Abstract group data - 648.114

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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': '36.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 36, 'aut_gen_orders': [6, 6, 36], 'aut_gens': [[1, 18], [337, 342], [1, 522], [523, 18]], 'aut_group': '1296.2571', 'aut_hash': 2571, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1296, 'aut_permdeg': 45, 'aut_perms': [50414276067165188259120972929234288834366066527295366864, 1273572335019782267809570810811924235625103543864327403, 33850521665094253078941232813982900585093702902666256716], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 1, 2], [3, 2, 1, 3], [4, 2, 1, 1], [4, 18, 2, 1], [6, 1, 1, 2], [6, 2, 1, 3], [9, 3, 3, 2], [9, 6, 1, 3], [9, 6, 3, 2], [12, 2, 1, 2], [12, 2, 2, 3], [12, 18, 2, 2], [18, 3, 3, 2], [18, 6, 1, 3], [18, 6, 3, 2], [36, 6, 2, 3], [36, 6, 3, 2], [36, 6, 6, 2], [36, 18, 6, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{36}:C_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '108.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 108, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{18}:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 2, 3], [4, 2, 1], [4, 18, 2], [6, 1, 2], [6, 2, 3], [9, 3, 6], [9, 6, 9], [12, 2, 8], [12, 18, 4], [18, 3, 6], [18, 6, 9], [36, 6, 24], [36, 18, 12]], 'center_label': '6.2', 'center_order': 6, 'central_product': False, 'central_quotient': '108.26', 'commutator_count': 1, 'commutator_label': '18.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 114, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [4, 18, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [9, 3, 6, 1], [9, 6, 1, 1], [9, 6, 2, 1], [9, 6, 6, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 18, 2, 2], [18, 3, 6, 1], [18, 6, 1, 1], [18, 6, 2, 1], [18, 6, 6, 1], [36, 6, 2, 1], [36, 6, 4, 1], [36, 6, 6, 1], [36, 6, 12, 1], [36, 18, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 4]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '36.12', 'hash': 114, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 18], 'inner_gens': [[1, 198], [469, 18]], 'inner_hash': 26, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': True, 'inner_tex': 'C_{18}:C_6', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 36], [2, 45], [6, 12]], 'label': '648.114', 'linC_count': 4, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 10, 'linQ_dim': 16, 'linQ_dim_count': 20, 'linR_count': 18, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C36.C18', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 93, 'number_divisions': 30, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 66, 'number_subgroups': 186, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 38], [6, 8], [9, 72], [12, 88], [18, 72], [36, 360]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [486, 0], 'outer_gens': [[163, 18], [331, 522]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [720, 28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 7], [4, 4], [6, 6], [8, 1], [12, 6], [24, 2]], 'representations': {'PC': {'code': 94462471996895124359500940797119557524758451, 'gens': [1, 4], 'pres': [7, -2, -3, -3, -2, -2, -3, -3, 14, 50, 1150, 5547, 3286, 80, 13864, 8201, 102, 6053, 6060, 166, 21174]}, 'Perm': {'d': 26, 'gens': [23906015495338, 45968909011200, 16805042056738846310416147, 68436399225600, 32964846860378393985024000, 63388, 109966]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 18], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{36}.C_{18}', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 139739306
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 114, 'group_order': 648, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 139739317
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 114, 'group_order': 648, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 324, 'size': 1}
  • id: 139739328
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 114, 'group_order': 648, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 330, 'size': 1}
  • id: 139739339
    {'aut_label': '3A-1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 114, 'group_order': 648, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 12, 'size': 1}
  • id: 139739350
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 114, 'group_order': 648, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 216, 'size': 2}
  • id: 139739361
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 114, 'group_order': 648, 'label': '3C1', 'order': 3, 'powers': [7, 1], 'representative': 546, 'size': 2}
  • id: 139739372
    {'aut_label': '3C-1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 114, 'group_order': 648, 'label': '3C-1', 'order': 3, 'powers': [6, 1], 'representative': 444, 'size': 2}
  • id: 139739383
    {'aut_label': '4A', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 114, 'group_order': 648, 'label': '4A', 'order': 4, 'powers': [2, 8], 'representative': 162, 'size': 2}
  • id: 139739394
    {'aut_label': '4B', 'centralizer': '18.f1.a1', 'counter': 9, 'group_counter': 114, 'group_order': 648, 'label': '4B', 'order': 4, 'powers': [2, 9], 'representative': 9, 'size': 18}
  • id: 139739307
    {'aut_label': '4B', 'centralizer': '18.f1.b1', 'counter': 10, 'group_counter': 114, 'group_order': 648, 'label': '4C', 'order': 4, 'powers': [2, 10], 'representative': 459, 'size': 18}
  • id: 139739308
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 114, 'group_order': 648, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 336, 'size': 1}
  • id: 139739309
    {'aut_label': '6A-1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 114, 'group_order': 648, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 6, 'size': 1}
  • id: 139739310
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 114, 'group_order': 648, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 108, 'size': 2}
  • id: 139739311
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 114, 'group_order': 648, 'label': '6C1', 'order': 6, 'powers': [6, 2], 'representative': 120, 'size': 2}
  • id: 139739312
    {'aut_label': '6C-1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 114, 'group_order': 648, 'label': '6C-1', 'order': 6, 'powers': [7, 2], 'representative': 222, 'size': 2}
  • id: 139739313
    {'aut_label': '9A1', 'centralizer': '3.b1.a1', 'counter': 16, 'group_counter': 114, 'group_order': 648, 'label': '9A1', 'order': 9, 'powers': [18, 3], 'representative': 224, 'size': 3}
  • id: 139739314
    {'aut_label': '9A-1', 'centralizer': '3.b1.a1', 'counter': 17, 'group_counter': 114, 'group_order': 648, 'label': '9A-1', 'order': 9, 'powers': [19, 4], 'representative': 118, 'size': 3}
  • id: 139739315
    {'aut_label': '9A-1', 'centralizer': '3.b1.a1', 'counter': 18, 'group_counter': 114, 'group_order': 648, 'label': '9A2', 'order': 9, 'powers': [20, 4], 'representative': 448, 'size': 3}
  • id: 139739316
    {'aut_label': '9A1', 'centralizer': '3.b1.a1', 'counter': 19, 'group_counter': 114, 'group_order': 648, 'label': '9A-2', 'order': 9, 'powers': [21, 3], 'representative': 542, 'size': 3}
  • id: 139739318
    {'aut_label': '9A1', 'centralizer': '3.b1.a1', 'counter': 20, 'group_counter': 114, 'group_order': 648, 'label': '9A4', 'order': 9, 'powers': [17, 3], 'representative': 554, 'size': 3}
  • id: 139739319
    {'aut_label': '9A-1', 'centralizer': '3.b1.a1', 'counter': 21, 'group_counter': 114, 'group_order': 648, 'label': '9A-4', 'order': 9, 'powers': [16, 4], 'representative': 436, 'size': 3}
  • id: 139739320
    {'aut_label': '9B', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 114, 'group_order': 648, 'label': '9B', 'order': 9, 'powers': [22, 5], 'representative': 72, 'size': 6}
  • id: 139739321
    {'aut_label': '9C1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 114, 'group_order': 648, 'label': '9C1', 'order': 9, 'powers': [24, 5], 'representative': 402, 'size': 6}
  • id: 139739322
    {'aut_label': '9C-1', 'centralizer': '6.b1.a1', 'counter': 24, 'group_counter': 114, 'group_order': 648, 'label': '9C-1', 'order': 9, 'powers': [23, 5], 'representative': 588, 'size': 6}
  • id: 139739323
    {'aut_label': '9D1', 'centralizer': '6.d1.a1', 'counter': 25, 'group_counter': 114, 'group_order': 648, 'label': '9D1', 'order': 9, 'powers': [27, 6], 'representative': 80, 'size': 6}
  • id: 139739324
    {'aut_label': '9D-1', 'centralizer': '6.d1.a1', 'counter': 26, 'group_counter': 114, 'group_order': 648, 'label': '9D-1', 'order': 9, 'powers': [28, 7], 'representative': 478, 'size': 6}
  • id: 139739325
    {'aut_label': '9D-1', 'centralizer': '6.d1.a1', 'counter': 27, 'group_counter': 114, 'group_order': 648, 'label': '9D2', 'order': 9, 'powers': [29, 7], 'representative': 376, 'size': 6}
  • id: 139739326
    {'aut_label': '9D1', 'centralizer': '6.d1.a1', 'counter': 28, 'group_counter': 114, 'group_order': 648, 'label': '9D-2', 'order': 9, 'powers': [30, 6], 'representative': 182, 'size': 6}
  • id: 139739327
    {'aut_label': '9D1', 'centralizer': '6.d1.a1', 'counter': 29, 'group_counter': 114, 'group_order': 648, 'label': '9D4', 'order': 9, 'powers': [26, 6], 'representative': 626, 'size': 6}
  • id: 139739329
    {'aut_label': '9D-1', 'centralizer': '6.d1.a1', 'counter': 30, 'group_counter': 114, 'group_order': 648, 'label': '9D-4', 'order': 9, 'powers': [25, 7], 'representative': 580, 'size': 6}
  • id: 139739330
    {'aut_label': '12A1', 'centralizer': '2.a1.a1', 'counter': 31, 'group_counter': 114, 'group_order': 648, 'label': '12A1', 'order': 12, 'powers': [13, 8], 'representative': 54, 'size': 2}
  • id: 139739331
    {'aut_label': '12A1', 'centralizer': '2.a1.a1', 'counter': 32, 'group_counter': 114, 'group_order': 648, 'label': '12A5', 'order': 12, 'powers': [13, 8], 'representative': 270, 'size': 2}
  • id: 139739332
    {'aut_label': '12B1', 'centralizer': '2.a1.a1', 'counter': 33, 'group_counter': 114, 'group_order': 648, 'label': '12B1', 'order': 12, 'powers': [11, 8], 'representative': 168, 'size': 2}
  • id: 139739333
    {'aut_label': '12B-1', 'centralizer': '2.a1.a1', 'counter': 34, 'group_counter': 114, 'group_order': 648, 'label': '12B-1', 'order': 12, 'powers': [12, 8], 'representative': 174, 'size': 2}
  • id: 139739334
    {'aut_label': '12C1', 'centralizer': '2.a1.a1', 'counter': 35, 'group_counter': 114, 'group_order': 648, 'label': '12C1', 'order': 12, 'powers': [14, 8], 'representative': 60, 'size': 2}
  • id: 139739335
    {'aut_label': '12C-1', 'centralizer': '2.a1.a1', 'counter': 36, 'group_counter': 114, 'group_order': 648, 'label': '12C-1', 'order': 12, 'powers': [15, 8], 'representative': 282, 'size': 2}
  • id: 139739336
    {'aut_label': '12C-1', 'centralizer': '2.a1.a1', 'counter': 37, 'group_counter': 114, 'group_order': 648, 'label': '12C5', 'order': 12, 'powers': [15, 8], 'representative': 606, 'size': 2}
  • id: 139739337
    {'aut_label': '12C1', 'centralizer': '2.a1.a1', 'counter': 38, 'group_counter': 114, 'group_order': 648, 'label': '12C-5', 'order': 12, 'powers': [14, 8], 'representative': 384, 'size': 2}
  • id: 139739338
    {'aut_label': '12D1', 'centralizer': '18.f1.a1', 'counter': 39, 'group_counter': 114, 'group_order': 648, 'label': '12D1', 'order': 12, 'powers': [12, 9], 'representative': 3, 'size': 18}
  • id: 139739340
    {'aut_label': '12D-1', 'centralizer': '18.f1.a1', 'counter': 40, 'group_counter': 114, 'group_order': 648, 'label': '12D-1', 'order': 12, 'powers': [11, 9], 'representative': 339, 'size': 18}
  • id: 139739341
    {'aut_label': '12D1', 'centralizer': '18.f1.b1', 'counter': 41, 'group_counter': 114, 'group_order': 648, 'label': '12E1', 'order': 12, 'powers': [12, 10], 'representative': 453, 'size': 18}
  • id: 139739342
    {'aut_label': '12D-1', 'centralizer': '18.f1.b1', 'counter': 42, 'group_counter': 114, 'group_order': 648, 'label': '12E-1', 'order': 12, 'powers': [11, 10], 'representative': 141, 'size': 18}
  • id: 139739343
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 43, 'group_counter': 114, 'group_order': 648, 'label': '18A1', 'order': 18, 'powers': [16, 11], 'representative': 112, 'size': 3}
  • id: 139739344
    {'aut_label': '18A-1', 'centralizer': '3.b1.a1', 'counter': 44, 'group_counter': 114, 'group_order': 648, 'label': '18A-1', 'order': 18, 'powers': [17, 12], 'representative': 230, 'size': 3}
  • id: 139739345
    {'aut_label': '18A-1', 'centralizer': '3.b1.a1', 'counter': 45, 'group_counter': 114, 'group_order': 648, 'label': '18A5', 'order': 18, 'powers': [21, 12], 'representative': 218, 'size': 3}
  • id: 139739346
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 46, 'group_counter': 114, 'group_order': 648, 'label': '18A-5', 'order': 18, 'powers': [20, 11], 'representative': 124, 'size': 3}
  • id: 139739347
    {'aut_label': '18A1', 'centralizer': '3.b1.a1', 'counter': 47, 'group_counter': 114, 'group_order': 648, 'label': '18A7', 'order': 18, 'powers': [19, 11], 'representative': 442, 'size': 3}
  • id: 139739348
    {'aut_label': '18A-1', 'centralizer': '3.b1.a1', 'counter': 48, 'group_counter': 114, 'group_order': 648, 'label': '18A-7', 'order': 18, 'powers': [18, 12], 'representative': 548, 'size': 3}
  • id: 139739349
    {'aut_label': '18B', 'centralizer': '6.b1.a1', 'counter': 49, 'group_counter': 114, 'group_order': 648, 'label': '18B', 'order': 18, 'powers': [22, 13], 'representative': 36, 'size': 6}
  • id: 139739351
    {'aut_label': '18C1', 'centralizer': '6.b1.a1', 'counter': 50, 'group_counter': 114, 'group_order': 648, 'label': '18C1', 'order': 18, 'powers': [23, 13], 'representative': 48, 'size': 6}
  • id: 139739352
    {'aut_label': '18C-1', 'centralizer': '6.b1.a1', 'counter': 51, 'group_counter': 114, 'group_order': 648, 'label': '18C-1', 'order': 18, 'powers': [24, 13], 'representative': 294, 'size': 6}
