nt': [36, 1982], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[-2, 0], [2, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[-4, 0], [-2, 1]], [[4, 0], [2, 1]], [[-2, 0], [2, 1]], [[-2, 0], [-4, 1]], [[2, 0], [-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]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319798
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 109, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.1067', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.1067.6j2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[4, 0], [2, 1]], [[-2, 0], [-4, 1]], [[-4, 0], [-2, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[-2, 0], [2, 1]], [[2, 0], [-2, 1]], [[-4, 0], [-2, 1]], [[2, 0], [4, 1]], [[4, 0], [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]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10319800
    {'center': '216.a1', 'center_index': 216, 'center_order': 6, 'counter': 110, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1296.1067', 'group_counter': 1067, 'group_order': 1296, 'image': None, 'image_isoclass': '432.360', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.1067.12a', 'nt': [36, 582], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 70613542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.1067.1.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': '1296.1067', 'subgroup_hash': 1067, 'subgroup_order': 1296, 'subgroup_tex': 'C_3\\wr S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.2.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': '648.328', 'subgroup_hash': 328, 'subgroup_order': 648, 'subgroup_tex': 'C_2^2\\times C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.160', 'subgroup_hash': 160, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.219', 'subgroup_hash': 219, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 648, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', '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': '648.128', 'subgroup_hash': 128, 'subgroup_order': 648, 'subgroup_tex': 'C_4\\times C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', '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': '648.129', 'subgroup_hash': 129, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 216, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '432.704', 'subgroup_hash': 704, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.86', 'subgroup_hash': 86, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': True, 'centralizer_order': 24, 'characteristic': True, 'core_order': 324, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.68', 'subgroup_hash': 68, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 324, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.68', 'subgroup_hash': 68, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 324, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.31', 'subgroup_hash': 31, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 324, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.13', 'subgroup_hash': 13, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 162, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '324.68', 'subgroup_hash': 68, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.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': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 216, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1', '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': '216.151', 'subgroup_hash': 151, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 70613631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.77', 'subgroup_hash': 77, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 216, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.68', 'subgroup_hash': 68, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '216.78', 'subgroup_hash': 78, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.136', 'subgroup_hash': 136, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.137', 'subgroup_hash': 137, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 162, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.28', 'subgroup_hash': 28, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': True, 'centralizer_order': 24, 'characteristic': False, 'core_order': 162, 'counter': 27, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.1067.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 81, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.28', 'subgroup_hash': 28, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 108, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 108, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 108, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 54, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 81, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1296.1067.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 3}
  • id: 70613702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 72, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 70613716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 54, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.24.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': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 70613727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 70613729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 27, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613741
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 70613746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 70613548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 27, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 70613556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 27, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], '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: 70613557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': True, 'centralizer_order': 324, 'characteristic': True, 'core_order': 24, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 18, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'C5'], 'split': False, '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: 70613581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 70613584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 70613590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.1067.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 70613601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 12, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 12, 'counter': 153, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.1067.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613615
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613616
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613617
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613618
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613619
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613621
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 70613622
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 9, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.162', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_6', '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: 70613628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 70613629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 70613630
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 70613632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 70613633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': True, 'centralizer_order': 324, 'characteristic': True, 'core_order': 8, 'counter': 181, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.1067.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 70613635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 6, 'counter': 186, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.1067.216.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': '216.110', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 110, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U1', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613639
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613641
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613643
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 190, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613644
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613645
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613646
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613647
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613648
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613649
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613650
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613651
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 198, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613652
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.216.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 70613655
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613656
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 4, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1067.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.68', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 68, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613658
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 4, 'counter': 203, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.1067.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.68', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 68, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.324.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613661
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 70613662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.1067.324.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 70613663
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 3, 'counter': 208, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.1067.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '432.360', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 360, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['D2', 'C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 70613664
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 70613666
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 70613667
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 70613668
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 2, 'counter': 212, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.1067.648.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': '648.328', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 328, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_3\\wr S_3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613669
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613670
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.648.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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.1067.648.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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 70613672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.1067', 'ambient_counter': 1067, 'ambient_order': 1296, 'ambient_tex': 'C_3\\wr S_3\\times D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1296.1067.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1296.1067', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1067, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\wr S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D3', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• 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: 70613597
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.j1', '36.m1', '36.y1'], 'contains': ['144.c1', '216.m1', '216.p1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [911, -1, 2774, -1], 'generators': [81, 432, 588], 'label': '1296.1067.72.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '72.q1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613715
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.45', 'aut_weyl_index': 108, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1'], 'contains': ['36.e1', '36.t1', '54.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5579, -1, 2915, -1], 'generators': [18, 432, 108, 1022, 648], 'label': '1296.1067.18.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '18.l1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 70613542
    {'ambient': '1296.1067', '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': '216.a1', 'complements': ['1296.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1', '3.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5450, 4985, 4941, 5031], 'generators': [3, 648, 588, 18, 2, 432, 936, 108], 'label': '1296.1067.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '216.110', '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': '216.110'}
  • id: 70613543
    {'ambient': '1296.1067', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '648.603', 'aut_weyl_index': 8, 'centralizer': '54.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '8.b1', '12.c1', '12.i1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3143, 9422, 2210, 475], 'generators': [3, 432, 936, 648, 2, 588], 'label': '1296.1067.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '216.110', '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': '54.5'}
