Abstract group data - 1056.234

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 60, 10, 10, 22, 10, 10], 'aut_gens': [[1, 2, 4], [913, 530, 724], [241, 90, 100], [97, 354, 932], [577, 2, 332], [721, 882, 92], [1009, 530, 428], [673, 706, 284]], 'aut_group': None, 'aut_hash': 5956886757194812668, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 38, 'aut_perms': [266331215863713235960583880839863312785409366, 1024968708838121452580634609121503549236174, 8794121720420980470858496232119102031817770, 216786771555898282526519154106626743154185249, 435650134534312755403554705431689503306061422, 213888807652531873911883297464802923204654600, 431256716863865616530956684993431709353841854], 'aut_phi_ratio': 66.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [2, 12, 1, 1], [2, 132, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 12, 1, 1], [4, 22, 1, 1], [4, 132, 1, 1], [6, 2, 1, 1], [6, 22, 2, 1], [8, 2, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 22, 2, 1], [22, 2, 5, 1], [22, 24, 5, 1], [24, 2, 4, 1], [24, 22, 4, 1], [33, 4, 5, 1], [44, 4, 5, 1], [44, 24, 5, 1], [66, 4, 5, 1], [88, 4, 10, 1], [132, 4, 10, 1], [264, 4, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{66}.C_{10}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': None, 'autcentquo_hash': 4845733366138083661, 'autcentquo_nilpotent': False, 'autcentquo_order': 2640, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{11}:(C_2^2\\times C_{10}\\times S_3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [2, 12, 1], [2, 132, 1], [3, 2, 1], [4, 2, 1], [4, 12, 1], [4, 22, 1], [4, 132, 1], [6, 2, 1], [6, 22, 2], [8, 2, 2], [8, 22, 2], [11, 2, 5], [12, 2, 2], [12, 22, 2], [22, 2, 5], [22, 24, 5], [24, 2, 4], [24, 22, 4], [33, 4, 5], [44, 4, 5], [44, 24, 5], [66, 4, 5], [88, 4, 10], [132, 4, 10], [264, 4, 20]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '528.107', 'commutator_count': 1, 'commutator_label': '132.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 234, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['22.1', 1], ['48.6', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [2, 12, 1, 1], [2, 132, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 12, 1, 1], [4, 22, 1, 1], [4, 132, 1, 1], [6, 2, 1, 1], [6, 22, 1, 2], [8, 2, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 22, 2, 1], [22, 2, 5, 1], [22, 24, 5, 1], [24, 2, 4, 1], [24, 22, 4, 1], [33, 4, 5, 1], [44, 4, 5, 1], [44, 24, 5, 1], [66, 4, 5, 1], [88, 4, 10, 1], [132, 4, 10, 1], [264, 4, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 16128, 'exponent': 264, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[4, 0, 20]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '264.34', 'hash': 234, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 132, 'inner_gen_orders': [2, 2, 132], 'inner_gens': [[1, 2, 964], [1, 2, 620], [97, 442, 4]], 'inner_hash': 107, 'inner_nilpotent': False, 'inner_order': 528, 'inner_split': True, 'inner_tex': 'D_{11}\\times D_{12}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 42], [4, 55]], 'label': '1056.234', 'linC_count': 180, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 32, 'linQ_dim': 16, 'linQ_dim_count': 32, 'linR_count': 80, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24:D22', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 105, 'number_divisions': 30, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 136, 'number_subgroups': 1808, 'old_label': None, 'order': 1056, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 167], [3, 2], [4, 168], [6, 46], [8, 48], [11, 10], [12, 48], [22, 130], [24, 96], [33, 20], [44, 140], [66, 20], [88, 40], [132, 40], [264, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 2, 260], [529, 2, 964], [1, 2, 628]], 'outer_group': '40.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [720, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 4], [8, 2], [10, 4], [20, 3], [40, 2], [80, 1]], 'representations': {'PC': {'code': 46518043711503110055521243574627999032625724760000019, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -11, 20246, 6519, 58, 24419, 2586, 80, 24084, 6451, 102, 13445, 15468, 166, 47046]}, 'GLZN': {'d': 2, 'p': 66, 'gens': [12413213, 6612431, 433456, 287893, 6806977, 291149, 13131557]}, 'Perm': {'d': 22, 'gens': [51347038427613296047, 506875508305689600, 109743842217993984000, 163498485693134592000, 51347038427612928000, 6706022400, 4364893]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:D_{22}', 'transitive_degree': 264, '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: 111635332
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 234, 'group_order': 1056, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 111635349
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 234, 'group_order': 1056, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 528, 'size': 1}
  • id: 111635360
    {'aut_label': '2B', 'centralizer': '11.a1.a1', 'counter': 3, 'group_counter': 234, 'group_order': 1056, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 385, 'size': 11}
  • id: 111635371
    {'aut_label': '2B', 'centralizer': '11.a1.a1', 'counter': 4, 'group_counter': 234, 'group_order': 1056, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 721, 'size': 11}
  • id: 111635382
    {'aut_label': '2D', 'centralizer': '12.d1.a1', 'counter': 5, 'group_counter': 234, 'group_order': 1056, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 2, 'size': 12}
  • id: 111635393
    {'aut_label': '2E', 'centralizer': '132.b1.a1', 'counter': 6, 'group_counter': 234, 'group_order': 1056, 'label': '2E', 'order': 2, 'powers': [1, 6, 6, 6], 'representative': 267, 'size': 132}
  • id: 111635404
    {'aut_label': '3A', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 234, 'group_order': 1056, 'label': '3A', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 352, 'size': 2}
  • id: 111635415
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 8, 'group_counter': 234, 'group_order': 1056, 'label': '4A', 'order': 4, 'powers': [2, 8, 8, 8], 'representative': 792, 'size': 2}
  • id: 111635426
    {'aut_label': '4B', 'centralizer': '12.e1.a1', 'counter': 9, 'group_counter': 234, 'group_order': 1056, 'label': '4B', 'order': 4, 'powers': [2, 9, 9, 9], 'representative': 1014, 'size': 12}
  • id: 111635333
    {'aut_label': '4C', 'centralizer': '22.d1.a1', 'counter': 10, 'group_counter': 234, 'group_order': 1056, 'label': '4C', 'order': 4, 'powers': [2, 10, 10, 10], 'representative': 889, 'size': 22}
  • id: 111635340
    {'aut_label': '4D', 'centralizer': '132.d1.a1', 'counter': 11, 'group_counter': 234, 'group_order': 1056, 'label': '4D', 'order': 4, 'powers': [2, 11, 11, 11], 'representative': 7, 'size': 132}
  • id: 111635341
    {'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 234, 'group_order': 1056, 'label': '6A', 'order': 6, 'powers': [7, 2, 12, 12], 'representative': 880, 'size': 2}