  • id: 139739353
    {'aut_label': '18D1', 'centralizer': '6.d1.a1', 'counter': 52, 'group_counter': 114, 'group_order': 648, 'label': '18D1', 'order': 18, 'powers': [25, 14], 'representative': 256, 'size': 6}
  • id: 139739354
    {'aut_label': '18D-1', 'centralizer': '6.d1.a1', 'counter': 53, 'group_counter': 114, 'group_order': 648, 'label': '18D-1', 'order': 18, 'powers': [26, 15], 'representative': 302, 'size': 6}
  • id: 139739355
    {'aut_label': '18D-1', 'centralizer': '6.d1.a1', 'counter': 54, 'group_counter': 114, 'group_order': 648, 'label': '18D5', 'order': 18, 'powers': [30, 15], 'representative': 506, 'size': 6}
  • id: 139739356
    {'aut_label': '18D1', 'centralizer': '6.d1.a1', 'counter': 55, 'group_counter': 114, 'group_order': 648, 'label': '18D-5', 'order': 18, 'powers': [29, 14], 'representative': 52, 'size': 6}
  • id: 139739357
    {'aut_label': '18D1', 'centralizer': '6.d1.a1', 'counter': 56, 'group_counter': 114, 'group_order': 648, 'label': '18D7', 'order': 18, 'powers': [28, 14], 'representative': 154, 'size': 6}
  • id: 139739358
    {'aut_label': '18D-1', 'centralizer': '6.d1.a1', 'counter': 57, 'group_counter': 114, 'group_order': 648, 'label': '18D-7', 'order': 18, 'powers': [27, 15], 'representative': 404, 'size': 6}
  • id: 139739359
    {'aut_label': '36A1', 'centralizer': '6.b1.a1', 'counter': 58, 'group_counter': 114, 'group_order': 648, 'label': '36A1', 'order': 36, 'powers': [49, 31], 'representative': 18, 'size': 6}
  • id: 139739360
    {'aut_label': '36A1', 'centralizer': '6.b1.a1', 'counter': 59, 'group_counter': 114, 'group_order': 648, 'label': '36A5', 'order': 36, 'powers': [49, 32], 'representative': 90, 'size': 6}
  • id: 139739362
    {'aut_label': '36B1', 'centralizer': '6.b1.a1', 'counter': 60, 'group_counter': 114, 'group_order': 648, 'label': '36B1', 'order': 36, 'powers': [50, 32], 'representative': 24, 'size': 6}
  • id: 139739363
    {'aut_label': '36B-1', 'centralizer': '6.b1.a1', 'counter': 61, 'group_counter': 114, 'group_order': 648, 'label': '36B-1', 'order': 36, 'powers': [51, 32], 'representative': 102, 'size': 6}
  • id: 139739364
    {'aut_label': '36B-1', 'centralizer': '6.b1.a1', 'counter': 62, 'group_counter': 114, 'group_order': 648, 'label': '36B5', 'order': 36, 'powers': [51, 31], 'representative': 30, 'size': 6}
  • id: 139739365
    {'aut_label': '36B1', 'centralizer': '6.b1.a1', 'counter': 63, 'group_counter': 114, 'group_order': 648, 'label': '36B-5', 'order': 36, 'powers': [50, 31], 'representative': 96, 'size': 6}
  • id: 139739366
    {'aut_label': '36C1', 'centralizer': '6.a1.a1', 'counter': 64, 'group_counter': 114, 'group_order': 648, 'label': '36C1', 'order': 36, 'powers': [43, 33], 'representative': 56, 'size': 6}
  • id: 139739367
    {'aut_label': '36C-1', 'centralizer': '6.a1.a1', 'counter': 65, 'group_counter': 114, 'group_order': 648, 'label': '36C-1', 'order': 36, 'powers': [44, 34], 'representative': 70, 'size': 6}
  • id: 139739368
    {'aut_label': '36C-1', 'centralizer': '6.a1.a1', 'counter': 66, 'group_counter': 114, 'group_order': 648, 'label': '36C5', 'order': 36, 'powers': [45, 34], 'representative': 64, 'size': 6}
  • id: 139739369
    {'aut_label': '36C1', 'centralizer': '6.a1.a1', 'counter': 67, 'group_counter': 114, 'group_order': 648, 'label': '36C-5', 'order': 36, 'powers': [46, 33], 'representative': 62, 'size': 6}
  • id: 139739370
    {'aut_label': '36C1', 'centralizer': '6.a1.a1', 'counter': 68, 'group_counter': 114, 'group_order': 648, 'label': '36C7', 'order': 36, 'powers': [47, 33], 'representative': 68, 'size': 6}
  • id: 139739371
    {'aut_label': '36C-1', 'centralizer': '6.a1.a1', 'counter': 69, 'group_counter': 114, 'group_order': 648, 'label': '36C-7', 'order': 36, 'powers': [48, 34], 'representative': 58, 'size': 6}
  • id: 139739373
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 70, 'group_counter': 114, 'group_order': 648, 'label': '36D1', 'order': 36, 'powers': [52, 35], 'representative': 20, 'size': 6}
  • id: 139739374
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 71, 'group_counter': 114, 'group_order': 648, 'label': '36D-1', 'order': 36, 'powers': [53, 36], 'representative': 106, 'size': 6}
  • id: 139739375
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 72, 'group_counter': 114, 'group_order': 648, 'label': '36D5', 'order': 36, 'powers': [54, 37], 'representative': 100, 'size': 6}
  • id: 139739376
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 73, 'group_counter': 114, 'group_order': 648, 'label': '36D-5', 'order': 36, 'powers': [55, 38], 'representative': 26, 'size': 6}
  • id: 139739377
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 74, 'group_counter': 114, 'group_order': 648, 'label': '36D7', 'order': 36, 'powers': [56, 38], 'representative': 104, 'size': 6}
  • id: 139739378
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 75, 'group_counter': 114, 'group_order': 648, 'label': '36D-7', 'order': 36, 'powers': [57, 37], 'representative': 22, 'size': 6}
  • id: 139739379
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 76, 'group_counter': 114, 'group_order': 648, 'label': '36D11', 'order': 36, 'powers': [57, 36], 'representative': 94, 'size': 6}
  • id: 139739380
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 77, 'group_counter': 114, 'group_order': 648, 'label': '36D-11', 'order': 36, 'powers': [56, 35], 'representative': 32, 'size': 6}
  • id: 139739381
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 78, 'group_counter': 114, 'group_order': 648, 'label': '36D13', 'order': 36, 'powers': [55, 35], 'representative': 98, 'size': 6}
  • id: 139739382
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 79, 'group_counter': 114, 'group_order': 648, 'label': '36D-13', 'order': 36, 'powers': [54, 36], 'representative': 28, 'size': 6}
  • id: 139739384
    {'aut_label': '36D-1', 'centralizer': '6.d1.a1', 'counter': 80, 'group_counter': 114, 'group_order': 648, 'label': '36D17', 'order': 36, 'powers': [53, 37], 'representative': 34, 'size': 6}
  • id: 139739385
    {'aut_label': '36D1', 'centralizer': '6.d1.a1', 'counter': 81, 'group_counter': 114, 'group_order': 648, 'label': '36D-17', 'order': 36, 'powers': [52, 38], 'representative': 92, 'size': 6}
  • id: 139739386
    {'aut_label': '36E1', 'centralizer': '18.f1.a1', 'counter': 82, 'group_counter': 114, 'group_order': 648, 'label': '36E1', 'order': 36, 'powers': [45, 39], 'representative': 1, 'size': 18}
  • id: 139739387
    {'aut_label': '36E-1', 'centralizer': '18.f1.a1', 'counter': 83, 'group_counter': 114, 'group_order': 648, 'label': '36E-1', 'order': 36, 'powers': [46, 40], 'representative': 17, 'size': 18}
  • id: 139739388
    {'aut_label': '36E-1', 'centralizer': '18.f1.a1', 'counter': 84, 'group_counter': 114, 'group_order': 648, 'label': '36E5', 'order': 36, 'powers': [47, 40], 'representative': 5, 'size': 18}
  • id: 139739389
    {'aut_label': '36E1', 'centralizer': '18.f1.a1', 'counter': 85, 'group_counter': 114, 'group_order': 648, 'label': '36E-5', 'order': 36, 'powers': [48, 39], 'representative': 13, 'size': 18}
  • id: 139739390
    {'aut_label': '36E1', 'centralizer': '18.f1.a1', 'counter': 86, 'group_counter': 114, 'group_order': 648, 'label': '36E7', 'order': 36, 'powers': [44, 39], 'representative': 7, 'size': 18}
  • id: 139739391
    {'aut_label': '36E-1', 'centralizer': '18.f1.a1', 'counter': 87, 'group_counter': 114, 'group_order': 648, 'label': '36E-7', 'order': 36, 'powers': [43, 40], 'representative': 11, 'size': 18}
  • id: 139739392
    {'aut_label': '36E1', 'centralizer': '18.f1.b1', 'counter': 88, 'group_counter': 114, 'group_order': 648, 'label': '36F1', 'order': 36, 'powers': [45, 41], 'representative': 19, 'size': 18}
  • id: 139739393
    {'aut_label': '36E-1', 'centralizer': '18.f1.b1', 'counter': 89, 'group_counter': 114, 'group_order': 648, 'label': '36F-1', 'order': 36, 'powers': [46, 42], 'representative': 35, 'size': 18}
  • id: 139739395
    {'aut_label': '36E-1', 'centralizer': '18.f1.b1', 'counter': 90, 'group_counter': 114, 'group_order': 648, 'label': '36F5', 'order': 36, 'powers': [47, 42], 'representative': 23, 'size': 18}
  • id: 139739396
    {'aut_label': '36E1', 'centralizer': '18.f1.b1', 'counter': 91, 'group_counter': 114, 'group_order': 648, 'label': '36F-5', 'order': 36, 'powers': [48, 41], 'representative': 31, 'size': 18}
  • id: 139739397
    {'aut_label': '36E1', 'centralizer': '18.f1.b1', 'counter': 92, 'group_counter': 114, 'group_order': 648, 'label': '36F7', 'order': 36, 'powers': [44, 41], 'representative': 25, 'size': 18}
  • id: 139739398
    {'aut_label': '36E-1', 'centralizer': '18.f1.b1', 'counter': 93, 'group_counter': 114, 'group_order': 648, 'label': '36F-7', 'order': 36, 'powers': [43, 42], 'representative': 29, 'size': 18}
• 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: 12761078
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1a', '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], 'schur_index': 1}
  • id: 12761089
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1b', '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], 'schur_index': 1}
  • id: 12761100
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1c', '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], 'schur_index': 1}
  • id: 12761102
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1d', '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], 'schur_index': 1}
  • id: 12761103
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12761104
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -2, 1, 1, -2, 1, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12761105
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -2, 1, 1, -2, 1, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12761106
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12761082
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761083
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761084
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 0, 0, 0, -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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 12761085
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2d', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761086
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2e', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, -4, 0, 0, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, -1, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761087
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2f', 'multiplicity': 2, 'nt': [24, 4], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, 4, 0, 0, 0, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, 2, -4, -4, 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], 'schur_index': 1}
  • id: 12761088
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2g', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, 4, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 12761107
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1i', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, 6, 6, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, -3, -3, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, -3, -3, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761079
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1j', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, -6, -6, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, 3, 3, 3, 3, -6, 3, 3, -6, 3, -3, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 3, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761080
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1k', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, -6, 6, -6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, 3, 3, 3, 3, -6, 3, 3, -6, -3, 3, 3, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 3, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761081
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.1l', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, -3, -3, 6, -6, -6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, -3, -3, -3, -3, 6, -3, -3, 6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, -3, -3, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761095
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, 6, 0, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12761096
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6b', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -6, 0, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12761090
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2h', 'multiplicity': 4, 'nt': [24, 64], 'qdim': 8, 'qvalues': [8, -8, 8, 8, 8, 8, 8, 0, 0, 0, -8, -8, -8, -8, -8, -4, -4, -4, -4, -4, -4, -4, 2, -4, 2, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, -2, 4, 4, -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], 'schur_index': 1}
  • id: 12761091
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2i', 'multiplicity': 6, 'nt': [18, 16], 'qdim': 12, 'qvalues': [12, 12, -6, -6, 12, -6, -6, 12, 0, 0, -6, -6, -6, 12, -6, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, -6, 0, 0, -6, -6, -6, -6, 12, -6, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 3, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761092
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2j', 'multiplicity': 6, 'nt': [36, 63], 'qdim': 12, 'qvalues': [12, 12, -6, -6, 12, -6, -6, -12, 0, 0, -6, -6, -6, 12, -6, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, -6, 0, 0, 6, 6, 6, 6, -12, 6, 6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, -3, -3, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761093
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2k', 'multiplicity': 6, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, -6, -6, 12, -6, -6, 0, 0, 0, 6, 6, 6, -12, 6, 0, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761097