  • id: 70613544
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.k1', '18.g1', '18.o1'], 'contains': ['72.a1', '108.n1', '108.r1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4771, -1, 5471, -1], 'generators': [117, 432, 648, 72], 'label': '1296.1067.36.q1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.q1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613545
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.k1', '18.p1', '18.t1'], 'contains': ['72.c1', '108.b1', '108.s1'], 'core': '108.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6075, -1, 7188, -1], 'generators': [774, 1020, 432, 648], 'label': '1296.1067.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.r1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613546
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.h1', '18.p1'], 'contains': ['72.c1', '108.n1', '108.t1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4132, -1, 5683, -1], 'generators': [117, 432, 648, 1020], 'label': '1296.1067.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.s1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613547
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '36.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.l1'], 'contains': ['72.d1', '108.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5477, -1, 2859, -1], 'generators': [126, 1022, 648, 432], 'label': '1296.1067.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '36.t1', 'projective_image': '216.110', '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': '6.2'}
  • id: 70613548
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '12.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.e1', '18.m1', '18.q1', '18.u1'], 'contains': ['72.e1', '108.o1', '108.q1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9331, -1, 8723, -1], 'generators': [774, 2, 72, 648], 'label': '1296.1067.36.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.u1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613549
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.k1', '18.i1', '18.q1'], 'contains': ['72.e1', '108.p1', '108.r1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8261, -1, 6392, -1], 'generators': [837, 2, 648, 72], 'label': '1296.1067.36.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.v1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613550
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.m1', '18.b1'], 'contains': ['72.f1', '72.k1', '72.o1', '108.u1', '108.v1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2080, -1, 2163, -1], 'generators': [3, 18, 2, 432], 'label': '1296.1067.36.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.w1', 'projective_image': '432.360', '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': '1.1'}
  • id: 70613551
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.m1', '12.n1', '18.c1'], 'contains': ['72.g1', '72.l1', '72.p1', '108.u1', '108.w1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1008, -1, 1011, -1], 'generators': [3, 18, 432, 504], 'label': '1296.1067.36.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '36.x1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613552
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.n1', '18.d1'], 'contains': ['72.h1', '72.m1', '72.q1', '108.u1', '108.x1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1605, -1, 2301, -1], 'generators': [3, 18, 432, 588], 'label': '1296.1067.36.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '36.y1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613553
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.m1', '18.e1'], 'contains': ['72.j1', '72.n1', '72.r1', '108.v1', '108.w1'], 'core': '1296.a1', 'coset_action_label': '36T1982', 'count': 72, 'diagramx': [3936, -1, 2472, -1], 'generators': [3, 18, 2, 504], 'label': '1296.1067.36.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '36.z1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613554
    {'ambient': '1296.1067', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '648.603', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['324.f1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.a1', '8.d1', '12.d1', '12.j1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3438, 6777, 2498, 4136], 'generators': [153, 432, 72, 648, 2, 156], 'label': '1296.1067.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.a1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613555
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '6.c1', 'complements': ['27.d1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.e1', '24.h1', '24.i1'], 'contains': ['144.a1', '144.b1', '144.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1170, 4019, 1601, 6625], 'generators': [2, 72, 432], 'label': '1296.1067.48.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '432.360', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613556
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '54.a1', 'complements': ['27.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.b1', '24.c1', '24.f1', '24.j1'], 'contains': ['144.a1', '144.c1'], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [252, 7425, 876, 4377], 'generators': [1020, 72], 'label': '1296.1067.48.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.a1', '24.b1', '24.c1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '432.360', 'quotient_action_image': '6.2', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613557
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 96, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.d1', '24.g1'], 'contains': ['144.a1', '144.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [563, -1, 661, -1], 'generators': [1022, 72], 'label': '1296.1067.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.c1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 70613558
    {'ambient': '1296.1067', 'aut_centralizer_order': 324, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.j1', '18.k1', '18.l1', '27.a1'], 'contains': ['108.a1', '108.b1', '162.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7685, 1739, 6998, 8760], 'generators': [18, 108, 432, 648], 'label': '1296.1067.54.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1'], 'normal_contains': ['108.a1', '108.b1', '162.a1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613559
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.c1', '18.d1', '27.a1'], 'contains': ['108.a1', '108.f1', '108.j1', '108.u1', '162.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3898, -1, 3832, -1], 'generators': [3, 18, 648, 432], 'label': '1296.1067.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.b1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613560
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.b1', '18.e1', '27.b1'], 'contains': ['108.c1', '108.g1', '108.k1', '108.v1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6306, -1, 5266, -1], 'generators': [3, 18, 648, 2], 'label': '1296.1067.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.c1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613561
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.e1', '27.c1'], 'contains': ['108.d1', '108.h1', '108.l1', '108.w1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7020, -1, 4619, -1], 'generators': [3, 18, 648, 504], 'label': '1296.1067.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.d1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613562
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '27.d1'], 'contains': ['108.e1', '108.i1', '108.m1', '108.x1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2608, -1, 7771, -1], 'generators': [3, 18, 648, 588], 'label': '1296.1067.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.e1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613563
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.f1', '18.g1', '18.h1', '27.a1'], 'contains': ['108.a1', '108.j1', '108.n1', '162.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4979, -1, 5875, -1], 'generators': [903, 18, 432, 648], 'label': '1296.1067.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.f1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613564
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.f1', '18.i1', '27.b1'], 'contains': ['108.c1', '108.k1', '108.p1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8378, -1, 7958, -1], 'generators': [903, 18, 2, 648], 'label': '1296.1067.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.g1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613565
    {'ambient': '1296.1067', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '648.603', 'aut_weyl_index': 8, 'centralizer': '108.b1', 'complements': ['324.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.a1', '12.e1', '12.f1', '12.l1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6419, 1639, 4940, 7924], 'generators': [774, 432, 936, 2, 1020, 648], 'label': '1296.1067.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '12.e1', '12.f1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '216.110', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613566
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '18.i1', '27.c1'], 'contains': ['108.d1', '108.l1', '108.r1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8180, -1, 6228, -1], 'generators': [903, 18, 648, 504], 'label': '1296.1067.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.h1', 'projective_image': '648.328', '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': '24.14'}
  • id: 70613567
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '27.d1'], 'contains': ['108.e1', '108.m1', '108.t1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4258, -1, 8104, -1], 'generators': [903, 18, 648, 1020], 'label': '1296.1067.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.i1', 'projective_image': '648.328', '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': '24.14'}
  • id: 70613568
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.j1', '18.m1', '27.b1'], 'contains': ['108.c1', '108.o1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9685, -1, 9294, -1], 'generators': [18, 108, 2, 648], 'label': '1296.1067.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.j1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613569
    {'ambient': '1296.1067', 'aut_centralizer_order': 108, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.m1', '27.c1'], 'contains': ['108.d1', '108.q1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8755, -1, 8420, -1], 'generators': [18, 108, 72, 648], 'label': '1296.1067.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.k1', 'projective_image': '648.328', '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': '8.5'}
  • id: 70613570
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '72.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '27.d1'], 'contains': ['108.e1', '108.s1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5472, -1, 9812, -1], 'generators': [18, 108, 1020, 648], 'label': '1296.1067.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.l1', 'projective_image': '648.328', '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': '8.5'}
  • id: 70613571
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '18.o1', '18.p1', '27.a1'], 'contains': ['108.b1', '108.f1', '108.n1', '162.d1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6811, -1, 6808, -1], 'generators': [3, 126, 432, 648], 'label': '1296.1067.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.m1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613572
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.n1', '18.q1', '27.b1'], 'contains': ['108.g1', '108.o1', '108.p1', '162.d1'], 'core': '324.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9341, -1, 8930, -1], 'generators': [3, 126, 2, 648], 'label': '1296.1067.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.n1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613573
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1', '18.q1', '27.c1'], 'contains': ['108.h1', '108.q1', '108.r1', '162.d1'], 'core': '324.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9047, -1, 8248, -1], 'generators': [3, 774, 648, 504], 'label': '1296.1067.54.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.o1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613574
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1', '27.d1'], 'contains': ['108.i1', '108.s1', '108.t1', '162.d1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4603, -1, 9466, -1], 'generators': [3, 774, 648, 588], 'label': '1296.1067.54.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.p1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613575
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1', '18.s1', '18.t1', '27.a1'], 'contains': ['108.b1', '108.j1', '162.e1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7507, -1, 7379, -1], 'generators': [903, 126, 432, 648], 'label': '1296.1067.54.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.q1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 70613576