  • id: 111635342
    {'aut_label': '6B', 'centralizer': '22.d1.a1', 'counter': 13, 'group_counter': 234, 'group_order': 1056, 'label': '6B', 'order': 6, 'powers': [7, 3, 13, 13], 'representative': 33, 'size': 22}
  • id: 111635343
    {'aut_label': '6B', 'centralizer': '22.d1.a1', 'counter': 14, 'group_counter': 234, 'group_order': 1056, 'label': '6C', 'order': 6, 'powers': [7, 4, 14, 14], 'representative': 17, 'size': 22}
  • id: 111635344
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 234, 'group_order': 1056, 'label': '8A1', 'order': 8, 'powers': [8, 15, 16, 15], 'representative': 132, 'size': 2}
  • id: 111635345
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 234, 'group_order': 1056, 'label': '8A-1', 'order': 8, 'powers': [8, 16, 15, 16], 'representative': 924, 'size': 2}
  • id: 111635346
    {'aut_label': '8B1', 'centralizer': '22.d1.a1', 'counter': 17, 'group_counter': 234, 'group_order': 1056, 'label': '8B1', 'order': 8, 'powers': [8, 17, 18, 17], 'representative': 973, 'size': 22}
  • id: 111635347
    {'aut_label': '8B1', 'centralizer': '22.d1.a1', 'counter': 18, 'group_counter': 234, 'group_order': 1056, 'label': '8B-1', 'order': 8, 'powers': [8, 18, 17, 18], 'representative': 181, 'size': 22}
  • id: 111635348
    {'aut_label': '11A1', 'centralizer': '2.d1.a1', 'counter': 19, 'group_counter': 234, 'group_order': 1056, 'label': '11A1', 'order': 11, 'powers': [20, 21, 23, 1], 'representative': 192, 'size': 2}
  • id: 111635350
    {'aut_label': '11A1', 'centralizer': '2.d1.a1', 'counter': 20, 'group_counter': 234, 'group_order': 1056, 'label': '11A2', 'order': 11, 'powers': [22, 23, 19, 1], 'representative': 384, 'size': 2}
  • id: 111635351
    {'aut_label': '11A1', 'centralizer': '2.d1.a1', 'counter': 21, 'group_counter': 234, 'group_order': 1056, 'label': '11A3', 'order': 11, 'powers': [23, 20, 22, 1], 'representative': 576, 'size': 2}
  • id: 111635352
    {'aut_label': '11A1', 'centralizer': '2.d1.a1', 'counter': 22, 'group_counter': 234, 'group_order': 1056, 'label': '11A4', 'order': 11, 'powers': [21, 19, 20, 1], 'representative': 768, 'size': 2}
  • id: 111635353
    {'aut_label': '11A1', 'centralizer': '2.d1.a1', 'counter': 23, 'group_counter': 234, 'group_order': 1056, 'label': '11A5', 'order': 11, 'powers': [19, 22, 21, 1], 'representative': 960, 'size': 2}
  • id: 111635354
    {'aut_label': '12A1', 'centralizer': '2.c1.a1', 'counter': 24, 'group_counter': 234, 'group_order': 1056, 'label': '12A1', 'order': 12, 'powers': [12, 8, 25, 24], 'representative': 968, 'size': 2}
  • id: 111635355
    {'aut_label': '12A1', 'centralizer': '2.c1.a1', 'counter': 25, 'group_counter': 234, 'group_order': 1056, 'label': '12A5', 'order': 12, 'powers': [12, 8, 24, 25], 'representative': 616, 'size': 2}
  • id: 111635356
    {'aut_label': '12B1', 'centralizer': '22.d1.a1', 'counter': 26, 'group_counter': 234, 'group_order': 1056, 'label': '12B1', 'order': 12, 'powers': [12, 10, 27, 26], 'representative': 9, 'size': 22}
  • id: 111635357
    {'aut_label': '12B1', 'centralizer': '22.d1.a1', 'counter': 27, 'group_counter': 234, 'group_order': 1056, 'label': '12B5', 'order': 12, 'powers': [12, 10, 26, 27], 'representative': 41, 'size': 22}
  • id: 111635358
    {'aut_label': '22A1', 'centralizer': '2.d1.a1', 'counter': 28, 'group_counter': 234, 'group_order': 1056, 'label': '22A1', 'order': 22, 'powers': [19, 29, 30, 2], 'representative': 624, 'size': 2}
  • id: 111635359
    {'aut_label': '22A1', 'centralizer': '2.d1.a1', 'counter': 29, 'group_counter': 234, 'group_order': 1056, 'label': '22A3', 'order': 22, 'powers': [21, 32, 31, 2], 'representative': 816, 'size': 2}
  • id: 111635361
    {'aut_label': '22A1', 'centralizer': '2.d1.a1', 'counter': 30, 'group_counter': 234, 'group_order': 1056, 'label': '22A5', 'order': 22, 'powers': [23, 31, 29, 2], 'representative': 1008, 'size': 2}
  • id: 111635362
    {'aut_label': '22A1', 'centralizer': '2.d1.a1', 'counter': 31, 'group_counter': 234, 'group_order': 1056, 'label': '22A7', 'order': 22, 'powers': [22, 28, 32, 2], 'representative': 144, 'size': 2}
  • id: 111635363
    {'aut_label': '22A1', 'centralizer': '2.d1.a1', 'counter': 32, 'group_counter': 234, 'group_order': 1056, 'label': '22A9', 'order': 22, 'powers': [20, 30, 28, 2], 'representative': 336, 'size': 2}
  • id: 111635364
    {'aut_label': '22B1', 'centralizer': '24.d1.a1', 'counter': 33, 'group_counter': 234, 'group_order': 1056, 'label': '22B1', 'order': 22, 'powers': [19, 34, 35, 5], 'representative': 98, 'size': 24}
  • id: 111635365
    {'aut_label': '22B1', 'centralizer': '24.d1.a1', 'counter': 34, 'group_counter': 234, 'group_order': 1056, 'label': '22B3', 'order': 22, 'powers': [21, 37, 36, 5], 'representative': 66, 'size': 24}
  • id: 111635366
    {'aut_label': '22B1', 'centralizer': '24.d1.a1', 'counter': 35, 'group_counter': 234, 'group_order': 1056, 'label': '22B5', 'order': 22, 'powers': [23, 36, 34, 5], 'representative': 482, 'size': 24}
  • id: 111635367
    {'aut_label': '22B1', 'centralizer': '24.d1.a1', 'counter': 36, 'group_counter': 234, 'group_order': 1056, 'label': '22B7', 'order': 22, 'powers': [22, 33, 37, 5], 'representative': 34, 'size': 24}
  • id: 111635368
    {'aut_label': '22B1', 'centralizer': '24.d1.a1', 'counter': 37, 'group_counter': 234, 'group_order': 1056, 'label': '22B9', 'order': 22, 'powers': [20, 35, 33, 5], 'representative': 18, 'size': 24}
  • id: 111635369
    {'aut_label': '24A1', 'centralizer': '2.c1.a1', 'counter': 38, 'group_counter': 234, 'group_order': 1056, 'label': '24A1', 'order': 24, 'powers': [24, 15, 40, 38], 'representative': 44, 'size': 2}
  • id: 111635370
    {'aut_label': '24A1', 'centralizer': '2.c1.a1', 'counter': 39, 'group_counter': 234, 'group_order': 1056, 'label': '24A-1', 'order': 24, 'powers': [24, 16, 41, 39], 'representative': 1012, 'size': 2}
  • id: 111635372
    {'aut_label': '24A1', 'centralizer': '2.c1.a1', 'counter': 40, 'group_counter': 234, 'group_order': 1056, 'label': '24A5', 'order': 24, 'powers': [25, 16, 38, 40], 'representative': 220, 'size': 2}
  • id: 111635373
    {'aut_label': '24A1', 'centralizer': '2.c1.a1', 'counter': 41, 'group_counter': 234, 'group_order': 1056, 'label': '24A-5', 'order': 24, 'powers': [25, 15, 39, 41], 'representative': 836, 'size': 2}
  • id: 111635374
    {'aut_label': '24B1', 'centralizer': '22.d1.a1', 'counter': 42, 'group_counter': 234, 'group_order': 1056, 'label': '24B1', 'order': 24, 'powers': [24, 17, 44, 42], 'representative': 5, 'size': 22}
  • id: 111635375
    {'aut_label': '24B1', 'centralizer': '22.d1.a1', 'counter': 43, 'group_counter': 234, 'group_order': 1056, 'label': '24B-1', 'order': 24, 'powers': [24, 18, 45, 43], 'representative': 53, 'size': 22}
  • id: 111635376
    {'aut_label': '24B1', 'centralizer': '22.d1.a1', 'counter': 44, 'group_counter': 234, 'group_order': 1056, 'label': '24B5', 'order': 24, 'powers': [25, 18, 42, 44], 'representative': 21, 'size': 22}