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6c', 'multiplicity': 2, 'nt': [18, 80], 'qdim': 12, 'qvalues': [12, 12, -6, -6, -6, 3, 3, 12, 0, 0, -6, -6, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12761098
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6d', 'multiplicity': 2, 'nt': [36, 474], 'qdim': 12, 'qvalues': [12, 12, -6, -6, -6, 3, 3, -12, 0, 0, -6, -6, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12761099
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6e', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, 12, 12, -6, -6, -6, 0, 0, 0, -12, -12, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 12761094
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.2l', 'multiplicity': 12, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, -12, -12, 24, -12, -12, 0, 0, 0, 12, 12, 12, -24, 12, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12761101
    {'cdim': 6, 'counter': 30, 'faithful': True, 'group': '648.114', 'group_order': 648, 'image': None, 'label': '648.114.6f', 'multiplicity': 4, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, -12, -12, -12, 6, 6, 0, 0, 0, 12, 12, -6, 12, -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], '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: 29491819
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 648, 'label': '648.114.1a', '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]]]}
  • id: 29491830
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 324, 'label': '648.114.1b', '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]]]}
  • id: 29491841
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 324, 'label': '648.114.1c', '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]]]}
  • id: 29491852
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 324, 'label': '648.114.1d', '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]]]}
  • id: 29491863
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 216, 'label': '648.114.1e1', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -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, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29491874
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 216, 'label': '648.114.1e2', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 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, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 29491885
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 108, 'label': '648.114.1f1', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[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, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -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, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29491896
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 108, 'label': '648.114.1f2', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[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, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 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, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 29491907
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 108, 'label': '648.114.1g1', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -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, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29491820
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 108, 'label': '648.114.1g2', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 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, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29491821
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 108, 'label': '648.114.1h1', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[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, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -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, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29491822
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 108, 'label': '648.114.1h2', '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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[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, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 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, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29491823
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 13, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i1', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 0]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 3]], [[1, -4]], [[1, 0]], [[1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]]]}
  • id: 29491824
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 14, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i2', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, 0]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -3]], [[1, 4]], [[1, 0]], [[1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]]]}
  • id: 29491825
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 15, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i3', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 0]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 0]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 3]], [[1, 2]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]]]}
  • id: 29491826
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 16, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i4', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 0]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, 0]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -3]], [[1, -2]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]]]}
  • id: 29491827
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 17, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i5', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, -1]], [[1, 0]], [[1, -4]], [[1, 0]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]]]}
  • id: 29491828
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 18, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 72, 'label': '648.114.1i6', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[1, 1]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]]]}
  • id: 29491829
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 19, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 0]], [[1, -1]], [[1, -2]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, -3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 0]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[-1, 4]], [[-1, -1]], [[-1, -3]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[-1, -4]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]]]}
  • id: 29491831
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 20, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 0]], [[1, 1]], [[1, 2]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, 3]], [[1, -3]], [[-1, -3]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, 0]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[-1, -4]], [[-1, 1]], [[-1, 3]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, -3]], [[-1, 4]], [[-1, 0]], [[-1, -2]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]]]}
  • id: 29491832
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 21, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 0]], [[1, -4]], [[1, 1]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, -3]], [[1, 3]], [[-1, 3]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 0]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -3]], [[-1, -2]], [[-1, -4]], [[-1, -3]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 3]], [[-1, 3]], [[-1, 2]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]]]}
  • id: 29491833
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 22, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 0]], [[1, 4]], [[1, -1]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, 3]], [[1, -3]], [[-1, -3]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, 0]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 3]], [[-1, 2]], [[-1, 4]], [[-1, 3]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -3]], [[-1, -3]], [[-1, -2]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]]]}
  • id: 29491834
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 23, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 2]], [[1, 4]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, -3]], [[1, 3]], [[-1, 3]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, -3]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 3]], [[-1, 3]], [[-1, -1]], [[-1, 0]], [[-1, -4]], [[-1, 0]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[1, 4]], [[1, -4]], [[-1, 4]], [[-1, -4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]]]}
  • id: 29491835
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 24, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 36, 'label': '648.114.1j6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, -2]], [[1, -4]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, 3]], [[1, -3]], [[-1, -3]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, 3]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -3]], [[-1, -3]], [[-1, 1]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[1, -4]], [[1, 4]], [[-1, -4]], [[-1, 4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]]]}
  • id: 29491836
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 25, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 0]], [[1, -1]], [[1, -2]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[1, -3]], [[-1, -3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 0]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[-1, 4]], [[-1, -1]], [[-1, -3]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[-1, -4]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, -1]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]]]}
  • id: 29491837
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 26, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 0]], [[1, 1]], [[1, 2]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[1, 3]], [[-1, 3]], [[-1, -3]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, 0]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[-1, -4]], [[-1, 1]], [[-1, 3]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, -3]], [[-1, 4]], [[-1, 0]], [[-1, -2]], [[-1, 0]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, 1]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]]]}
  • id: 29491838
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 27, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 0]], [[1, -4]], [[1, 1]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[1, -3]], [[-1, -3]], [[-1, 3]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 0]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -3]], [[-1, -2]], [[-1, -4]], [[-1, -3]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 3]], [[-1, 3]], [[-1, 2]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, -4]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -4]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 2]]]}
  • id: 29491839
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 28, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 0]], [[1, 4]], [[1, -1]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[1, 3]], [[-1, 3]], [[-1, -3]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, 0]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 3]], [[-1, 2]], [[-1, 4]], [[-1, 3]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -3]], [[-1, -3]], [[-1, -2]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 4]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -2]]]}
  • id: 29491840
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 29, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 2]], [[1, 4]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[1, -3]], [[-1, -3]], [[-1, 3]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, -3]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 3]], [[-1, 3]], [[-1, -1]], [[-1, 0]], [[-1, -4]], [[-1, 0]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, 4]], [[-1, -4]], [[1, 4]], [[1, -4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]]]}
  • id: 29491842
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 30, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 36, 'label': '648.114.1k6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, -2]], [[1, -4]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[1, 3]], [[-1, 3]], [[-1, -3]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, 3]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -3]], [[-1, -3]], [[-1, 1]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, -4]], [[-1, 4]], [[1, -4]], [[1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]]]}
  • id: 29491843
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 31, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 0]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 3]], [[1, -4]], [[1, 0]], [[1, 2]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 4]], [[1, -1]], [[-1, 1]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]]]}
  • id: 29491844
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 32, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, 0]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -4]], [[1, 1]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -3]], [[1, 4]], [[1, 0]], [[1, -2]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -4]], [[1, 1]], [[-1, -1]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]]]}