    {'ambient': '1296.1067', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '648.603', 'aut_weyl_index': 8, 'centralizer': '108.b1', 'complements': ['324.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.a1', '12.g1', '12.k1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [3838, 7985, 4356, 1406], 'generators': [837, 432, 72, 2, 648, 588], 'label': '1296.1067.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.a1', '12.g1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '216.110', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613577
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.r1', '18.u1', '27.b1'], 'contains': ['108.k1', '108.o1', '162.e1'], 'core': '324.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9886, -1, 9639, -1], 'generators': [903, 126, 866, 648], 'label': '1296.1067.54.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.r1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 70613578
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 108, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1', '18.u1', '27.c1'], 'contains': ['108.l1', '108.q1', '162.e1'], 'core': '324.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8902, -1, 8564, -1], 'generators': [903, 774, 648, 504], 'label': '1296.1067.54.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.s1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613579
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.38', 'aut_weyl_index': 108, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1', '27.d1'], 'contains': ['108.m1', '108.s1', '162.e1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5275, -1, 9955, -1], 'generators': [903, 774, 648, 1020], 'label': '1296.1067.54.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.t1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613580
    {'ambient': '1296.1067', 'aut_centralizer_order': 432, 'aut_label': '72.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.b1', '24.d1', '36.a1', '36.b1', '36.h1', '36.l1', '36.q1'], 'contains': ['144.a1', '216.a1', '216.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3123, 3218, 3727, 7120], 'generators': [648, 72, 432], 'label': '1296.1067.72.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '24.b1', '36.a1', '36.b1'], 'normal_contains': ['144.a1', '216.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '216.110', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613581
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.c1', '36.g1', '36.k1', '36.o1', '36.p1'], 'contains': ['144.b1', '216.a1', '216.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5868, -1, 4589, -1], 'generators': [648, 2, 432], 'label': '1296.1067.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.b1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613582
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.d1', '36.i1', '36.m1', '36.r1', '36.s1'], 'contains': ['144.c1', '216.a1', '216.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2403, -1, 4244, -1], 'generators': [648, 1020, 432], 'label': '1296.1067.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.c1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613583
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '18.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '36.e1', '36.t1'], 'contains': ['144.d1', '216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3268, -1, 1494, -1], 'generators': [648, 1022, 432], 'label': '1296.1067.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '72.d1', 'projective_image': '216.110', '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': '3.1'}
  • id: 70613584
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '36.f1', '36.j1', '36.n1', '36.u1', '36.v1'], 'contains': ['144.e1', '216.b1', '216.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7576, -1, 5207, -1], 'generators': [648, 2, 72], 'label': '1296.1067.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.e1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613585
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '36.c1', '36.w1'], 'contains': ['144.b1', '216.e1', '216.f1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1852, -1, 2084, -1], 'generators': [18, 2, 432], 'label': '1296.1067.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '72.f1', 'projective_image': '432.360', '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': '1.1'}
  • id: 70613586
    {'ambient': '1296.1067', 'aut_centralizer_order': 108, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.f1', '24.g1', '36.a1', '36.x1'], 'contains': ['144.a1', '216.e1', '216.g1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [158, -1, 1008, -1], 'generators': [18, 72, 432], 'label': '1296.1067.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.g1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613587
    {'ambient': '1296.1067', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '12.m1', '12.n1'], 'core': '8.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1343, -1, 851, -1], 'generators': [3, 432, 936, 18, 2, 588], 'label': '1296.1067.4.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.f1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613588
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '36.d1', '36.y1'], 'contains': ['144.c1', '216.e1', '216.h1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1088, -1, 2429, -1], 'generators': [18, 1020, 432], 'label': '1296.1067.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.h1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613589
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '36.e1'], 'contains': ['144.d1', '216.e1'], 'core': '432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1431, -1, 775, -1], 'generators': [18, 1022, 432], 'label': '1296.1067.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1', 'old_label': '72.i1', 'projective_image': '432.360', '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': '3.1'}
  • id: 70613590
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.e1', '36.f1', '36.z1'], 'contains': ['144.e1', '216.f1', '216.g1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4705, -1, 3210, -1], 'generators': [18, 2, 72], 'label': '1296.1067.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '72.j1', 'projective_image': '1296.1067', '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': '2.1'}
  • id: 70613591
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '36.g1', '36.w1'], 'contains': ['144.b1', '216.i1', '216.j1'], 'core': '432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1626, -1, 1912, -1], 'generators': [3, 2, 432], 'label': '1296.1067.72.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.k1', 'projective_image': '432.360', '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': '1.1'}
  • id: 70613592
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.h1', '36.h1', '36.x1'], 'contains': ['144.a1', '216.i1', '216.k1'], 'core': '144.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [561, -1, 1181, -1], 'generators': [3, 432, 504], 'label': '1296.1067.72.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.l1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613593
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '36.i1', '36.y1'], 'contains': ['144.c1', '216.i1', '216.l1'], 'core': '432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [736, -1, 2257, -1], 'generators': [3, 432, 588], 'label': '1296.1067.72.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.m1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613594
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '36.j1', '36.z1'], 'contains': ['144.e1', '216.j1', '216.k1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4005, -1, 3038, -1], 'generators': [3, 2, 504], 'label': '1296.1067.72.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.n1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613595
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.i1', '36.k1', '36.w1'], 'contains': ['144.b1', '216.m1', '216.n1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2078, -1, 2601, -1], 'generators': [153, 74, 432], 'label': '1296.1067.72.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.o1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613596
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.i1', '24.j1', '36.l1', '36.x1'], 'contains': ['144.a1', '216.m1', '216.o1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [335, -1, 1352, -1], 'generators': [81, 432, 72], 'label': '1296.1067.72.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '72.p1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613598
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 12, 'centralizer': '108.a1', 'complements': ['216.f1', '216.n1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.b1', '12.c1', '12.d1', '12.n1', '18.c1', '18.d1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3532, 6311, 2774, 3146], 'generators': [3, 432, 504, 18, 648, 588], 'label': '1296.1067.6.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.b1', '12.c1', '12.d1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '216.110', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613599
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '36.n1', '36.z1'], 'contains': ['144.e1', '216.n1', '216.o1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4528, -1, 3382, -1], 'generators': [153, 2, 72], 'label': '1296.1067.72.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '72.r1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613600
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.c1', '27.d1'], 'contains': ['162.a1', '162.b1', '162.c1', '162.d1', '162.e1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8315, -1, 9120, -1], 'generators': [3, 18, 108], 'label': '1296.1067.81.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '81.a1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613601
    {'ambient': '1296.1067', 'aut_centralizer_order': 648, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.c1', '36.d1', '36.e1', '54.a1', '54.b1', '54.f1'], 'contains': ['216.a1', '216.e1', '324.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3702, 2186, 4072, 7738], 'generators': [18, 648, 432], 'label': '1296.1067.108.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1', '54.a1'], 'normal_contains': ['216.a1', '324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.5', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613602
    {'ambient': '1296.1067', 'aut_centralizer_order': 1296, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.o1', '36.r1', '36.t1', '54.a1', '54.m1', '54.q1'], 'contains': ['216.a1', '324.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7065, 2846, 6342, 8247], 'generators': [126, 432, 648], 'label': '1296.1067.108.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.b1', 'normal_contained_in': ['36.b1', '54.a1'], 'normal_contains': ['216.a1', '324.b1'], 'normalizer': '1.a1', 'old_label': '108.b1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.5', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613603
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.c1', '36.f1', '54.c1', '54.g1', '54.j1'], 'contains': ['216.b1', '216.f1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6365, -1, 5656, -1], 'generators': [18, 648, 2], 'label': '1296.1067.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.c1', 'projective_image': '648.328', '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: 70613604
    {'ambient': '1296.1067', 'aut_centralizer_order': 216, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.f1', '54.d1', '54.h1', '54.k1'], 'contains': ['216.c1', '216.g1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6744, -1, 4944, -1], 'generators': [18, 648, 72], 'label': '1296.1067.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.d1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613605
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '54.e1', '54.i1', '54.l1'], 'contains': ['216.d1', '216.h1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2911, -1, 6575, -1], 'generators': [18, 648, 1020], 'label': '1296.1067.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.e1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613606
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.h1', '36.i1', '54.b1', '54.m1'], 'contains': ['216.a1', '216.i1', '324.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3104, -1, 3899, -1], 'generators': [3, 648, 432], 'label': '1296.1067.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.f1', 'projective_image': '216.110', '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': '1.1'}
  • id: 70613607
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.g1', '36.j1', '54.c1', '54.n1'], 'contains': ['216.b1', '216.j1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5868, -1, 5380, -1], 'generators': [3, 648, 2], 'label': '1296.1067.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.g1', 'projective_image': '648.328', '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': '1.1'}
  • id: 70613608
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '36.j1', '54.d1', '54.o1'], 'contains': ['216.c1', '216.k1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6053, -1, 4812, -1], 'generators': [3, 648, 504], 'label': '1296.1067.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.h1', 'projective_image': '648.328', '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: 70613609