  • id: 111635377
    {'aut_label': '24B1', 'centralizer': '22.d1.a1', 'counter': 45, 'group_counter': 234, 'group_order': 1056, 'label': '24B-5', 'order': 24, 'powers': [25, 17, 43, 45], 'representative': 69, 'size': 22}
  • id: 111635378
    {'aut_label': '33A1', 'centralizer': '4.f1.a1', 'counter': 46, 'group_counter': 234, 'group_order': 1056, 'label': '33A1', 'order': 33, 'powers': [47, 23, 49, 7], 'representative': 32, 'size': 4}
  • id: 111635379
    {'aut_label': '33A1', 'centralizer': '4.f1.a1', 'counter': 47, 'group_counter': 234, 'group_order': 1056, 'label': '33A2', 'order': 33, 'powers': [48, 19, 46, 7], 'representative': 64, 'size': 4}
  • id: 111635380
    {'aut_label': '33A1', 'centralizer': '4.f1.a1', 'counter': 48, 'group_counter': 234, 'group_order': 1056, 'label': '33A4', 'order': 33, 'powers': [50, 20, 47, 7], 'representative': 128, 'size': 4}
  • id: 111635381
    {'aut_label': '33A1', 'centralizer': '4.f1.a1', 'counter': 49, 'group_counter': 234, 'group_order': 1056, 'label': '33A5', 'order': 33, 'powers': [46, 21, 50, 7], 'representative': 160, 'size': 4}
  • id: 111635383
    {'aut_label': '33A1', 'centralizer': '4.f1.a1', 'counter': 50, 'group_counter': 234, 'group_order': 1056, 'label': '33A8', 'order': 33, 'powers': [49, 22, 48, 7], 'representative': 256, 'size': 4}
  • id: 111635384
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 234, 'group_order': 1056, 'label': '44A1', 'order': 44, 'powers': [30, 52, 53, 8], 'representative': 24, 'size': 4}
  • id: 111635385
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 52, 'group_counter': 234, 'group_order': 1056, 'label': '44A3', 'order': 44, 'powers': [31, 55, 54, 8], 'representative': 72, 'size': 4}
  • id: 111635386
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 53, 'group_counter': 234, 'group_order': 1056, 'label': '44A5', 'order': 44, 'powers': [29, 54, 52, 8], 'representative': 120, 'size': 4}
  • id: 111635387
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 54, 'group_counter': 234, 'group_order': 1056, 'label': '44A7', 'order': 44, 'powers': [32, 51, 55, 8], 'representative': 168, 'size': 4}
  • id: 111635388
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 55, 'group_counter': 234, 'group_order': 1056, 'label': '44A9', 'order': 44, 'powers': [28, 53, 51, 8], 'representative': 216, 'size': 4}
  • id: 111635389
    {'aut_label': '44B1', 'centralizer': '24.f1.a1', 'counter': 56, 'group_counter': 234, 'group_order': 1056, 'label': '44B1', 'order': 44, 'powers': [28, 57, 58, 9], 'representative': 6, 'size': 24}
  • id: 111635390
    {'aut_label': '44B1', 'centralizer': '24.f1.a1', 'counter': 57, 'group_counter': 234, 'group_order': 1056, 'label': '44B3', 'order': 44, 'powers': [29, 60, 59, 9], 'representative': 102, 'size': 24}
  • id: 111635391
    {'aut_label': '44B1', 'centralizer': '24.f1.a1', 'counter': 58, 'group_counter': 234, 'group_order': 1056, 'label': '44B5', 'order': 44, 'powers': [30, 59, 57, 9], 'representative': 22, 'size': 24}
  • id: 111635392
    {'aut_label': '44B1', 'centralizer': '24.f1.a1', 'counter': 59, 'group_counter': 234, 'group_order': 1056, 'label': '44B7', 'order': 44, 'powers': [31, 56, 60, 9], 'representative': 294, 'size': 24}
  • id: 111635394
    {'aut_label': '44B1', 'centralizer': '24.f1.a1', 'counter': 60, 'group_counter': 234, 'group_order': 1056, 'label': '44B9', 'order': 44, 'powers': [32, 58, 56, 9], 'representative': 38, 'size': 24}
  • id: 111635395
    {'aut_label': '66A1', 'centralizer': '4.f1.a1', 'counter': 61, 'group_counter': 234, 'group_order': 1056, 'label': '66A1', 'order': 66, 'powers': [46, 30, 62, 12], 'representative': 16, 'size': 4}
  • id: 111635396
    {'aut_label': '66A1', 'centralizer': '4.f1.a1', 'counter': 62, 'group_counter': 234, 'group_order': 1056, 'label': '66A5', 'order': 66, 'powers': [49, 29, 65, 12], 'representative': 80, 'size': 4}
  • id: 111635397
    {'aut_label': '66A1', 'centralizer': '4.f1.a1', 'counter': 63, 'group_counter': 234, 'group_order': 1056, 'label': '66A7', 'order': 66, 'powers': [48, 32, 64, 12], 'representative': 112, 'size': 4}
  • id: 111635398
    {'aut_label': '66A1', 'centralizer': '4.f1.a1', 'counter': 64, 'group_counter': 234, 'group_order': 1056, 'label': '66A13', 'order': 66, 'powers': [47, 28, 61, 12], 'representative': 208, 'size': 4}
  • id: 111635399
    {'aut_label': '66A1', 'centralizer': '4.f1.a1', 'counter': 65, 'group_counter': 234, 'group_order': 1056, 'label': '66A19', 'order': 66, 'powers': [50, 31, 63, 12], 'representative': 304, 'size': 4}
  • id: 111635400
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 66, 'group_counter': 234, 'group_order': 1056, 'label': '88A1', 'order': 88, 'powers': [51, 68, 70, 15], 'representative': 12, 'size': 4}
  • id: 111635401
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 67, 'group_counter': 234, 'group_order': 1056, 'label': '88A-1', 'order': 88, 'powers': [51, 69, 71, 16], 'representative': 1044, 'size': 4}
  • id: 111635402
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 68, 'group_counter': 234, 'group_order': 1056, 'label': '88A3', 'order': 88, 'powers': [52, 74, 72, 15], 'representative': 36, 'size': 4}
  • id: 111635403
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 69, 'group_counter': 234, 'group_order': 1056, 'label': '88A-3', 'order': 88, 'powers': [52, 75, 73, 16], 'representative': 1020, 'size': 4}
  • id: 111635405
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 70, 'group_counter': 234, 'group_order': 1056, 'label': '88A5', 'order': 88, 'powers': [53, 72, 68, 16], 'representative': 60, 'size': 4}
  • id: 111635406
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 71, 'group_counter': 234, 'group_order': 1056, 'label': '88A-5', 'order': 88, 'powers': [53, 73, 69, 15], 'representative': 996, 'size': 4}
  • id: 111635407
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 72, 'group_counter': 234, 'group_order': 1056, 'label': '88A7', 'order': 88, 'powers': [54, 67, 74, 16], 'representative': 84, 'size': 4}
  • id: 111635408
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 73, 'group_counter': 234, 'group_order': 1056, 'label': '88A-7', 'order': 88, 'powers': [54, 66, 75, 15], 'representative': 972, 'size': 4}
  • id: 111635409
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 74, 'group_counter': 234, 'group_order': 1056, 'label': '88A9', 'order': 88, 'powers': [55, 71, 67, 15], 'representative': 108, 'size': 4}
  • id: 111635410
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 75, 'group_counter': 234, 'group_order': 1056, 'label': '88A-9', 'order': 88, 'powers': [55, 70, 66, 16], 'representative': 948, 'size': 4}
  • id: 111635411
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 76, 'group_counter': 234, 'group_order': 1056, 'label': '132A1', 'order': 132, 'powers': [61, 51, 77, 24], 'representative': 8, 'size': 4}