  • id: 29491845
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 33, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 0]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 0]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 3]], [[1, 2]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -2]], [[1, -4]], [[-1, 4]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 2]]]}
  • id: 29491846
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 34, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 0]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, 0]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -3]], [[1, -2]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 2]], [[1, 4]], [[-1, -4]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -2]]]}
  • id: 29491847
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 35, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, -1]], [[1, 0]], [[1, -4]], [[1, 0]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]]]}
  • id: 29491848
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 36, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 36, 'label': '648.114.1l6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[1, 1]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]]]}
  • id: 29491849
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 108, 'label': '648.114.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491850
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 54, 'label': '648.114.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491851
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 39, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.a1.a1', 'kernel_order': 81, 'label': '648.114.2c', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491853
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 36, 'label': '648.114.2d1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491854
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 36, 'label': '648.114.2d2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491855
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 18, 'label': '648.114.2e1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-2, -1]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491856
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 18, 'label': '648.114.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-2, 1]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491857
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '24.11', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 27, 'label': '648.114.2f1', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[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]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-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]]]}
  • id: 29491858
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 45, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '24.11', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 27, 'label': '648.114.2f2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[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]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-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]]]}
  • id: 29491859
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 46, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 27, 'label': '648.114.2g1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491860
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 47, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 27, 'label': '648.114.2g2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491861
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 48, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.26', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 9, 'label': '648.114.2h1', 'nt': [24, 64], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 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]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 1], [2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 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]]]}
  • id: 29491862
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 49, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.26', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 9, 'label': '648.114.2h2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[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]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 1], [-1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 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]]]}
  • id: 29491864
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 50, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.26', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 9, 'label': '648.114.2h3', 'nt': [24, 64], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 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]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 1], [-2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 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]]]}
  • id: 29491865
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 51, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.26', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 9, 'label': '648.114.2h4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[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]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 1], [1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 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]]]}
  • id: 29491866
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 52, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i1', 'nt': [18, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -3]], [[-1, 2]], [[-1, 3]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -4]], [[2, -2]], [[2, 4]], [[2, -1]], [[-1, 3]], [[-1, 4]], [[-1, -3]], [[-1, 0]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[2, -2]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[2, 4]], [[2, -1]], [[-1, -3]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[2, -4]], [[-1, 0]], [[2, 2]], [[-1, 0]], [[-1, -2]], [[2, 1]], [[-1, 4]], [[-1, -1]], [[-1, 4]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491867
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 53, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i2', 'nt': [18, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 3]], [[-1, -2]], [[-1, -3]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 4]], [[2, 2]], [[2, -4]], [[2, 1]], [[-1, -3]], [[-1, -4]], [[-1, 3]], [[-1, 0]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[2, 2]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[2, -4]], [[2, 1]], [[-1, 3]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, -3]], [[2, 4]], [[-1, 0]], [[2, -2]], [[-1, 0]], [[-1, 2]], [[2, -1]], [[-1, -4]], [[-1, 1]], [[-1, -4]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491868
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 54, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i3', 'nt': [18, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 0]], [[-1, -4]], [[-1, 1]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, -1]], [[2, 2]], [[2, 1]], [[2, -2]], [[2, -4]], [[-1, 3]], [[-1, -2]], [[-1, -3]], [[-1, 0]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]], [[-1, 4]], [[2, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -3]], [[2, -2]], [[2, -4]], [[-1, -3]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, 3]], [[-1, 3]], [[2, 2]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[2, 4]], [[-1, -2]], [[-1, -4]], [[-1, -2]], [[-1, -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]]]}
  • id: 29491869
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 55, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i4', 'nt': [18, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[-1, -1]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -4]], [[2, 1]], [[2, -2]], [[2, -1]], [[2, 2]], [[2, 4]], [[-1, -3]], [[-1, 2]], [[-1, 3]], [[-1, 0]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[-1, -4]], [[2, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 3]], [[2, 2]], [[2, 4]], [[-1, 3]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, -3]], [[-1, -3]], [[2, -2]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[2, -4]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 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]]]}
  • id: 29491870
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 56, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i5', 'nt': [18, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[-1, -3]], [[-1, -4]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 0]], [[-1, 2]], [[-1, 4]], [[2, -3]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, -4]], [[2, -1]], [[2, 4]], [[2, 1]], [[2, 2]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, 0]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[-1, -2]], [[2, 4]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -3]], [[2, 1]], [[2, 2]], [[-1, -3]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 3]], [[-1, 3]], [[2, -1]], [[-1, 0]], [[2, -4]], [[-1, 0]], [[-1, 4]], [[2, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491871
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 57, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.4', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1.a1', 'kernel_order': 12, 'label': '648.114.2i6', 'nt': [18, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[-1, 3]], [[-1, 4]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 0]], [[-1, -2]], [[-1, -4]], [[2, 3]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 4]], [[2, 1]], [[2, -4]], [[2, -1]], [[2, -2]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, 0]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[-1, 2]], [[2, -4]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, 3]], [[2, -1]], [[2, -2]], [[-1, 3]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -3]], [[-1, -3]], [[2, 1]], [[-1, 0]], [[2, 4]], [[-1, 0]], [[-1, -4]], [[2, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491872
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 58, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j1', 'nt': [36, 63], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[-1, -3]], [[-1, 2]], [[-1, 3]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 0]], [[-1, -1]], [[-1, -2]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -4]], [[2, -2]], [[2, 4]], [[2, -1]], [[-1, 3]], [[-1, 4]], [[-1, -3]], [[-1, 0]], [[-1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[1, 1]], [[-2, -2]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, -3]], [[-2, 4]], [[-2, -1]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 3]], [[-2, -4]], [[1, 0]], [[-2, 2]], [[1, 0]], [[1, -2]], [[-2, 1]], [[1, 4]], [[1, -1]], [[1, 4]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491873
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 59, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j2', 'nt': [36, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[-1, 3]], [[-1, -2]], [[-1, -3]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, 0]], [[-1, 1]], [[-1, 2]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 4]], [[2, 2]], [[2, -4]], [[2, 1]], [[-1, -3]], [[-1, -4]], [[-1, 3]], [[-1, 0]], [[-1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[1, -1]], [[-2, 2]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, 3]], [[-2, -4]], [[-2, 1]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -3]], [[-2, 4]], [[1, 0]], [[-2, -2]], [[1, 0]], [[1, 2]], [[-2, -1]], [[1, -4]], [[1, 1]], [[1, -4]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491875
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 60, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j3', 'nt': [36, 63], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 0]], [[-1, -4]], [[-1, 1]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, -1]], [[2, 2]], [[2, 1]], [[2, -2]], [[2, -4]], [[-1, 3]], [[-1, -2]], [[-1, -3]], [[-1, 0]], [[-1, 2]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, 4]], [[1, 4]], [[-2, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -3]], [[-2, -2]], [[-2, -4]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, 3]], [[1, 3]], [[-2, 2]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[-2, 4]], [[1, -2]], [[1, -4]], [[1, -2]], [[1, -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]]]}
  • id: 29491876
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 61, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j4', 'nt': [36, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[-1, -1]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -4]], [[2, 1]], [[2, -2]], [[2, -1]], [[2, 2]], [[2, 4]], [[-1, -3]], [[-1, 2]], [[-1, 3]], [[-1, 0]], [[-1, -2]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, -4]], [[1, -4]], [[-2, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 3]], [[-2, 2]], [[-2, 4]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, -3]], [[1, -3]], [[-2, -2]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[-2, -4]], [[1, 2]], [[1, 4]], [[1, 2]], [[1, 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]]]}
  • id: 29491877
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 62, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j5', 'nt': [36, 63], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[-1, -3]], [[-1, -4]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 0]], [[-1, 2]], [[-1, 4]], [[-2, -3]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, 3]], [[-2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, -4]], [[2, -1]], [[2, 4]], [[2, 1]], [[2, 2]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, 0]], [[-1, -1]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -2]], [[1, -2]], [[-2, 4]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, -3]], [[-2, 1]], [[-2, 2]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[-2, -1]], [[1, 0]], [[-2, -4]], [[1, 0]], [[1, 4]], [[-2, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491878