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 12, 'centralizer': '216.a1', 'complements': ['216.f1', '216.j1', '216.n1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.d1', '12.g1', '18.g1', '18.h1'], 'core': '6.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3982, 4944, 4633, 5231], 'generators': [903, 432, 504, 18, 648, 1020], 'label': '1296.1067.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.b1', '12.d1', '12.g1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '216.110'}
  • id: 70613610
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '54.e1', '54.p1'], 'contains': ['216.d1', '216.l1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2455, -1, 6443, -1], 'generators': [3, 648, 588], 'label': '1296.1067.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.i1', 'projective_image': '648.328', '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': '6.1'}
  • id: 70613611
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '36.l1', '36.m1', '54.b1', '54.f1', '54.q1'], 'contains': ['216.a1', '216.m1', '324.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4958, -1, 4416, -1], 'generators': [81, 648, 432], 'label': '1296.1067.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.j1', 'projective_image': '216.110', '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: 70613612
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.k1', '36.n1', '54.c1', '54.g1', '54.r1'], 'contains': ['216.b1', '216.n1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7460, -1, 5828, -1], 'generators': [153, 648, 74], 'label': '1296.1067.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.k1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613613
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '36.n1', '54.d1', '54.h1', '54.s1'], 'contains': ['216.c1', '216.o1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7694, -1, 5076, -1], 'generators': [81, 648, 72], 'label': '1296.1067.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.l1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613614
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '54.e1', '54.i1', '54.t1'], 'contains': ['216.d1', '216.p1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2713, -1, 6818, -1], 'generators': [81, 648, 588], 'label': '1296.1067.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.m1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613615
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.q1', '36.s1', '54.f1', '54.m1'], 'contains': ['216.a1', '324.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5389, -1, 5970, -1], 'generators': [117, 432, 648], 'label': '1296.1067.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.n1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613616
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '6.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.o1', '36.u1', '54.j1', '54.n1', '54.r1'], 'contains': ['216.b1', '324.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9488, -1, 8698, -1], 'generators': [126, 2, 648], 'label': '1296.1067.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.o1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613617
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.p1', '36.v1', '54.g1', '54.n1'], 'contains': ['216.b1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8710, -1, 6717, -1], 'generators': [837, 74, 648], 'label': '1296.1067.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.p1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613618
    {'ambient': '1296.1067', 'aut_centralizer_order': 432, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '12.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.u1', '54.k1', '54.o1', '54.s1'], 'contains': ['216.c1', '324.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9070, -1, 8273, -1], 'generators': [774, 72, 648], 'label': '1296.1067.108.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.q1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613619
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.v1', '54.h1', '54.o1'], 'contains': ['216.c1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8563, -1, 6228, -1], 'generators': [117, 648, 72], 'label': '1296.1067.108.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.r1', 'projective_image': '648.328', '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: 70613620
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.992', 'aut_weyl_index': 18, 'centralizer': '24.a1', 'complements': ['216.l1', '216.p1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.a1', '12.e1', '18.a1', '18.j1', '18.m1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7775, 413, 6614, 9682], 'generators': [18, 648, 432, 108, 2, 72], 'label': '1296.1067.6.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['12.a1', '12.e1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '216.110', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613621
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '36.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '54.l1', '54.p1', '54.t1'], 'contains': ['216.d1', '324.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5275, -1, 9196, -1], 'generators': [774, 1020, 648], 'label': '1296.1067.108.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.s1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613622
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '54.i1', '54.p1'], 'contains': ['216.d1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4366, -1, 7014, -1], 'generators': [117, 648, 1020], 'label': '1296.1067.108.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.t1', 'projective_image': '648.328', '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: 70613623
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.w1', '36.x1', '36.y1', '54.b1'], 'contains': ['216.e1', '216.i1', '216.m1', '324.f1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1400, -1, 1740, -1], 'generators': [3, 18, 432], 'label': '1296.1067.108.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.u1', 'projective_image': '432.360', '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': '1.1'}
  • id: 70613624
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.w1', '36.z1', '54.c1'], 'contains': ['216.f1', '216.j1', '216.n1', '324.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [3878, -1, 3555, -1], 'generators': [3, 18, 2], 'label': '1296.1067.108.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.v1', 'projective_image': '1296.1067', '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': '1.1'}
  • id: 70613625
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.x1', '36.z1', '54.d1'], 'contains': ['216.g1', '216.k1', '216.o1', '324.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4145, -1, 2906, -1], 'generators': [3, 18, 504], 'label': '1296.1067.108.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '108.w1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613626
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.y1', '54.e1'], 'contains': ['216.h1', '216.l1', '216.p1', '324.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2098, -1, 4721, -1], 'generators': [3, 18, 588], 'label': '1296.1067.108.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '108.x1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613627
    {'ambient': '1296.1067', 'aut_centralizer_order': 432, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.b1', '48.c1', '72.a1', '72.g1', '72.l1', '72.p1'], 'contains': ['432.a1', '432.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [398, 3771, 1352, 6875], 'generators': [72, 432], 'label': '1296.1067.144.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['48.a1', '48.b1', '72.a1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '432.360', 'quotient_action_image': '6.1', 'quotient_action_kernel': '24.10', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613628
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.b1', '72.f1', '72.k1', '72.o1'], 'contains': ['432.a1', '432.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1872, -1, 2340, -1], 'generators': [2, 432], 'label': '1296.1067.144.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.b1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613629
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '72.c1', '72.h1', '72.m1', '72.q1'], 'contains': ['432.a1', '432.d1'], 'core': '432.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [920, -1, 2444, -1], 'generators': [1020, 432], 'label': '1296.1067.144.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.c1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613630
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 864, 'centralizer': '18.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '72.d1', '72.i1'], 'contains': ['432.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1540, -1, 1015, -1], 'generators': [1022], 'label': '1296.1067.144.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '144.d1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 70613631
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 6, 'centralizer': '216.a1', 'complements': ['216.j1', '216.n1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.b1', '12.f1', '18.a1', '18.k1'], 'core': '6.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7139, 2346, 5683, 8883], 'generators': [18, 432, 648, 108, 1020, 72], 'label': '1296.1067.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.c1', '3.a1'], 'normal_contains': ['12.b1', '12.f1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '216.110'}
  • id: 70613632
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.a1', '72.e1', '72.j1', '72.n1', '72.r1'], 'contains': ['432.b1', '432.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4690, -1, 3290, -1], 'generators': [2, 72], 'label': '1296.1067.144.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.e1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613633
    {'ambient': '1296.1067', 'aut_centralizer_order': 648, 'aut_label': '162.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '4.b1', 'complements': ['8.b1', '8.d1'], 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.j1', '54.k1', '54.l1', '81.a1'], 'contains': ['324.a1', '324.b1'], 'core': '162.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8265, 1739, 8547, 8610], 'generators': [18, 108], 'label': '1296.1067.162.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': ['54.a1'], 'normal_contains': ['324.a1', '324.b1'], 'normalizer': '1.a1', 'old_label': '162.a1', 'projective_image': '648.328', 'quotient_action_image': '1.1', 'quotient_action_kernel': '162.10', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 70613634
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.c1', '54.d1', '54.e1', '81.a1'], 'contains': ['324.a1', '324.c1', '324.d1', '324.f1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5514, -1, 5518, -1], 'generators': [3, 18, 648], 'label': '1296.1067.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.b1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613635
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.f1', '54.g1', '54.h1', '54.i1', '81.a1'], 'contains': ['324.a1', '324.d1', '324.e1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7822, -1, 6910, -1], 'generators': [903, 18], 'label': '1296.1067.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.c1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613636
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.m1', '54.n1', '54.o1', '54.p1', '81.a1'], 'contains': ['324.b1', '324.c1', '324.e1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8547, -1, 8415, -1], 'generators': [3, 126], 'label': '1296.1067.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.d1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613637
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.q1', '54.r1', '54.s1', '54.t1', '81.a1'], 'contains': ['324.b1', '324.d1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8359, -1, 8799, -1], 'generators': [903, 126], 'label': '1296.1067.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.e1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613638
    {'ambient': '1296.1067', 'aut_centralizer_order': 2592, 'aut_label': '216.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.d1', '108.a1', '108.b1', '108.f1', '108.j1', '108.n1'], 'contains': ['432.a1', '648.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3541, 2958, 4158, 7643], 'generators': [648, 432], 'label': '1296.1067.216.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '108.a1', '108.b1'], 'normal_contains': ['432.a1', '648.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '216.110', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.110', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613639
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.b1', '72.e1', '108.c1', '108.g1', '108.k1', '108.o1', '108.p1'], 'contains': ['432.b1', '648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6150, -1, 5616, -1], 'generators': [648, 2], 'label': '1296.1067.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.b1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613640