  • id: 111635412
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 77, 'group_counter': 234, 'group_order': 1056, 'label': '132A5', 'order': 132, 'powers': [62, 53, 81, 25], 'representative': 40, 'size': 4}
  • id: 111635413
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 78, 'group_counter': 234, 'group_order': 1056, 'label': '132A7', 'order': 132, 'powers': [63, 54, 79, 25], 'representative': 56, 'size': 4}
  • id: 111635414
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 79, 'group_counter': 234, 'group_order': 1056, 'label': '132A13', 'order': 132, 'powers': [64, 55, 84, 24], 'representative': 104, 'size': 4}
  • id: 111635416
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 80, 'group_counter': 234, 'group_order': 1056, 'label': '132A19', 'order': 132, 'powers': [65, 52, 83, 25], 'representative': 152, 'size': 4}
  • id: 111635417
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 81, 'group_counter': 234, 'group_order': 1056, 'label': '132A25', 'order': 132, 'powers': [65, 52, 78, 24], 'representative': 200, 'size': 4}
  • id: 111635418
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 82, 'group_counter': 234, 'group_order': 1056, 'label': '132A31', 'order': 132, 'powers': [64, 55, 76, 25], 'representative': 248, 'size': 4}
  • id: 111635419
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 83, 'group_counter': 234, 'group_order': 1056, 'label': '132A37', 'order': 132, 'powers': [63, 54, 82, 24], 'representative': 296, 'size': 4}
  • id: 111635420
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 84, 'group_counter': 234, 'group_order': 1056, 'label': '132A43', 'order': 132, 'powers': [61, 51, 85, 25], 'representative': 344, 'size': 4}
  • id: 111635421
    {'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 85, 'group_counter': 234, 'group_order': 1056, 'label': '132A49', 'order': 132, 'powers': [62, 53, 80, 24], 'representative': 392, 'size': 4}
  • id: 111635422
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 86, 'group_counter': 234, 'group_order': 1056, 'label': '264A1', 'order': 264, 'powers': [76, 66, 88, 38], 'representative': 4, 'size': 4}
  • id: 111635423
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 87, 'group_counter': 234, 'group_order': 1056, 'label': '264A-1', 'order': 264, 'powers': [76, 67, 89, 39], 'representative': 92, 'size': 4}
  • id: 111635424
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 88, 'group_counter': 234, 'group_order': 1056, 'label': '264A5', 'order': 264, 'powers': [77, 70, 96, 40], 'representative': 20, 'size': 4}
  • id: 111635425
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 89, 'group_counter': 234, 'group_order': 1056, 'label': '264A-5', 'order': 264, 'powers': [77, 71, 97, 41], 'representative': 68, 'size': 4}
  • id: 111635427
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 90, 'group_counter': 234, 'group_order': 1056, 'label': '264A7', 'order': 264, 'powers': [78, 72, 93, 40], 'representative': 116, 'size': 4}
  • id: 111635428
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 91, 'group_counter': 234, 'group_order': 1056, 'label': '264A-7', 'order': 264, 'powers': [78, 73, 92, 41], 'representative': 644, 'size': 4}
  • id: 111635429
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 92, 'group_counter': 234, 'group_order': 1056, 'label': '264A13', 'order': 264, 'powers': [79, 75, 102, 39], 'representative': 52, 'size': 4}
  • id: 111635430
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 93, 'group_counter': 234, 'group_order': 1056, 'label': '264A-13', 'order': 264, 'powers': [79, 74, 103, 38], 'representative': 388, 'size': 4}
  • id: 111635431
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 94, 'group_counter': 234, 'group_order': 1056, 'label': '264A19', 'order': 264, 'powers': [80, 68, 100, 41], 'representative': 164, 'size': 4}
  • id: 111635432
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 95, 'group_counter': 234, 'group_order': 1056, 'label': '264A-19', 'order': 264, 'powers': [80, 69, 101, 40], 'representative': 692, 'size': 4}
  • id: 111635433
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 96, 'group_counter': 234, 'group_order': 1056, 'label': '264A25', 'order': 264, 'powers': [81, 68, 90, 38], 'representative': 100, 'size': 4}
  • id: 111635434
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 97, 'group_counter': 234, 'group_order': 1056, 'label': '264A-25', 'order': 264, 'powers': [81, 69, 91, 39], 'representative': 340, 'size': 4}
  • id: 111635435
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 98, 'group_counter': 234, 'group_order': 1056, 'label': '264A31', 'order': 264, 'powers': [82, 75, 86, 40], 'representative': 212, 'size': 4}
  • id: 111635436
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 99, 'group_counter': 234, 'group_order': 1056, 'label': '264A-31', 'order': 264, 'powers': [82, 74, 87, 41], 'representative': 740, 'size': 4}
  • id: 111635334
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 100, 'group_counter': 234, 'group_order': 1056, 'label': '264A37', 'order': 264, 'powers': [83, 72, 99, 39], 'representative': 148, 'size': 4}
  • id: 111635335
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 101, 'group_counter': 234, 'group_order': 1056, 'label': '264A-37', 'order': 264, 'powers': [83, 73, 98, 38], 'representative': 292, 'size': 4}
  • id: 111635336
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 102, 'group_counter': 234, 'group_order': 1056, 'label': '264A43', 'order': 264, 'powers': [84, 66, 105, 41], 'representative': 260, 'size': 4}
  • id: 111635337
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 103, 'group_counter': 234, 'group_order': 1056, 'label': '264A-43', 'order': 264, 'powers': [84, 67, 104, 40], 'representative': 788, 'size': 4}
  • id: 111635338
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 104, 'group_counter': 234, 'group_order': 1056, 'label': '264A49', 'order': 264, 'powers': [85, 71, 95, 38], 'representative': 196, 'size': 4}
  • id: 111635339
    {'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 105, 'group_counter': 234, 'group_order': 1056, 'label': '264A-49', 'order': 264, 'powers': [85, 70, 94, 39], 'representative': 244, 'size': 4}
• 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: 4957110
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957121
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957132
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957134
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957135
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957136
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957137
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957138
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957139