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 63, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.24', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.114.2j6', 'nt': [36, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[-1, 3]], [[-1, 4]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 0]], [[-1, -2]], [[-1, -4]], [[-2, 3]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, -3]], [[-2, 3]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 4]], [[2, 1]], [[2, -4]], [[2, -1]], [[2, -2]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, 0]], [[-1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-2, -4]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, 3]], [[-2, -1]], [[-2, -2]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[-2, 1]], [[1, 0]], [[-2, 4]], [[1, 0]], [[1, -4]], [[-2, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491879
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 64, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k1', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, 3]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, -3]], [[2, 2]], [[2, 3]], [[2, -4]], [[2, 1]], [[2, 4]], [[2, 0]], [[2, -1]], [[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]], [[-2, 1]], [[-2, 2]], [[-2, -4]], [[-2, -2]], [[-2, 4]], [[-2, -1]], [[-2, 3]], [[-2, 4]], [[-2, -3]], [[-2, 0]], [[-2, -4]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-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]]]}
  • id: 29491880
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 65, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k2', 'nt': [72, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, -3]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, 3]], [[2, -2]], [[2, -3]], [[2, 4]], [[2, -1]], [[2, -4]], [[2, 0]], [[2, 1]], [[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]], [[-2, -1]], [[-2, -2]], [[-2, 4]], [[-2, 2]], [[-2, -4]], [[-2, 1]], [[-2, -3]], [[-2, -4]], [[-2, 3]], [[-2, 0]], [[-2, 4]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-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]]]}
  • id: 29491881
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 66, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k3', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, 3]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[2, -1]], [[2, 1]], [[2, -3]], [[2, -1]], [[2, 3]], [[2, 2]], [[2, 4]], [[2, -2]], [[2, 0]], [[2, -4]], [[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]], [[-2, 4]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[-2, -4]], [[-2, 3]], [[-2, -2]], [[-2, -3]], [[-2, 0]], [[-2, 2]], [[-2, -4]], [[-2, 1]], [[-2, -1]], [[-2, 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]]]}
  • id: 29491882
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 67, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k4', 'nt': [72, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, -3]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[2, 1]], [[2, -1]], [[2, 3]], [[2, 1]], [[2, -3]], [[2, -2]], [[2, -4]], [[2, 2]], [[2, 0]], [[2, 4]], [[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]], [[-2, -4]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[-2, 2]], [[-2, 4]], [[-2, -3]], [[-2, 2]], [[-2, 3]], [[-2, 0]], [[-2, -2]], [[-2, 4]], [[-2, -1]], [[-2, 1]], [[-2, -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]]]}
  • id: 29491883
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 68, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k5', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, -3]], [[2, 3]], [[2, 0]], [[2, -3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, -3]], [[-2, -3]], [[-2, 0]], [[-2, 3]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -4]], [[2, 4]], [[2, -3]], [[2, -4]], [[2, 3]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 0]], [[2, 2]], [[2, 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]], [[-2, -2]], [[-2, -4]], [[-2, -1]], [[-2, 4]], [[-2, 1]], [[-2, 2]], [[-2, 3]], [[-2, 1]], [[-2, -3]], [[-2, 0]], [[-2, -1]], [[-2, 2]], [[-2, 4]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491884
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 162, 'counter': 69, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '72.11', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 9, 'label': '648.114.2k6', 'nt': [72, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 3]], [[2, -3]], [[2, 0]], [[2, 3]], [[2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -3]], [[-2, 3]], [[-2, 3]], [[-2, 0]], [[-2, -3]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 4]], [[2, -4]], [[2, 3]], [[2, 4]], [[2, -3]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, 0]], [[2, -2]], [[2, -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]], [[-2, 2]], [[-2, 4]], [[-2, 1]], [[-2, -4]], [[-2, -1]], [[-2, -2]], [[-2, -3]], [[-2, -1]], [[-2, 3]], [[-2, 0]], [[-2, 1]], [[-2, -2]], [[-2, -4]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491886
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 70, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l1', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[-2, 2]], [[2, 16]], [[2, 4]], [[-2, 14]], [[2, 8]], [[-2, 10]], [[1, 6]], [[-1, 8]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[-1, 16]], [[-1, 0]], [[1, 14]], [[1, 10]], [[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, 4]], [[-2, 8]], [[2, 2]], [[2, 10]], [[-2, 16]], [[2, 14]], [[1, 12]], [[1, 16]], [[-1, 6]], [[1, 0]], [[-1, 2]], [[-1, 14]], [[-1, 10]], [[1, 8]], [[1, 4]], [[-1, 1], [-1, 7]], [[0, 0]], [[2, 5], [-1, 11]], [[1, 5], [1, 11]], [[-1, 1], [2, 7]], [[-1, 3], [-1, 9]], [[0, 0]], [[0, 0]], [[1, 3], [1, 9]], [[-2, 5], [1, 11]], [[1, 1], [1, 7]], [[-1, 5], [-1, 11]], [[1, 3], [-2, 9]], [[-1, 3], [2, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 1], [-2, 7]], [[0, 0]], [[-2, 1], [1, 7]], [[1, 5], [-2, 11]], [[2, 1], [-1, 7]], [[-1, 5], [2, 11]], [[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: 29491895
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 79, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l10', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[2, 4]], [[-2, 14]], [[2, 8]], [[-2, 10]], [[2, 16]], [[-2, 2]], [[-1, 12]], [[-1, 16]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 14]], [[-1, 0]], [[1, 10]], [[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]], [[-2, 8]], [[-2, 16]], [[-2, 4]], [[2, 2]], [[2, 14]], [[2, 10]], [[-1, 6]], [[-1, 14]], [[1, 12]], [[1, 0]], [[1, 4]], [[-1, 10]], [[-1, 2]], [[1, 16]], [[1, 8]], [[-1, 5], [-1, 11]], [[0, 0]], [[-1, 1], [-1, 7]], [[-2, 1], [1, 7]], [[2, 5], [-1, 11]], [[-1, 3], [2, 9]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 9]], [[1, 1], [1, 7]], [[1, 5], [1, 11]], [[2, 1], [-1, 7]], [[1, 3], [1, 9]], [[-1, 3], [-1, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[-2, 5], [1, 11]], [[0, 0]], [[1, 5], [-2, 11]], [[1, 1], [-2, 7]], [[-1, 5], [2, 11]], [[-1, 1], [2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491897
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 80, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l11', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[-2, 14]], [[2, 4]], [[-2, 10]], [[2, 8]], [[-2, 2]], [[2, 16]], [[1, 6]], [[1, 2]], [[-1, 12]], [[1, 14]], [[1, 10]], [[-1, 4]], [[-1, 0]], [[-1, 8]], [[-1, 16]], [[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, 10]], [[2, 2]], [[2, 14]], [[-2, 16]], [[-2, 4]], [[-2, 8]], [[1, 12]], [[1, 4]], [[-1, 6]], [[1, 0]], [[-1, 14]], [[1, 8]], [[1, 16]], [[-1, 2]], [[-1, 10]], [[1, 1], [-2, 7]], [[0, 0]], [[1, 5], [-2, 11]], [[2, 5], [-1, 11]], [[-2, 1], [1, 7]], [[1, 3], [1, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 9]], [[-1, 5], [2, 11]], [[-1, 1], [2, 7]], [[-2, 5], [1, 11]], [[-1, 3], [2, 9]], [[1, 3], [-2, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[2, 1], [-1, 7]], [[0, 0]], [[-1, 1], [-1, 7]], [[-1, 5], [-1, 11]], [[1, 1], [1, 7]], [[1, 5], [1, 11]], [[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: 29491898
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 81, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l12', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[2, 4]], [[-2, 14]], [[2, 8]], [[-2, 10]], [[2, 16]], [[-2, 2]], [[-1, 12]], [[-1, 16]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 14]], [[-1, 0]], [[1, 10]], [[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]], [[-2, 8]], [[-2, 16]], [[-2, 4]], [[2, 2]], [[2, 14]], [[2, 10]], [[-1, 6]], [[-1, 14]], [[1, 12]], [[1, 0]], [[1, 4]], [[-1, 10]], [[-1, 2]], [[1, 16]], [[1, 8]], [[1, 5], [1, 11]], [[0, 0]], [[1, 1], [1, 7]], [[2, 1], [-1, 7]], [[-2, 5], [1, 11]], [[1, 3], [-2, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 9]], [[-1, 1], [-1, 7]], [[-1, 5], [-1, 11]], [[-2, 1], [1, 7]], [[-1, 3], [-1, 9]], [[1, 3], [1, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[2, 5], [-1, 11]], [[0, 0]], [[-1, 5], [2, 11]], [[-1, 1], [2, 7]], [[1, 5], [-2, 11]], [[1, 1], [-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491887
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 71, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l2', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[2, 16]], [[-2, 2]], [[-2, 14]], [[2, 4]], [[-2, 10]], [[2, 8]], [[-1, 12]], [[1, 10]], [[1, 6]], [[-1, 16]], [[1, 14]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 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]], [[2, 14]], [[2, 10]], [[-2, 16]], [[-2, 8]], [[2, 2]], [[-2, 4]], [[-1, 6]], [[-1, 2]], [[1, 12]], [[1, 0]], [[1, 16]], [[1, 4]], [[1, 8]], [[-1, 10]], [[-1, 14]], [[-1, 5], [2, 11]], [[0, 0]], [[2, 1], [-1, 7]], [[1, 1], [-2, 7]], [[-1, 5], [-1, 11]], [[-1, 3], [2, 9]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 9]], [[-2, 1], [1, 7]], [[1, 5], [-2, 11]], [[-1, 1], [2, 7]], [[1, 3], [1, 9]], [[-1, 3], [-1, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 5], [1, 11]], [[0, 0]], [[-2, 5], [1, 11]], [[1, 1], [1, 7]], [[2, 5], [-1, 11]], [[-1, 1], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491888
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 72, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l3', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[-2, 2]], [[2, 16]], [[2, 4]], [[-2, 14]], [[2, 8]], [[-2, 10]], [[1, 6]], [[-1, 8]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[-1, 16]], [[-1, 0]], [[1, 14]], [[1, 10]], [[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, 4]], [[-2, 8]], [[2, 2]], [[2, 10]], [[-2, 16]], [[2, 14]], [[1, 12]], [[1, 16]], [[-1, 6]], [[1, 0]], [[-1, 2]], [[-1, 14]], [[-1, 10]], [[1, 8]], [[1, 4]], [[1, 1], [1, 7]], [[0, 0]], [[-2, 5], [1, 11]], [[-1, 5], [-1, 11]], [[1, 1], [-2, 7]], [[1, 3], [1, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 9]], [[2, 5], [-1, 11]], [[-1, 1], [-1, 7]], [[1, 5], [1, 11]], [[-1, 3], [2, 9]], [[1, 3], [-2, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 1], [2, 7]], [[0, 0]], [[2, 1], [-1, 7]], [[-1, 5], [2, 11]], [[-2, 1], [1, 7]], [[1, 5], [-2, 11]], [[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: 29491889
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 73, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l4', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[2, 16]], [[-2, 2]], [[-2, 14]], [[2, 4]], [[-2, 10]], [[2, 8]], [[-1, 12]], [[1, 10]], [[1, 6]], [[-1, 16]], [[1, 14]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 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]], [[2, 14]], [[2, 10]], [[-2, 16]], [[-2, 8]], [[2, 2]], [[-2, 4]], [[-1, 6]], [[-1, 2]], [[1, 12]], [[1, 0]], [[1, 16]], [[1, 4]], [[1, 8]], [[-1, 10]], [[-1, 14]], [[1, 5], [-2, 11]], [[0, 0]], [[-2, 1], [1, 7]], [[-1, 1], [2, 7]], [[1, 5], [1, 11]], [[1, 3], [-2, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 9]], [[2, 1], [-1, 7]], [[-1, 5], [2, 11]], [[1, 1], [-2, 7]], [[-1, 3], [-1, 9]], [[1, 3], [1, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 5], [-1, 11]], [[0, 0]], [[2, 5], [-1, 11]], [[-1, 1], [-1, 7]], [[-2, 5], [1, 11]], [[1, 1], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491890
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 74, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l5', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[2, 8]], [[-2, 10]], [[2, 16]], [[-2, 2]], [[-2, 14]], [[2, 4]], [[1, 6]], [[1, 14]], [[-1, 12]], [[-1, 8]], [[-1, 16]], [[1, 10]], [[-1, 0]], [[1, 2]], [[-1, 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]], [[-2, 16]], [[2, 14]], [[-2, 8]], [[-2, 4]], [[2, 10]], [[2, 2]], [[1, 12]], [[-1, 10]], [[-1, 6]], [[1, 0]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 14]], [[1, 16]], [[-2, 1], [1, 7]], [[0, 0]], [[1, 5], [1, 11]], [[-1, 5], [2, 11]], [[1, 1], [1, 7]], [[1, 3], [1, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 9]], [[-1, 5], [-1, 11]], [[2, 1], [-1, 7]], [[1, 5], [-2, 11]], [[-1, 3], [2, 9]], [[1, 3], [-2, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 1], [-1, 7]], [[0, 0]], [[-1, 1], [2, 7]], [[2, 5], [-1, 11]], [[1, 1], [-2, 7]], [[-2, 5], [1, 11]], [[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: 29491891