    {'ambient': '1296.1067', 'aut_centralizer_order': 864, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.e1', '108.d1', '108.h1', '108.l1', '108.q1', '108.r1'], 'contains': ['432.c1', '648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6298, -1, 5076, -1], 'generators': [648, 72], 'label': '1296.1067.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.c1', 'projective_image': '648.328', '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: 70613641
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '108.e1', '108.i1', '108.m1', '108.s1', '108.t1'], 'contains': ['432.d1', '648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2779, -1, 6509, -1], 'generators': [648, 1020], 'label': '1296.1067.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.d1', 'projective_image': '648.328', '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: 70613642
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.545', 'aut_weyl_index': 12, 'centralizer': '108.b1', 'complements': ['216.f1', '216.n1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.c1', '12.f1', '12.g1', '18.o1', '18.p1'], 'core': '6.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5059, 8368, 5442, 2246], 'generators': [3, 432, 504, 774, 648, 588], 'label': '1296.1067.6.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': ['2.d1', '3.a1'], 'normal_contains': ['12.c1', '12.f1', '12.g1'], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613643
    {'ambient': '1296.1067', 'aut_centralizer_order': 648, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '72.g1', '72.h1', '72.i1', '108.a1', '108.u1'], 'contains': ['432.a1', '648.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1541, -1, 2117, -1], 'generators': [18, 432], 'label': '1296.1067.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.e1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613644
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.f1', '72.j1', '108.c1', '108.v1'], 'contains': ['432.b1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4272, -1, 3582, -1], 'generators': [18, 2], 'label': '1296.1067.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '216.f1', 'projective_image': '1296.1067', '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: 70613645
    {'ambient': '1296.1067', 'aut_centralizer_order': 216, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '72.j1', '108.d1', '108.w1'], 'contains': ['432.c1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4649, -1, 3101, -1], 'generators': [18, 72], 'label': '1296.1067.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '216.g1', 'projective_image': '1296.1067', '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: 70613646
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '108.e1', '108.x1'], 'contains': ['432.d1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2274, -1, 4340, -1], 'generators': [18, 1020], 'label': '1296.1067.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '216.h1', 'projective_image': '1296.1067', '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': '2.1'}
  • id: 70613647
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.l1', '72.m1', '108.f1', '108.u1'], 'contains': ['432.a1', '648.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [680, -1, 2243, -1], 'generators': [3, 432], 'label': '1296.1067.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.i1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613648
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.k1', '72.n1', '108.g1', '108.v1'], 'contains': ['432.b1', '648.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3837, -1, 3387, -1], 'generators': [3, 2], 'label': '1296.1067.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.j1', 'projective_image': '1296.1067', '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': '1.1'}
  • id: 70613649
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '72.n1', '108.h1', '108.w1'], 'contains': ['432.c1', '648.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4085, -1, 3010, -1], 'generators': [3, 504], 'label': '1296.1067.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.k1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613650
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '108.i1', '108.x1'], 'contains': ['432.d1', '648.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2049, -1, 4249, -1], 'generators': [3, 588], 'label': '1296.1067.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.l1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613651
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '72.p1', '72.q1', '108.j1', '108.u1'], 'contains': ['432.a1', '648.d1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1329, -1, 2601, -1], 'generators': [81, 432], 'label': '1296.1067.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.m1', 'projective_image': '432.360', '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': '1.1'}
  • id: 70613652
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.o1', '72.r1', '108.k1', '108.v1'], 'contains': ['432.b1', '648.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4178, -1, 3674, -1], 'generators': [153, 74], 'label': '1296.1067.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.n1', 'projective_image': '1296.1067', '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: 70613653
    {'ambient': '1296.1067', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1296.3033', 'aut_weyl_index': 4, 'centralizer': '108.a1', 'complements': ['648.b1', '648.d1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.f1', '6.a1', '6.g1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3438, 6583, 2498, 3622], 'generators': [3, 936, 588, 18, 432, 648, 2], 'label': '1296.1067.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '216.110', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613654
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 6, 'centralizer': '216.a1', 'complements': ['216.f1', '216.j1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.d1', '12.f1', '18.s1', '18.t1'], 'core': '6.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [6531, 3665, 5870, 7175], 'generators': [903, 432, 504, 774, 648, 1020], 'label': '1296.1067.6.f1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.f1', 'normal_contained_in': ['2.e1', '3.a1'], 'normal_contains': ['12.d1', '12.f1'], 'normalizer': '1.a1', 'old_label': '6.f1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '216.110'}
  • id: 70613655
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.p1', '72.r1', '108.l1', '108.w1'], 'contains': ['432.c1', '648.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4456, -1, 3192, -1], 'generators': [81, 72], 'label': '1296.1067.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '216.o1', 'projective_image': '1296.1067', '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': '6.1'}
  • id: 70613656
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '108.m1', '108.x1'], 'contains': ['432.d1', '648.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2181, -1, 4432, -1], 'generators': [81, 588], 'label': '1296.1067.216.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '216.p1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613657
    {'ambient': '1296.1067', 'aut_centralizer_order': 1296, 'aut_label': '324.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1', 'complements': ['4.f1'], 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.c1', '108.d1', '108.e1', '162.a1', '162.b1', '162.c1'], 'contains': ['648.a1', '648.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5662, 2057, 5518, 7993], 'generators': [18, 648], 'label': '1296.1067.324.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': ['108.a1', '162.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '648.328', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.68', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613658
    {'ambient': '1296.1067', 'aut_centralizer_order': 2592, 'aut_label': '324.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.d1', 'complements': ['4.f1'], 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '108.o1', '108.q1', '108.s1', '162.a1', '162.d1', '162.e1'], 'contains': ['648.a1'], 'core': '324.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8326, 2511, 8481, 8342], 'generators': [126], 'label': '1296.1067.324.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '324.b1', 'normal_contained_in': ['108.b1', '162.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '324.b1', 'projective_image': '648.328', 'quotient_action_image': '2.1', 'quotient_action_kernel': '162.10', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613659
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1', '108.g1', '108.h1', '108.i1', '162.b1', '162.d1'], 'contains': ['648.a1', '648.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5514, -1, 5396, -1], 'generators': [3, 648], 'label': '1296.1067.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.c1', 'projective_image': '648.328', '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': '1.1'}
  • id: 70613660
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '108.k1', '108.l1', '108.m1', '162.b1', '162.c1', '162.e1'], 'contains': ['648.a1', '648.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5867, -1, 5713, -1], 'generators': [81, 648], 'label': '1296.1067.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.d1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613661
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.n1', '108.p1', '108.r1', '108.t1', '162.c1', '162.d1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7874, -1, 6717, -1], 'generators': [117], 'label': '1296.1067.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.e1', 'projective_image': '648.328', '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': '2.1'}
  • id: 70613662
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.u1', '108.v1', '108.w1', '108.x1', '162.b1'], 'contains': ['648.b1', '648.c1', '648.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3614, -1, 3485, -1], 'generators': [3, 18], 'label': '1296.1067.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.f1', 'projective_image': '1296.1067', '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: 70613663
    {'ambient': '1296.1067', 'aut_centralizer_order': 2592, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.b1', '144.c1', '144.d1', '216.a1', '216.e1', '216.i1', '216.m1'], 'contains': ['1296.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1329, 3159, 2340, 7643], 'generators': [432], 'label': '1296.1067.432.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1', 'normal_contained_in': ['144.a1', '216.a1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '432.a1', 'projective_image': '432.360', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.360', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613664
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.b1', '144.e1', '216.b1', '216.f1', '216.j1', '216.n1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4272, -1, 3579, -1], 'generators': [2], 'label': '1296.1067.432.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.b1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613665
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.195', 'aut_weyl_index': 36, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.i1', '12.j1', '12.m1', '18.b1', '18.c1', '18.e1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4763, -1, 3634, -1], 'generators': [3, 504, 432, 18, 648, 2], 'label': '1296.1067.6.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613666
    {'ambient': '1296.1067', 'aut_centralizer_order': 864, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.e1', '216.c1', '216.g1', '216.k1', '216.o1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4631, -1, 3192, -1], 'generators': [72], 'label': '1296.1067.432.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.c1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613667
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '216.d1', '216.h1', '216.l1', '216.p1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2362, -1, 4295, -1], 'generators': [1020], 'label': '1296.1067.432.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.d1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613668
    {'ambient': '1296.1067', 'aut_centralizer_order': 5184, 'aut_label': '648.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '216.c1', '216.d1', '324.a1', '324.b1', '324.c1', '324.d1', '324.e1'], 'contains': ['1296.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5745, 2669, 5566, 7979], 'generators': [648], 'label': '1296.1067.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '324.a1', '324.b1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '648.328', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.328', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613669
    {'ambient': '1296.1067', 'aut_centralizer_order': 1296, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '216.f1', '216.g1', '216.h1', '324.a1', '324.f1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3890, -1, 3487, -1], 'generators': [18], 'label': '1296.1067.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '648.b1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613670
    {'ambient': '1296.1067', 'aut_centralizer_order': 288, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.i1', '216.j1', '216.k1', '216.l1', '324.c1', '324.f1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3442, -1, 3396, -1], 'generators': [3], 'label': '1296.1067.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.c1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613671