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -1, 2, 0, 2, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957111
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 2, -2, 0, 2, 0, 2, -2, -2, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 4957112
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, -2, 0, -2, 0, 2, 2, 2, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 4957113
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, -1, 2, 0, -2, 0, -1, 1, 1, -2, -2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957114
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, -1, 2, 0, -2, 0, -1, 1, 1, 2, 2, -2, -2, 2, 2, 2, 2, 2, -1, -1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957115
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -1, 2, 0, 2, 0, -1, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957116
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2g', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -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], 'schur_index': 1}
  • id: 4957117
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2h', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -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], 'schur_index': 1}
  • id: 4957118
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2i', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -2, -4, 0, 4, 0, -2, 2, 2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 2, 2, -2, -2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 4957119
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2j', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -2, -4, 0, -4, 0, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 4957120
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2k', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, -4, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 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], 'schur_index': 1}
  • id: 4957122
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2l', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, -4, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 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], 'schur_index': 1}
  • id: 4957123
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2m', 'multiplicity': 5, 'nt': [11, 2], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 10, 0, 10, 10, 10, 0, 0, 10, 0, 0, 10, 10, 0, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 10, 10, 10, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4957124
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2n', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -10, 0, 10, 10, -10, 0, 0, 10, 0, 0, 10, 10, 0, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 10, 10, 10, 10, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4957125
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2o', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -10, 0, 10, 10, 10, 0, 0, 10, 0, 0, -10, -10, 0, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -10, -10, -10, -10, 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, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -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: 4957126
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.2p', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 10, 0, 10, 10, -10, 0, 0, 10, 0, 0, -10, -10, 0, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -10, -10, -10, -10, 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, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -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: 4957127
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4a', 'multiplicity': 5, 'nt': [33, 5], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 0, 0, -10, 20, 0, 0, 0, -10, 0, 0, 20, 20, 0, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, -10, -10, -10, -10, 0, 0, 0, 0, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4957128
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4b', 'multiplicity': 5, 'nt': [44, 12], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 0, 0, 20, -20, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -20, -20, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 4957129
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4c', 'multiplicity': 5, 'nt': [66, 0], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 0, 0, -10, 20, 0, 0, 0, -10, 0, 0, -20, -20, 0, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 10, 10, 10, 10, 0, 0, 0, 0, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4957130
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4d', 'multiplicity': 10, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 0, 0, 40, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 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], 'schur_index': 1}
  • id: 4957131
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4e', 'multiplicity': 10, 'nt': [132, 0], 'qdim': 40, 'qvalues': [40, 40, 0, 0, 0, 0, -20, -40, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 20, 20, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 4957133
    {'cdim': 4, 'counter': 30, 'faithful': True, 'group': '1056.234', 'group_order': 1056, 'image': None, 'label': '1056.234.4f', 'multiplicity': 20, 'nt': [264, 0], 'qdim': 80, 'qvalues': [80, -80, 0, 0, 0, 0, -40, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -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], '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: 8390257
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1056, 'label': '1056.234.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8390274
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 528, 'label': '1056.234.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8390285
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 528, 'label': '1056.234.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8390296
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 528, 'label': '1056.234.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8390307
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 528, 'label': '1056.234.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8390318
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 528, 'label': '1056.234.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8390329
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 528, 'label': '1056.234.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8390340
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 528, 'label': '1056.234.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8390351
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 176, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 176, 'label': '1056.234.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8390258