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 75, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l6', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[-2, 10]], [[2, 8]], [[-2, 2]], [[2, 16]], [[2, 4]], [[-2, 14]], [[-1, 12]], [[-1, 4]], [[1, 6]], [[1, 10]], [[1, 2]], [[-1, 8]], [[-1, 0]], [[-1, 16]], [[1, 14]], [[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, 2]], [[-2, 4]], [[2, 10]], [[2, 14]], [[-2, 8]], [[-2, 16]], [[-1, 6]], [[1, 8]], [[1, 12]], [[1, 0]], [[-1, 10]], [[1, 16]], [[-1, 14]], [[1, 4]], [[-1, 2]], [[-2, 5], [1, 11]], [[0, 0]], [[1, 1], [-2, 7]], [[-1, 1], [-1, 7]], [[1, 5], [-2, 11]], [[1, 3], [-2, 9]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 9]], [[-1, 1], [2, 7]], [[2, 5], [-1, 11]], [[1, 1], [1, 7]], [[-1, 3], [-1, 9]], [[1, 3], [1, 9]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 5], [2, 11]], [[0, 0]], [[-1, 5], [-1, 11]], [[2, 1], [-1, 7]], [[1, 5], [1, 11]], [[-2, 1], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491892
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 76, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l7', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[2, 8]], [[-2, 10]], [[2, 16]], [[-2, 2]], [[-2, 14]], [[2, 4]], [[1, 6]], [[1, 14]], [[-1, 12]], [[-1, 8]], [[-1, 16]], [[1, 10]], [[-1, 0]], [[1, 2]], [[-1, 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]], [[-2, 16]], [[2, 14]], [[-2, 8]], [[-2, 4]], [[2, 10]], [[2, 2]], [[1, 12]], [[-1, 10]], [[-1, 6]], [[1, 0]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 14]], [[1, 16]], [[2, 1], [-1, 7]], [[0, 0]], [[-1, 5], [-1, 11]], [[1, 5], [-2, 11]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, 9]], [[0, 0]], [[0, 0]], [[1, 3], [1, 9]], [[1, 5], [1, 11]], [[-2, 1], [1, 7]], [[-1, 5], [2, 11]], [[1, 3], [-2, 9]], [[-1, 3], [2, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, 7]], [[0, 0]], [[1, 1], [-2, 7]], [[-2, 5], [1, 11]], [[-1, 1], [2, 7]], [[2, 5], [-1, 11]], [[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: 29491893
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 77, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l8', 'nt': [72, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 12]], [[-2, 6]], [[2, 0]], [[2, 12]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 12]], [[-2, 12]], [[-2, 0]], [[2, 6]], [[-2, 10]], [[2, 8]], [[-2, 2]], [[2, 16]], [[2, 4]], [[-2, 14]], [[-1, 12]], [[-1, 4]], [[1, 6]], [[1, 10]], [[1, 2]], [[-1, 8]], [[-1, 0]], [[-1, 16]], [[1, 14]], [[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, 2]], [[-2, 4]], [[2, 10]], [[2, 14]], [[-2, 8]], [[-2, 16]], [[-1, 6]], [[1, 8]], [[1, 12]], [[1, 0]], [[-1, 10]], [[1, 16]], [[-1, 14]], [[1, 4]], [[-1, 2]], [[2, 5], [-1, 11]], [[0, 0]], [[-1, 1], [2, 7]], [[1, 1], [1, 7]], [[-1, 5], [2, 11]], [[-1, 3], [2, 9]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 9]], [[1, 1], [-2, 7]], [[-2, 5], [1, 11]], [[-1, 1], [-1, 7]], [[1, 3], [1, 9]], [[-1, 3], [-1, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 5], [-2, 11]], [[0, 0]], [[1, 5], [1, 11]], [[-2, 1], [1, 7]], [[-1, 5], [-1, 11]], [[2, 1], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29491894
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 54, 'counter': 78, 'cyclotomic_n': 36, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.44', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.114.2l9', 'nt': [72, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 6]], [[2, 12]], [[2, 0]], [[-2, 6]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12]], [[2, 6]], [[2, 6]], [[-2, 0]], [[-2, 12]], [[-2, 14]], [[2, 4]], [[-2, 10]], [[2, 8]], [[-2, 2]], [[2, 16]], [[1, 6]], [[1, 2]], [[-1, 12]], [[1, 14]], [[1, 10]], [[-1, 4]], [[-1, 0]], [[-1, 8]], [[-1, 16]], [[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, 10]], [[2, 2]], [[2, 14]], [[-2, 16]], [[-2, 4]], [[-2, 8]], [[1, 12]], [[1, 4]], [[-1, 6]], [[1, 0]], [[-1, 14]], [[1, 8]], [[1, 16]], [[-1, 2]], [[-1, 10]], [[-1, 1], [2, 7]], [[0, 0]], [[-1, 5], [2, 11]], [[-2, 5], [1, 11]], [[2, 1], [-1, 7]], [[-1, 3], [-1, 9]], [[0, 0]], [[0, 0]], [[1, 3], [1, 9]], [[1, 5], [-2, 11]], [[1, 1], [-2, 7]], [[2, 5], [-1, 11]], [[1, 3], [-2, 9]], [[-1, 3], [2, 9]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[-1, 3], [-1, -3]], [[-2, 1], [1, 7]], [[0, 0]], [[1, 1], [1, 7]], [[1, 5], [1, 11]], [[-1, 1], [-1, 7]], [[-1, 5], [-1, 11]], [[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: 29491899
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 82, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1.a1', 'kernel_order': 12, 'label': '648.114.6a', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491900
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 83, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 6, 'label': '648.114.6b', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491901
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 84, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '162.6', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 4, 'label': '648.114.6c1', 'nt': [18, 80], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491902
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 85, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '162.6', 'image_order': 162, 'indicator': 0, 'kernel': '162.a1.a1', 'kernel_order': 4, 'label': '648.114.6c2', 'nt': [18, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491903
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 86, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '324.64', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 2, 'label': '648.114.6d1', 'nt': [36, 474], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491904
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 12, 'counter': 87, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '324.64', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1.a1', 'kernel_order': 2, 'label': '648.114.6d2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 0]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491905
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 88, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.52', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1.a1', 'kernel_order': 3, 'label': '648.114.6e1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491906
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 89, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '216.52', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1.a1', 'kernel_order': 3, 'label': '648.114.6e2', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491908
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 90, 'cyclotomic_n': 12, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '648.114', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.114.6f1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 4]], [[6, 2]], [[-3, 2]], [[3, 0]], [[3, 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]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[-3, 1], [6, 3]], [[3, 1], [-6, 3]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491909
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 91, 'cyclotomic_n': 12, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '648.114', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.114.6f2', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[-6, 4]], [[3, 4]], [[3, 0]], [[-3, 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]], [[-3, 1], [6, 3]], [[3, 1], [-6, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491910
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 92, 'cyclotomic_n': 12, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '648.114', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.114.6f3', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 4]], [[6, 2]], [[-3, 2]], [[3, 0]], [[3, 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]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[3, 1], [-6, 3]], [[-3, 1], [6, 3]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29491911
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 93, 'cyclotomic_n': 12, 'dim': 6, 'faithful': True, 'field': [1, 0, 1], 'group': '648.114', 'group_counter': 114, 'group_order': 648, 'image': None, 'image_isoclass': '648.114', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.114.6f4', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[-6, 4]], [[3, 4]], [[3, 0]], [[-3, 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]], [[3, 1], [-6, 3]], [[-3, 1], [6, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 110346370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '648.114.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, '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': '648.114', 'subgroup_hash': 114, 'subgroup_order': 648, 'subgroup_tex': 'C_{36}.C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.28', 'subgroup_hash': 28, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.9', 'subgroup_hash': 9, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.9', 'subgroup_hash': 9, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.43', 'subgroup_hash': 43, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110346425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, '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': '216.44', 'subgroup_hash': 44, 'subgroup_order': 216, 'subgroup_tex': 'C_{12}.C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 162, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, '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': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, '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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '648.114.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.4', 'subgroup_hash': 4, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_9', 'supersolvable': True, 'sylow': 3}
  • id: 110346377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 72, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.4', 'subgroup_hash': 4, 'subgroup_order': 72, 'subgroup_tex': 'C_9:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110346378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, '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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110346379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '72.11', 'subgroup_hash': 11, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, '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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 36, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346385
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346386
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346387
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346393
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.18.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1.b1', 'outer_equivalence': False, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346394
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346395
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 110346396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110346400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110346401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 18, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, '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': ['Phi', 'S'], '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: 110346402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 18, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346405
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346406
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110346407
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': ['U0'], '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: 110346408
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', '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: 110346409
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346410
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346411
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346412
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.114.54.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.b1', 'outer_equivalence': False, 'perfect': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346413
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110346415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.114.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:Q_8', '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: 110346416
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 9, 'counter': 51, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times C_9', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346417
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346418
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110346420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '648.114.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 2}
  • id: 110346421
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 6, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110346422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 6, 'counter': 57, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.24', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110346423
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110346424
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346426
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346427
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.162.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.b1', 'outer_equivalence': False, 'perfect': False, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110346428
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.52', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 52, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}.C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110346429