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.m1', '216.n1', '216.o1', '216.p1', '324.d1', '324.f1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3797, -1, 3670, -1], 'generators': [81], 'label': '1296.1067.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.d1', 'projective_image': '1296.1067', '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': '1.1'}
  • id: 70613672
    {'ambient': '1296.1067', 'aut_centralizer_order': None, 'aut_label': '1296.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': ['432.a1', '432.b1', '432.c1', '432.d1', '648.a1', '648.b1', '648.c1', '648.d1'], 'contains': [], 'core': '1296.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3843, 2858, 3533, 7806], 'generators': [], 'label': '1296.1067.1296.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1', 'normal_contained_in': ['432.a1', '648.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1296.a1', 'projective_image': '1296.1067', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70613673
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.195', 'aut_weyl_index': 36, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.j1', '12.k1', '18.f1', '18.g1', '18.i1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5303, -1, 5204, -1], 'generators': [903, 504, 648, 18, 2, 432], 'label': '1296.1067.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.h1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613674
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.390', 'aut_weyl_index': 12, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['12.h1', '12.l1', '18.a1', '18.l1'], 'core': '18.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6197, -1, 3012, -1], 'generators': [18, 432, 648, 108, 1022, 72], 'label': '1296.1067.6.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '6.i1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '108.30'}
  • id: 70613675
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.195', 'aut_weyl_index': 36, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.b1'], 'contains': ['12.e1', '12.i1', '12.k1', '18.n1', '18.o1', '18.q1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': [7420, -1, 6363, -1], 'generators': [3, 504, 648, 774, 2, 432], 'label': '1296.1067.6.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.j1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613676
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.992', 'aut_weyl_index': 18, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.b1'], 'contains': ['12.e1', '12.j1', '18.r1', '18.s1', '18.u1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': [7999, -1, 7100, -1], 'generators': [903, 504, 648, 774, 2, 432], 'label': '1296.1067.6.k1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.k1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613677
    {'ambient': '1296.1067', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '54.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '24.a1', '24.b1', '24.d1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3087, 6901, 1727, 3945], 'generators': [648, 432, 2, 1020, 936], 'label': '1296.1067.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613678
    {'ambient': '1296.1067', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '54.a1', 'complements': ['162.a1', '162.c1', '162.e1'], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.f1'], 'contains': ['16.a1', '24.c1', '24.h1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1176, 9587, 551, 1769], 'generators': [3, 432, 2, 588, 936], 'label': '1296.1067.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.a1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '432.360', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613679
    {'ambient': '1296.1067', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.f1'], 'contains': ['16.a1', '24.e1', '24.f1', '24.g1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [575, -1, 310, -1], 'generators': [18, 432, 2, 1020, 936], 'label': '1296.1067.8.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.c1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613680
    {'ambient': '1296.1067', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.f1'], 'contains': ['16.a1', '24.i1', '24.j1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1423, -1, 743, -1], 'generators': [153, 432, 2, 156, 72], 'label': '1296.1067.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.d1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613681
    {'ambient': '1296.1067', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1296.3033', 'aut_weyl_index': 4, 'centralizer': '216.a1', 'complements': ['648.b1', '648.c1', '648.d1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.e1', '6.b1', '6.h1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3939, 5309, 4372, 4608], 'generators': [903, 936, 1020, 18, 432, 2, 648], 'label': '1296.1067.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.e1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '216.110', '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': '216.110'}
  • id: 70613682
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.221', 'aut_weyl_index': 54, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['18.b1', '18.f1', '18.j1', '18.n1', '18.r1', '27.a1', '27.b1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8264, -1, 7442, -1], 'generators': [3, 648, 432, 18, 108, 2], 'label': '1296.1067.9.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613683
    {'ambient': '1296.1067', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 27, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.c1', '18.g1', '18.o1', '18.s1', '27.a1', '27.c1'], 'core': '18.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6789, -1, 6079, -1], 'generators': [3, 504, 648, 18, 108, 432], 'label': '1296.1067.9.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.b1', 'projective_image': '216.110', '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': '24.14'}
  • id: 70613684
    {'ambient': '1296.1067', 'aut_centralizer_order': 3, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 27, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.d1', '18.h1', '18.k1', '18.p1', '18.t1', '27.a1', '27.d1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5769, -1, 6849, -1], 'generators': [3, 588, 648, 18, 108, 432], 'label': '1296.1067.9.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '9.c1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613685
    {'ambient': '1296.1067', 'aut_centralizer_order': 3, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 27, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['18.e1', '18.i1', '18.m1', '18.q1', '18.u1', '27.b1', '27.c1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9310, -1, 8605, -1], 'generators': [3, 504, 648, 18, 108, 2], 'label': '1296.1067.9.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.d1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613686
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '72.48', 'aut_weyl_index': 72, 'centralizer': '12.a1', 'complements': ['108.x1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.c1', '6.g1', '6.h1'], 'contains': ['24.a1', '24.e1', '36.a1', '36.c1', '36.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4506, 1773, 3634, 7520], 'generators': [18, 432, 648, 2, 72], 'label': '1296.1067.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.c1'], 'normal_contains': ['24.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '216.110', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613687
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '108.a1', 'complements': ['108.v1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.b1', '6.d1'], 'contains': ['24.b1', '24.f1', '36.a1', '36.d1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2956, 4237, 2244, 5798], 'generators': [18, 432, 648, 1020, 72], 'label': '1296.1067.12.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.a1', '6.b1', '6.d1'], 'normal_contains': ['24.b1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613688
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '54.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.a1', '6.e1'], 'contains': ['24.b1', '24.c1', '36.h1', '36.i1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2412, 7784, 1991, 2541], 'generators': [3, 432, 648, 588, 504], 'label': '1296.1067.12.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.a1', '6.e1'], 'normal_contains': ['24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613689
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '108.a1', 'complements': ['108.v1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.a1', '6.b1', '6.f1'], 'contains': ['24.b1', '24.j1', '36.l1', '36.m1'], 'core': '12.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3216, 5415, 2498, 4890], 'generators': [81, 432, 648, 588, 72], 'label': '1296.1067.12.d1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1', 'normal_contained_in': ['4.c1', '6.a1', '6.b1', '6.f1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '216.110', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613690
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.48', 'aut_weyl_index': 72, 'centralizer': '12.e1', 'complements': ['108.x1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.c1', '6.j1', '6.k1'], 'contains': ['24.a1', '36.b1', '36.o1', '36.u1'], 'core': '12.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7847, 766, 7119, 8297], 'generators': [774, 648, 2, 72, 432], 'label': '1296.1067.12.e1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1', 'normal_contained_in': ['4.d1', '6.c1'], 'normal_contains': ['24.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.e1', 'projective_image': '216.110', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613691
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '108.b1', 'complements': ['108.v1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.d1', '6.e1', '6.f1'], 'contains': ['24.b1', '36.b1', '36.r1'], 'core': '12.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [7200, 3035, 5647, 6725], 'generators': [774, 432, 1020, 72, 648], 'label': '1296.1067.12.f1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1', 'normal_contained_in': ['4.d1', '6.d1', '6.e1', '6.f1'], 'normal_contains': ['24.b1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.f1', 'projective_image': '216.110', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613692
    {'ambient': '1296.1067', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '216.a1', 'complements': ['648.c1', '648.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '6.c1', '6.d1', '6.i1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6339, 1639, 4652, 7924], 'generators': [18, 936, 648, 108, 432, 2, 1020], 'label': '1296.1067.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '6.c1', '6.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '216.110', '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': '216.110'}
  • id: 70613693
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.g1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '108.b1', 'complements': ['108.v1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.b1', '6.e1'], 'contains': ['24.b1', '36.q1', '36.s1'], 'core': '12.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [3859, 8633, 4798, 3196], 'generators': [117, 432, 648, 1020, 72], 'label': '1296.1067.12.g1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.g1', 'normal_contained_in': ['4.e1', '6.b1', '6.e1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.g1', 'projective_image': '216.110', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613694
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.28', 'aut_weyl_index': 48, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.i1'], 'contains': ['24.d1', '24.g1', '36.a1', '36.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3508, -1, 1197, -1], 'generators': [18, 432, 648, 1022, 72], 'label': '1296.1067.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '12.h1', 'projective_image': '216.110', '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': '54.10'}
  • id: 70613695
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.48', 'aut_weyl_index': 72, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.g1', '6.j1'], 'contains': ['24.a1', '24.h1', '36.g1', '36.h1', '36.j1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4217, -1, 3401, -1], 'generators': [3, 504, 648, 2, 432], 'label': '1296.1067.12.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.i1', 'projective_image': '216.110', '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': '6.1'}
  • id: 70613696
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.48', 'aut_weyl_index': 72, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.g1', '6.h1', '6.k1'], 'contains': ['24.a1', '24.i1', '36.k1', '36.l1', '36.n1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4744, -1, 3868, -1], 'generators': [153, 72, 648, 2, 432], 'label': '1296.1067.12.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.j1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613697