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 264, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 132, 'label': '1056.234.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[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]], [[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]], [[-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]]]}
  • id: 8390265
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 264, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 132, 'label': '1056.234.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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]], [[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]], [[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]], [[-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]]]}
  • id: 8390266
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 176, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 88, 'label': '1056.234.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8390267
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 176, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 88, 'label': '1056.234.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8390268
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 176, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 88, 'label': '1056.234.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8390269
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 132, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 66, 'label': '1056.234.2g1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 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]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 8390270
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 132, 'counter': 16, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 66, 'label': '1056.234.2g2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 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]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 8390271
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 132, 'counter': 17, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 66, 'label': '1056.234.2h1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 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]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 8390272
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 132, 'counter': 18, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 66, 'label': '1056.234.2h2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 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]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 8390273
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 88, 'counter': 19, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.a1', 'kernel_order': 44, 'label': '1056.234.2i1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-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: 8390275
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 88, 'counter': 20, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.a1', 'kernel_order': 44, 'label': '1056.234.2i2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[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: 8390276
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 88, 'counter': 21, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 44, 'label': '1056.234.2j1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-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: 8390277
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 88, 'counter': 22, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 44, 'label': '1056.234.2j2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[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: 8390278
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 23, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 22, 'label': '1056.234.2k1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]]]}
  • id: 8390279
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 24, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 22, 'label': '1056.234.2k2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]]]}
  • id: 8390280
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 25, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 22, 'label': '1056.234.2k3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
  • id: 8390281
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 26, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 22, 'label': '1056.234.2k4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
  • id: 8390282
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 27, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 22, 'label': '1056.234.2l1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]]]}
  • id: 8390283
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 28, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 22, 'label': '1056.234.2l2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]]]}
  • id: 8390284
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 29, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 22, 'label': '1056.234.2l3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
  • id: 8390286
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 44, 'counter': 30, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 22, 'label': '1056.234.2l4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
  • id: 8390287
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 31, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 48, 'label': '1056.234.2m1', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 8390288
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 32, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 48, 'label': '1056.234.2m2', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]]]}
  • id: 8390289
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 33, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 48, 'label': '1056.234.2m3', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 8390290
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 34, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 48, 'label': '1056.234.2m4', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 8390291
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 35, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 48, 'label': '1056.234.2m5', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]]]}
  • id: 8390292
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 36, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.234.2n1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 8390293
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 37, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.234.2n2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]]]}
  • id: 8390294