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.C_{18}', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110346430
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.114.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 110346431
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.114.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '324.64', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 64, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_{18}', '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: 110346432
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.114', 'ambient_counter': 114, 'ambient_order': 648, 'ambient_tex': 'C_{36}.C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '648.114.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '648.114', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 114, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}.C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 110346370
    {'ambient': '648.114', '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': '108.a1.a1', 'complements': ['648.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4041, 6718, 4730, 5976, 4650, 3703, 3848, 4753], 'generators': [9, 72, 330, 162, 216, 326, 324], 'label': '648.114.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346371
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.c1.a1', '18.d1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6838, 6204, 7026, 8085, 7029, 5340, 7923, 3658], 'generators': [9, 216, 330, 324, 72], 'label': '648.114.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346372
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.c1.b1', '18.d1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6838, 6204, 8108, 6342, 7029, 5340, 6255, 1829], 'generators': [243, 216, 330, 324, 72], 'label': '648.114.6.c1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.b1', 'normal_contained_in': ['2.b1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346373
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '18.5', 'aut_weyl_index': 72, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '18.h1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4827, -1, 1018, -1, 2228, -1, 617, -1], 'generators': [162, 546, 182, 216, 324], 'label': '648.114.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346374
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 36, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.d1.a1', '18.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2222, -1, 4189, -1, 4209, -1, 4607, -1], 'generators': [9, 216, 326, 324, 330], 'label': '648.114.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346375
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 36, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.d1.b1', '18.f1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2222, -1, 6140, -1, 4209, -1, 3089, -1], 'generators': [243, 216, 326, 324, 330], 'label': '648.114.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346376
    {'ambient': '648.114', 'aut_centralizer_order': 24, 'aut_label': '8.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '54.12', 'aut_weyl_index': 24, 'centralizer': '18.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1624, 1454, 2073, 2887, 223, 667, 1001, 5892], 'generators': [326, 504], 'label': '648.114.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '216.52', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110346377
    {'ambient': '648.114', 'aut_centralizer_order': 3, 'aut_label': '9.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 3, 'centralizer': '108.a1.a1', 'complements': ['72.e1.a1', '72.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.c1.b1', '27.b1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7437, 9241, 9815, 8837, 9040, 9208, 8897, 405], 'generators': [9, 216, 162, 324, 72], 'label': '648.114.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.b1.a1', '18.c1.a1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '324.64', 'quotient_action_image': '9.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346378
    {'ambient': '648.114', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 27, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.d1.a1', '18.d1.b1', '27.a1.a1', '27.b1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5566, -1, 7827, -1, 8037, -1, 7089, -1], 'generators': [9, 216, 162, 330, 324], 'label': '648.114.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346379
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.10', 'aut_weyl_index': 54, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.e1.a1', '18.f1.a1', '18.f1.b1', '27.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3559, -1, 4868, -1, 5127, -1, 3848, -1], 'generators': [9, 330, 162, 326, 324], 'label': '648.114.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110346380
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [979, 3038, 2821, 756, 1981, 2356, 2080, 9080], 'generators': [324, 326, 216, 330], 'label': '648.114.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110346381
    {'ambient': '648.114', 'aut_centralizer_order': 12, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '108.42', 'aut_weyl_index': 12, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.d1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3742, 6718, 3139, 3565, 3213, 3703, 2265, 7272], 'generators': [162, 216, 330, 326, 504, 324], 'label': '648.114.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110346382
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1'], 'contains': ['24.b1.a1', '36.a1.a1', '36.b1.a1', '36.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8316, 5637, 6072, 5413, 4565, 4508, 5031, 4490], 'generators': [324, 330, 504, 216], 'label': '648.114.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110346383
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '9.2', 'aut_weyl_index': 144, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '36.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2721, -1, 1055, -1, 996, -1, 362, -1], 'generators': [324, 182, 216, 546], 'label': '648.114.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346384
    {'ambient': '648.114', 'aut_centralizer_order': 324, 'aut_label': '18.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.d1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1', '54.e1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6035, 5419, 2657, 3116, 5550, 6660, 4217, 7294], 'generators': [162, 330, 216, 324], 'label': '648.114.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1'], 'normal_contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346385
    {'ambient': '648.114', 'aut_centralizer_order': 108, 'aut_label': '18.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 108, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.b1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8838, 8713, 8564, 7344, 8677, 9538, 8447, 3110], 'generators': [162, 504, 324, 216], 'label': '648.114.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.b1.a1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '324.64', 'quotient_action_image': '6.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110346386
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '18.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.d1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7677, 7555, 9242, 9244, 9221, 8350, 9816, 2125], 'generators': [9, 324, 72, 216], 'label': '648.114.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.c1.a1', '9.a1.a1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346387
    {'ambient': '648.114', 'aut_centralizer_order': 6, 'aut_label': '18.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.d1.b1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7677, 7555, 9731, 8283, 9221, 8350, 8897, 1117], 'generators': [243, 324, 72, 216], 'label': '648.114.18.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': ['6.c1.b1', '9.a1.a1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346388
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '54.c1.a1', '54.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4844, -1, 6808, -1, 7077, -1, 7813, -1], 'generators': [9, 330, 324, 216], 'label': '648.114.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346389
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '6.e1.b1', '9.b1.a1'], 'contains': ['36.a1.a1', '54.c1.b1', '54.d1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4844, -1, 7890, -1, 7077, -1, 6295, -1], 'generators': [243, 330, 324, 216], 'label': '648.114.18.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.d1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346390
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.c1.a1'], 'contains': ['36.c1.a1', '54.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3361, -1, 3728, -1, 3273, -1, 2709, -1], 'generators': [162, 326, 324, 330], 'label': '648.114.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346391
    {'ambient': '648.114', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '18.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.c1.a1'], 'contains': ['36.c1.a1', '54.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2076, -1, 4195, -1, 3804, -1, 3588, -1], 'generators': [9, 326, 324, 330], 'label': '648.114.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.f1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346392
    {'ambient': '648.114', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.140', 'aut_weyl_index': 4, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '6.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2821, 4697, 4231, 6738, 4179, 1630, 4632, 5553], 'generators': [9, 216, 72, 326, 324, 330], 'label': '648.114.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346393
    {'ambient': '648.114', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '18.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '9.c1.a1'], 'contains': ['36.c1.a1', '54.c1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2076, -1, 4862, -1, 3804, -1, 3149, -1], 'generators': [243, 542, 324, 330], 'label': '648.114.18.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.f1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346394
    {'ambient': '648.114', 'aut_centralizer_order': 108, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['36.d1.a1', '54.b1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9578, -1, 5732, -1, 6310, -1, 5661, -1], 'generators': [162, 186, 324, 216], 'label': '648.114.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346395
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['36.e1.a1', '54.e1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4099, -1, 185, -1, 2742, -1, 1451, -1], 'generators': [162, 182, 324, 546], 'label': '648.114.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '18.h1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346396
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['72.a1.a1', '72.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [346, 759, 1718, 756, 1920, 917, 2270, 8390], 'generators': [326, 216], 'label': '648.114.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '216.52', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110346397
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '24.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7806, 2510, 4407, 5381, 3804, 2713, 3403, 4447], 'generators': [330, 504], 'label': '648.114.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '216.52', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110346398
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '9.2', 'aut_weyl_index': 144, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1'], 'contains': ['72.a1.a1', '72.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1812, -1, 393, -1, 1081, -1, 1001, -1], 'generators': [182, 216], 'label': '648.114.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '216.52', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346399
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 162, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.c1.a1'], 'contains': ['54.a1.a1', '54.c1.a1', '54.c1.b1', '81.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4903, -1, 6745, -1, 7995, -1, 7054, -1], 'generators': [9, 162, 330, 324], 'label': '648.114.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '27.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110346400
    {'ambient': '648.114', 'aut_centralizer_order': 9, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 27, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1'], 'contains': ['54.b1.a1', '54.d1.a1', '54.d1.b1', '81.a1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6692, -1, 9443, -1, 9777, -1, 9356, -1], 'generators': [9, 162, 324, 216], 'label': '648.114.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346401
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '18.a1.a1', '18.d1.a1', '18.d1.b1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3782, 4118, 3399, 3168, 4626, 4508, 4522, 6900], 'generators': [324, 330, 216], 'label': '648.114.36.a1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1', '18.a1.a1'], 'normal_contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346402
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.b1.a1', '18.c1.a1', '18.c1.b1'], 'contains': ['72.b1.a1', '108.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8463, 6718, 8150, 7344, 7427, 5987, 7279, 3187], 'generators': [324, 504, 216], 'label': '648.114.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.b1.a1', '18.b1.a1', '18.c1.a1', '18.c1.b1'], 'normal_contains': ['72.b1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '324.64', 'quotient_action_image': '6.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110346403