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.48', 'aut_weyl_index': 72, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.h1', '6.j1'], 'contains': ['24.a1', '36.p1', '36.q1', '36.v1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5349, -1, 5193, -1], 'generators': [837, 72, 2, 432, 648], 'label': '1296.1067.12.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.k1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613698
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.28', 'aut_weyl_index': 48, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.i1'], 'contains': ['24.d1', '36.b1', '36.t1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6296, -1, 2722, -1], 'generators': [774, 432, 1022, 72, 648], 'label': '1296.1067.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '12.l1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '54.10'}
  • id: 70613699
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '6.g1'], 'contains': ['24.e1', '24.h1', '24.i1', '36.w1', '36.x1', '36.z1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1701, -1, 1449, -1], 'generators': [3, 504, 18, 2, 432], 'label': '1296.1067.12.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '12.m1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613700
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '6.a1'], 'contains': ['24.c1', '24.f1', '24.j1', '36.x1', '36.y1'], 'core': '24.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [1254, -1, 959, -1], 'generators': [3, 432, 18, 588, 504], 'label': '1296.1067.12.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.n1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613701
    {'ambient': '1296.1067', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '324.117', 'aut_weyl_index': 16, 'centralizer': '54.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['48.a1', '48.b1', '48.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [651, 8521, 297, 4022], 'generators': [2, 1020], 'label': '1296.1067.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['48.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '432.360', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613702
    {'ambient': '1296.1067', 'aut_centralizer_order': 54, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '24.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.d1', '6.i1', '9.b1'], 'contains': ['36.a1', '36.b1', '54.a1', '54.k1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7850, 1408, 6489, 9073], 'generators': [18, 648, 108, 72, 432], 'label': '1296.1067.18.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1', 'normal_contained_in': ['6.c1', '6.d1'], 'normal_contains': ['36.a1', '36.b1', '54.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613703
    {'ambient': '1296.1067', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.3033', 'aut_weyl_index': 4, 'centralizer': '108.b1', 'complements': ['648.b1', '648.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.e1', '6.e1', '6.j1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5168, 7985, 4941, 2246], 'generators': [3, 936, 588, 774, 432, 2, 648], 'label': '1296.1067.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1', '4.e1', '6.e1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613704
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.15', 'aut_weyl_index': 216, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.c1', '36.g1', '36.k1', '36.w1', '54.b1', '54.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5388, -1, 4367, -1], 'generators': [3, 432, 18, 648, 2], 'label': '1296.1067.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613705
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.g1', '9.b1'], 'contains': ['36.a1', '36.h1', '36.l1', '36.x1', '54.b1', '54.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3636, -1, 3135, -1], 'generators': [3, 504, 18, 648, 432], 'label': '1296.1067.18.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.c1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613706
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.c1'], 'contains': ['36.d1', '36.i1', '36.m1', '36.y1', '54.b1', '54.e1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2869, -1, 4134, -1], 'generators': [3, 588, 18, 648, 432], 'label': '1296.1067.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.d1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613707
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.g1', '9.d1'], 'contains': ['36.f1', '36.j1', '36.n1', '36.z1', '54.c1', '54.d1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6935, -1, 4600, -1], 'generators': [3, 504, 18, 648, 2], 'label': '1296.1067.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.e1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613708
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.15', 'aut_weyl_index': 216, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.c1', '36.k1', '36.p1', '54.f1', '54.g1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6338, -1, 5870, -1], 'generators': [903, 648, 18, 2, 432], 'label': '1296.1067.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.f1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613709
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.h1', '9.b1'], 'contains': ['36.a1', '36.l1', '36.q1', '54.f1', '54.h1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4980, -1, 4968, -1], 'generators': [903, 504, 18, 432, 648], 'label': '1296.1067.18.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.g1', 'projective_image': '216.110', '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': '24.14'}
  • id: 70613710
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '9.c1'], 'contains': ['36.d1', '36.m1', '36.s1', '54.f1', '54.i1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3979, -1, 5419, -1], 'generators': [903, 1020, 18, 432, 648], 'label': '1296.1067.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.h1', 'projective_image': '216.110', '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': '24.14'}
  • id: 70613711
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.h1', '9.d1'], 'contains': ['36.f1', '36.n1', '36.v1', '54.g1', '54.h1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7590, -1, 6077, -1], 'generators': [903, 504, 18, 2, 648], 'label': '1296.1067.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.i1', 'projective_image': '648.328', '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': '24.14'}
  • id: 70613712
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.45', 'aut_weyl_index': 108, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.c1', '36.o1', '54.a1', '54.j1'], 'core': '54.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8687, -1, 8125, -1], 'generators': [18, 648, 108, 2, 432], 'label': '1296.1067.18.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.j1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613713
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '72.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.c1'], 'contains': ['36.d1', '36.r1', '54.a1', '54.l1'], 'core': '54.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6132, -1, 7717, -1], 'generators': [18, 648, 108, 1020, 432], 'label': '1296.1067.18.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.k1', 'projective_image': '216.110', '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': '24.14'}
  • id: 70613714
    {'ambient': '1296.1067', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '216.a1', 'complements': ['648.b1', '648.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '6.f1', '6.k1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [6699, 3771, 5202, 6534], 'generators': [903, 936, 1020, 774, 432, 2, 648], 'label': '1296.1067.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '6.f1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '216.110'}
  • id: 70613716
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 162, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.c1', '9.d1'], 'contains': ['36.f1', '36.u1', '54.j1', '54.k1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9419, -1, 8903, -1], 'generators': [18, 648, 108, 2, 504], 'label': '1296.1067.18.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.m1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 70613717
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 216, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.g1', '36.o1', '36.p1', '54.m1', '54.n1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8108, -1, 7513, -1], 'generators': [3, 648, 126, 2, 432], 'label': '1296.1067.18.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.n1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 70613718
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.j1', '9.b1'], 'contains': ['36.b1', '36.h1', '36.q1', '54.m1', '54.o1'], 'core': '36.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6644, -1, 6286, -1], 'generators': [3, 504, 774, 432, 648], 'label': '1296.1067.18.o1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.o1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613719
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.c1'], 'contains': ['36.i1', '36.r1', '36.s1', '54.m1', '54.p1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4766, -1, 6692, -1], 'generators': [3, 588, 774, 432, 648], 'label': '1296.1067.18.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.p1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613720
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 108, 'centralizer': '36.o1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.j1', '9.d1'], 'contains': ['36.j1', '36.u1', '36.v1', '54.n1', '54.o1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8429, -1, 8700, -1], 'generators': [3, 504, 774, 2, 648], 'label': '1296.1067.18.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.q1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613721
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.45', 'aut_weyl_index': 108, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.a1'], 'contains': ['36.k1', '36.o1', '54.q1', '54.r1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8918, -1, 8325, -1], 'generators': [903, 648, 126, 2, 432], 'label': '1296.1067.18.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.r1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 70613722
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.k1', '9.b1'], 'contains': ['36.b1', '36.l1', '54.q1', '54.s1'], 'core': '36.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7326, -1, 6898, -1], 'generators': [903, 504, 774, 432, 648], 'label': '1296.1067.18.s1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.s1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613723
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '9.c1'], 'contains': ['36.m1', '36.r1', '54.q1', '54.t1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5825, -1, 7921, -1], 'generators': [903, 1020, 774, 432, 648], 'label': '1296.1067.18.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.t1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613724
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.k1', '9.d1'], 'contains': ['36.n1', '36.u1', '54.r1', '54.s1'], 'core': '324.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9628, -1, 9107, -1], 'generators': [903, 504, 774, 2, 648], 'label': '1296.1067.18.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.u1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613725
    {'ambient': '1296.1067', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.30804', 'aut_weyl_index': 3, 'centralizer': '216.a1', 'complements': ['432.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.d1', '6.e1', '6.f1', '9.b1', '9.c1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5450, 4655, 5562, 5458], 'generators': [3, 504, 588, 18, 432, 108, 648], 'label': '1296.1067.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.b1', '6.d1', '6.e1', '6.f1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '216.110', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '216.110'}
  • id: 70613726
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.e1', '12.i1', '12.j1', '12.k1'], 'contains': ['48.a1', '72.a1', '72.b1', '72.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4238, 3376, 3462, 6975], 'generators': [648, 2, 72, 432], 'label': '1296.1067.24.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.e1'], 'normal_contains': ['48.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '216.110', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613727
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '24.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '54.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.c1', '12.d1', '12.f1', '12.g1'], 'contains': ['48.b1', '72.a1', '72.c1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2361, 6788, 2680, 4849], 'generators': [648, 1020, 72, 432], 'label': '1296.1067.24.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.b1', '12.c1', '12.d1', '12.f1', '12.g1'], 'normal_contains': ['48.b1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '216.110', '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': '54.5'}
  • id: 70613728
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '54.a1', 'complements': ['54.j1', '54.g1', '54.r1'], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.c1', '12.n1'], 'contains': ['48.b1', '72.l1', '72.m1'], 'core': '24.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [361, 8162, 466, 2541], 'generators': [3, 588, 504, 432], 'label': '1296.1067.24.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.b1', '12.c1'], 'normal_contains': ['48.b1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '432.360', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613729