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 38, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.234.2n3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 8390295
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 39, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.234.2n4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 8390297
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 40, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.234.2n5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]]]}
  • id: 8390298
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.234.2o1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 8390299
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 42, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.234.2o2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]]]}
  • id: 8390300
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 43, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.234.2o3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 8390301
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 44, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.234.2o4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 8390302
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 45, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.234.2o5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]]]}
  • id: 8390303
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 24, 'label': '1056.234.2p1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 8390304
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 47, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 24, 'label': '1056.234.2p2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]]]}
  • id: 8390305
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 48, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 24, 'label': '1056.234.2p3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 8390306
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 49, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 24, 'label': '1056.234.2p4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 8390308
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 50, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 24, 'label': '1056.234.2p5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]]]}
  • id: 8390309
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '132.5', 'image_order': 132, 'indicator': 1, 'kernel': '132.a1.a1', 'kernel_order': 8, 'label': '1056.234.4a1', 'nt': [33, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 8390310
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '132.5', 'image_order': 132, 'indicator': 1, 'kernel': '132.a1.a1', 'kernel_order': 8, 'label': '1056.234.4a2', 'nt': [33, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]]]}
  • id: 8390311
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '132.5', 'image_order': 132, 'indicator': 1, 'kernel': '132.a1.a1', 'kernel_order': 8, 'label': '1056.234.4a3', 'nt': [33, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
  • id: 8390312
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '132.5', 'image_order': 132, 'indicator': 1, 'kernel': '132.a1.a1', 'kernel_order': 8, 'label': '1056.234.4a4', 'nt': [33, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 8390313
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 55, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '132.5', 'image_order': 132, 'indicator': 1, 'kernel': '132.a1.a1', 'kernel_order': 8, 'label': '1056.234.4a5', 'nt': [33, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]]]}
  • id: 8390314
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 56, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 6, 'label': '1056.234.4b1', 'nt': [44, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[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, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[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, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 8390315
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 57, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 6, 'label': '1056.234.4b2', 'nt': [44, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [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]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 4], [-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]]]}
  • id: 8390316
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 58, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 6, 'label': '1056.234.4b3', 'nt': [44, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [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]], [[0, 0]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 3], [-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8390317
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 59, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 6, 'label': '1056.234.4b4', 'nt': [44, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[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]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8390319
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 60, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 6, 'label': '1056.234.4b5', 'nt': [44, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-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]]]}
  • id: 8390320
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 61, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '264.34', 'image_order': 264, 'indicator': 1, 'kernel': '264.a1.a1', 'kernel_order': 4, 'label': '1056.234.4c1', 'nt': [66, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 8390321
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 62, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '264.34', 'image_order': 264, 'indicator': 1, 'kernel': '264.a1.a1', 'kernel_order': 4, 'label': '1056.234.4c2', 'nt': [66, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]]]}
  • id: 8390322
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 63, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '264.34', 'image_order': 264, 'indicator': 1, 'kernel': '264.a1.a1', 'kernel_order': 4, 'label': '1056.234.4c3', 'nt': [66, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
  • id: 8390323
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 64, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '264.34', 'image_order': 264, 'indicator': 1, 'kernel': '264.a1.a1', 'kernel_order': 4, 'label': '1056.234.4c4', 'nt': [66, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 8390324
    {'center': '132.a1.a1', 'center_index': 132, 'center_order': 8, 'counter': 65, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '264.34', 'image_order': 264, 'indicator': 1, 'kernel': '264.a1.a1', 'kernel_order': 4, 'label': '1056.234.4c5', 'nt': [66, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]]]}