    {'ambient': '648.114', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.140', 'aut_weyl_index': 4, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.b1', '6.e1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2821, 4697, 5679, 5214, 4179, 1630, 3064, 3954], 'generators': [243, 216, 72, 326, 324, 330], 'label': '648.114.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346404
    {'ambient': '648.114', 'aut_centralizer_order': 144, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.e1.a1', '18.f1.a1', '18.f1.b1'], 'contains': ['72.c1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1302, -1, 4195, -1, 3128, -1, 2844, -1], 'generators': [324, 326, 330], 'label': '648.114.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346405
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.g1.a1'], 'contains': ['72.d1.a1', '108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9654, -1, 5786, -1, 5833, -1, 5521, -1], 'generators': [324, 186, 216], 'label': '648.114.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346406
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.h1.a1'], 'contains': ['72.e1.a1', '108.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2527, -1, 812, -1, 2597, -1, 1561, -1], 'generators': [324, 182, 546], 'label': '648.114.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.e1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346407
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5167, 5419, 3611, 1634, 6365, 7148, 5081, 9616], 'generators': [162, 330, 324], 'label': '648.114.54.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.a1.a1', '162.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.4', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346408
    {'ambient': '648.114', 'aut_centralizer_order': 324, 'aut_label': '54.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.g1.a1', '27.b1.a1'], 'contains': ['108.b1.a1', '162.a1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7830, 7619, 7080, 5130, 7959, 8310, 6839, 5673], 'generators': [162, 216, 324], 'label': '648.114.54.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.a1'], 'normal_contains': ['108.b1.a1', '162.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '324.64', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346409
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3296, -1, 5944, -1, 6896, -1, 6400, -1], 'generators': [9, 330, 324], 'label': '648.114.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346410
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.f1.b1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.b1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3296, -1, 6612, -1, 6896, -1, 5960, -1], 'generators': [243, 330, 324], 'label': '648.114.54.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.c1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346411
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.d1.a1', '27.b1.a1'], 'contains': ['108.b1.a1', '162.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6756, -1, 8341, -1, 8503, -1, 8547, -1], 'generators': [9, 324, 216], 'label': '648.114.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.d1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346412
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '18.d1.b1', '27.b1.a1'], 'contains': ['108.b1.a1', '162.b1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6756, -1, 8946, -1, 8503, -1, 7728, -1], 'generators': [243, 324, 216], 'label': '648.114.54.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.d1.b1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346413
    {'ambient': '648.114', 'aut_centralizer_order': 324, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.h1.a1'], 'contains': ['108.c1.a1', '162.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5918, -1, 1909, -1, 5302, -1, 3963, -1], 'generators': [162, 546, 324], 'label': '648.114.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346414
    {'ambient': '648.114', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 3, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.c1.b1', '9.a1.a1', '9.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6838, 8134, 8511, 7803, 7029, 6977, 6669, 2234], 'generators': [9, 216, 72, 162, 330, 324], 'label': '648.114.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1', '6.c1.a1', '6.c1.b1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 110346415
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2674, 2471, 2264, 3450, 3804, 3069, 3633, 6517], 'generators': [330, 216], 'label': '648.114.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['216.a1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '216.52', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.8', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346416
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '72.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '6.b1.a1', 'complements': ['9.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.b1.a1'], 'contains': ['216.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7283, 3462, 5583, 6687, 5573, 4086, 5386, 4447], 'generators': [504], 'label': '648.114.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.b1.a1', '36.b1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '648.114', 'quotient_action_image': '6.2', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110346417
    {'ambient': '648.114', 'aut_centralizer_order': 144, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.c1.a1'], 'contains': ['216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1273, -1, 3277, -1, 3128, -1, 2844, -1], 'generators': [326], 'label': '648.114.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.52', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346418
    {'ambient': '648.114', 'aut_centralizer_order': 216, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.d1.a1'], 'contains': ['216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8967, -1, 4688, -1, 4704, -1, 4562, -1], 'generators': [186], 'label': '648.114.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.114', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110346419
    {'ambient': '648.114', 'aut_centralizer_order': 72, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.a1'], 'contains': ['216.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1918, -1, 679, -1, 2597, -1, 1561, -1], 'generators': [182], 'label': '648.114.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.e1.a1', 'projective_image': '648.114', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346420
    {'ambient': '648.114', 'aut_centralizer_order': 18, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 162, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.b1.b1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5524, -1, 8108, -1, 8997, -1, 8137, -1], 'generators': [9, 162], 'label': '648.114.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '81.a1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110346421
    {'ambient': '648.114', 'aut_centralizer_order': 1296, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '54.a1.a1', '54.c1.a1', '54.c1.b1'], 'contains': ['216.a1.a1', '324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3132, 4659, 4195, 1853, 5139, 5036, 5026, 8148], 'generators': [324, 330], 'label': '648.114.108.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '54.a1.a1'], 'normal_contains': ['216.a1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.26', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346422
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.d1.a1', '54.b1.a1', '54.d1.a1', '54.d1.b1'], 'contains': ['216.b1.a1', '324.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7061, 6229, 6814, 5089, 6008, 5987, 6694, 5673], 'generators': [324, 216], 'label': '648.114.108.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '54.b1.a1'], 'normal_contains': ['216.b1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '324.64', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.9', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346423
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.e1.a1', '54.e1.a1'], 'contains': ['216.c1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3795, -1, 1909, -1, 4269, -1, 4018, -1], 'generators': [324, 546], 'label': '648.114.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346424
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '162.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.e1.a1', '81.a1.a1'], 'contains': ['324.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5847, 6114, 5875, 3544, 6443, 7148, 6140, 7360], 'generators': [162], 'label': '648.114.162.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': ['54.a1.a1', '54.b1.a1'], 'normal_contains': ['324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '324.64', 'quotient_action_image': '2.1', 'quotient_action_kernel': '81.4', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346425
    {'ambient': '648.114', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.162', 'aut_weyl_index': 9, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.e1.a1', '6.e1.b1', '9.b1.a1', '9.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4087, -1, 4730, -1, 5127, -1, 3848, -1], 'generators': [9, 216, 330, 162, 326, 324], 'label': '648.114.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110346426
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.d1.a1', '81.a1.a1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4880, -1, 7922, -1, 7699, -1, 7983, -1], 'generators': [9], 'label': '648.114.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '162.b1.a1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346427
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '54.d1.b1', '81.a1.a1'], 'contains': ['324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4880, -1, 7185, -1, 7699, -1, 7418, -1], 'generators': [243], 'label': '648.114.162.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '162.b1.b1', 'projective_image': '324.64', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346428
    {'ambient': '648.114', 'aut_centralizer_order': 1296, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.a1', '108.a1.a1'], 'contains': ['648.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2527, 2960, 3489, 2396, 4263, 3373, 4197, 7908], 'generators': [330], 'label': '648.114.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '108.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.52', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.52', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346429
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '216.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '108.b1.a1'], 'contains': ['648.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7061, 3939, 5382, 4890, 4704, 4323, 4562, 6090], 'generators': [216], 'label': '648.114.216.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.a1.a1', '72.b1.a1', '108.b1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '648.114', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.12', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110346430
    {'ambient': '648.114', 'aut_centralizer_order': 648, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.e1.a1', '108.c1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3044, -1, 1999, -1, 3816, -1, 3828, -1], 'generators': [546], 'label': '648.114.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '648.114', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346431
    {'ambient': '648.114', 'aut_centralizer_order': 1296, 'aut_label': '324.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '162.a1.a1', '162.b1.a1', '162.b1.b1'], 'contains': ['648.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 5160, 5875, 3544, 5573, 5749, 6140, 7119], 'generators': [324], 'label': '648.114.324.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.a1.a1', '108.b1.a1', '162.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '324.64', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.64', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346432
    {'ambient': '648.114', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '324.a1.a1'], 'contains': [], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3876, 3939, 4868, 3544, 4481, 4323, 4377, 7119], 'generators': [], 'label': '648.114.648.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['216.a1.a1', '216.b1.a1', '324.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.114', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110346433
    {'ambient': '648.114', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '54.12', 'aut_weyl_index': 24, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2821, 2780, 2598, 3555, 1232, 983, 1441, 7272], 'generators': [324, 216, 326, 504, 330], 'label': '648.114.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110346434
    {'ambient': '648.114', 'aut_centralizer_order': 36, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 36, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.e1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3419, 4080, 3113, 756, 3213, 3162, 2265, 9080], 'generators': [162, 330, 326, 216, 324], 'label': '648.114.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110346435
    {'ambient': '648.114', 'aut_centralizer_order': 108, 'aut_label': '6.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 108, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.a1.a1', '18.b1.a1', '18.g1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8257, 8327, 5266, 4620, 6033, 7518, 5431, 5465], 'generators': [162, 216, 330, 504, 324], 'label': '648.114.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}