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 96, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.h1', '12.l1'], 'contains': ['48.c1', '72.a1', '72.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3045, -1, 1202, -1], 'generators': [648, 1022, 72, 432], 'label': '1296.1067.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.d1', 'projective_image': '216.110', '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': '27.3'}
  • id: 70613730
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.a1', '12.m1'], 'contains': ['48.a1', '72.f1', '72.g1', '72.j1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1248, -1, 1813, -1], 'generators': [18, 2, 72, 432], 'label': '1296.1067.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.e1', 'projective_image': '432.360', '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': '6.1'}
  • id: 70613731
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.b1', '12.n1'], 'contains': ['48.b1', '72.g1', '72.h1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [114, -1, 660, -1], 'generators': [18, 1020, 72, 432], 'label': '1296.1067.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.f1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613732
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.8', 'aut_weyl_index': 96, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.h1'], 'contains': ['48.c1', '72.g1', '72.i1'], 'core': '144.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [737, -1, 94, -1], 'generators': [18, 1022, 72, 432], 'label': '1296.1067.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.g1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 70613733
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.i1', '12.m1'], 'contains': ['48.a1', '72.k1', '72.l1', '72.n1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1767, -1, 1614, -1], 'generators': [3, 2, 432, 504], 'label': '1296.1067.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.h1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613734
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.12', 'aut_weyl_index': 144, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.j1', '12.m1'], 'contains': ['48.a1', '72.o1', '72.p1', '72.r1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1565, -1, 2012, -1], 'generators': [153, 2, 432, 72], 'label': '1296.1067.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '24.i1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 70613735
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.d1', '12.n1'], 'contains': ['48.b1', '72.p1', '72.q1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [507, -1, 854, -1], 'generators': [81, 588, 72, 432], 'label': '1296.1067.24.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.j1', 'projective_image': '432.360', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 70613736
    {'ambient': '1296.1067', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 9, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.c1', '6.g1', '6.h1', '6.j1', '6.k1', '9.a1', '9.b1', '9.d1'], 'core': '6.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7648, -1, 6363, -1], 'generators': [3, 648, 432, 18, 504, 108, 2], 'label': '1296.1067.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '216.110', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613737
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 162, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1', '9.c1'], 'contains': ['54.a1', '54.b1', '54.f1', '54.m1', '54.q1', '81.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7309, -1, 7323, -1], 'generators': [3, 648, 18, 108, 432], 'label': '1296.1067.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.a1', 'projective_image': '216.110', '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': '4.2'}
  • id: 70613738
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.46', 'aut_weyl_index': 162, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.a1', '9.d1'], 'contains': ['54.c1', '54.g1', '54.j1', '54.n1', '54.r1', '81.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9738, -1, 9299, -1], 'generators': [3, 648, 18, 108, 2], 'label': '1296.1067.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.b1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613739
    {'ambient': '1296.1067', 'aut_centralizer_order': 18, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.d1'], 'contains': ['54.d1', '54.h1', '54.k1', '54.o1', '54.s1', '81.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8672, -1, 8512, -1], 'generators': [3, 504, 18, 108, 648], 'label': '1296.1067.27.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.c1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613740
    {'ambient': '1296.1067', 'aut_centralizer_order': 6, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 54, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['54.e1', '54.i1', '54.l1', '54.p1', '54.t1', '81.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5206, -1, 9473, -1], 'generators': [3, 588, 18, 108, 648], 'label': '1296.1067.27.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '27.d1', 'projective_image': '648.328', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 70613741
    {'ambient': '1296.1067', 'aut_centralizer_order': 108, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '12.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.b1', '12.h1', '18.a1', '18.c1', '18.g1'], 'contains': ['72.a1', '72.g1', '108.a1', '108.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3463, 2799, 3139, 7520], 'generators': [18, 648, 72, 432], 'label': '1296.1067.36.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1', '18.a1'], 'normal_contains': ['72.a1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '216.110', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613742
    {'ambient': '1296.1067', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '12.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.f1', '12.l1', '18.a1', '18.o1', '18.s1'], 'contains': ['72.a1', '108.b1', '108.q1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7948, 2074, 6602, 8079], 'generators': [774, 72, 432, 648], 'label': '1296.1067.36.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1', 'normal_contained_in': ['12.e1', '12.f1', '18.a1'], 'normal_contains': ['72.a1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '216.110', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 70613743
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '18.b1', '18.f1', '18.j1'], 'contains': ['72.b1', '72.f1', '108.a1', '108.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5794, -1, 4364, -1], 'generators': [18, 648, 2, 432], 'label': '1296.1067.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.c1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613744
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.d1', '18.h1', '18.k1'], 'contains': ['72.c1', '72.h1', '108.a1', '108.e1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2615, -1, 4088, -1], 'generators': [18, 648, 1020, 432], 'label': '1296.1067.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.d1', 'projective_image': '216.110', '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: 70613745
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.l1'], 'contains': ['72.d1', '72.i1', '108.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3672, -1, 1411, -1], 'generators': [18, 648, 1022, 432], 'label': '1296.1067.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '36.e1', 'projective_image': '216.110', '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': '6.2'}
  • id: 70613746
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.a1', '18.e1', '18.i1', '18.m1'], 'contains': ['72.e1', '72.j1', '108.c1', '108.d1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7217, -1, 4943, -1], 'generators': [18, 648, 2, 504], 'label': '1296.1067.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.f1', 'projective_image': '648.328', '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': '4.2'}
  • id: 70613747
    {'ambient': '1296.1067', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '648.603', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['324.f1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.c1', '12.a1', '12.b1', '12.h1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2834, 3047, 1908, 6375], 'generators': [18, 432, 936, 648, 2, 1020], 'label': '1296.1067.4.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', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '216.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 70613748
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.b1', '18.n1'], 'contains': ['72.b1', '72.k1', '108.f1', '108.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5179, -1, 3984, -1], 'generators': [3, 648, 2, 432], 'label': '1296.1067.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.g1', 'projective_image': '216.110', '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': '1.1'}
  • id: 70613749
    {'ambient': '1296.1067', 'aut_centralizer_order': 72, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.i1', '18.c1', '18.o1'], 'contains': ['72.a1', '72.l1', '108.f1', '108.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3143, -1, 3001, -1], 'generators': [3, 648, 432, 504], 'label': '1296.1067.36.h1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.h1', 'projective_image': '216.110', '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': '6.1'}
  • id: 70613750
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.d1', '18.p1'], 'contains': ['72.c1', '72.m1', '108.f1', '108.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1939, -1, 3647, -1], 'generators': [3, 648, 432, 588], 'label': '1296.1067.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.i1', 'projective_image': '216.110', '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': '6.1'}
  • id: 70613751
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.i1', '18.e1', '18.q1'], 'contains': ['72.e1', '72.n1', '108.g1', '108.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6631, -1, 4804, -1], 'generators': [3, 648, 2, 504], 'label': '1296.1067.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.j1', 'projective_image': '648.328', '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': '6.1'}
  • id: 70613752
    {'ambient': '1296.1067', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '18.b1', '18.f1', '18.r1'], 'contains': ['72.b1', '72.o1', '108.j1', '108.k1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5637, -1, 4468, -1], 'generators': [153, 648, 74, 432], 'label': '1296.1067.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.k1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613753
    {'ambient': '1296.1067', 'aut_centralizer_order': 36, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.j1', '18.c1', '18.g1', '18.s1'], 'contains': ['72.a1', '72.p1', '108.j1', '108.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4377, -1, 3277, -1], 'generators': [81, 648, 432, 72], 'label': '1296.1067.36.l1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.l1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613754
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.d1', '18.h1', '18.t1'], 'contains': ['72.c1', '72.q1', '108.j1', '108.m1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2759, -1, 4226, -1], 'generators': [81, 648, 432, 588], 'label': '1296.1067.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.m1', 'projective_image': '216.110', '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': '12.4'}
  • id: 70613755
    {'ambient': '1296.1067', 'aut_centralizer_order': 12, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '18.e1', '18.i1', '18.u1'], 'contains': ['72.e1', '72.r1', '108.k1', '108.l1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7507, -1, 5081, -1], 'generators': [153, 648, 2, 72], 'label': '1296.1067.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.n1', 'projective_image': '648.328', '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': '12.4'}
  • id: 70613756
    {'ambient': '1296.1067', 'aut_centralizer_order': 144, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '6.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.j1', '18.n1', '18.r1'], 'contains': ['72.b1', '108.b1', '108.o1'], 'core': '108.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9068, -1, 7569, -1], 'generators': [126, 2, 432, 648], 'label': '1296.1067.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.o1', 'projective_image': '216.110', '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': '2.1'}
  • id: 70613757
    {'ambient': '1296.1067', 'aut_centralizer_order': 48, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 432, 'centralizer': '18.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.f1', '18.n1'], 'contains': ['72.b1', '108.n1', '108.p1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6387, -1, 6065, -1], 'generators': [837, 74, 432, 648], 'label': '1296.1067.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.p1', 'projective_image': '216.110', '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': '2.1'}