  • id: 8390325
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d1', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]]]}
  • id: 8390335
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 75, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d10', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[-2, 16], [-2, -16]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]]]}
  • id: 8390326
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d2', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]]]}
  • id: 8390327
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d3', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16], [-2, -16]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[2, 20], [2, -20]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]]]}
  • id: 8390328
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d4', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16], [-2, -16]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[2, 20], [2, -20]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]]]}
  • id: 8390330
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d5', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 4], [2, -4]], [[2, 20], [2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]]]}
  • id: 8390331
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 71, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d6', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[-2, 12], [-2, -12]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 4], [2, -4]], [[2, 20], [2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]]]}
  • id: 8390332
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 72, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d7', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[2, 12], [2, -12]], [[-2, 16], [-2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]]]}
  • id: 8390333
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 73, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d8', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8], [-2, -8]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[2, 12], [2, -12]], [[-2, 16], [-2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[-2, 4], [-2, -4]], [[2, 16], [2, -16]], [[2, 8], [2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]]]}
  • id: 8390334
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 74, 'cyclotomic_n': 88, 'dim': 4, 'faithful': False, 'field': [32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '352.108', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 3, 'label': '1056.234.4d9', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[2, 8], [2, -8]], [[2, 16], [2, -16]], [[-2, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 12], [2, -12]], [[2, 20], [2, -20]], [[-2, 16], [-2, -16]], [[-2, 8], [-2, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, 33]], [[-2, 11], [-2, 33]], [[2, 11], [2, 33]], [[2, 11], [2, 33]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 16], [2, -16]], [[-2, 12], [-2, -12]], [[-2, 20], [-2, -20]], [[2, 8], [2, -8]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[2, 4], [2, -4]], [[-2, 8], [-2, -8]], [[-2, 16], [-2, -16]], [[2, 12], [2, -12]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [1, 21], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [1, 13], [1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 7], [-1, 15], [-1, 29], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [-1, 13], [-1, 31], [1, 35]], [[1, 5], [-1, 17], [-1, 27], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 19], [-1, 21], [-1, 29], [1, 33], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 19], [1, 21], [1, 29], [-1, 33], [1, 37]], [[-1, 5], [1, 17], [1, 27], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [-1, 21], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [1, 37]]]}
  • id: 8390336
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 76, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e1', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 30], [1, -30]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[-2, 24], [-2, -24]], [[2, 18], [2, -18]], [[2, 30], [2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 30], [-1, -30]], [[-1, 6], [-1, -6]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]]]}
  • id: 8390346
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 85, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e10', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[-2, 24], [-2, -24]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 30], [2, -30]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 30], [-1, -30]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[2, 5], [2, 17], [-1, 27], [-1, 39]]]}
  • id: 8390337
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 77, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e2', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 30], [1, -30]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[-2, 24], [-2, -24]], [[2, 18], [2, -18]], [[2, 30], [2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 30], [-1, -30]], [[-1, 6], [-1, -6]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]]]}
  • id: 8390338
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 78, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e3', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 24], [-1, -24]], [[2, 30], [2, -30]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[-2, 24], [-2, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 24], [1, -24]], [[-1, 18], [-1, -18]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]]]}
  • id: 8390339
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 79, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e4', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 24], [-1, -24]], [[2, 30], [2, -30]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[-2, 24], [-2, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 24], [1, -24]], [[-1, 18], [-1, -18]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]]]}
  • id: 8390341
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 80, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e5', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 30], [1, -30]], [[1, 18], [1, -18]], [[2, 6], [2, -6]], [[2, 30], [2, -30]], [[-2, 12], [-2, -12]], [[-2, 24], [-2, -24]], [[2, 18], [2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 24], [1, -24]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 30], [-1, -30]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]]]}
  • id: 8390342
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 81, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e6', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 30], [1, -30]], [[1, 18], [1, -18]], [[2, 6], [2, -6]], [[2, 30], [2, -30]], [[-2, 12], [-2, -12]], [[-2, 24], [-2, -24]], [[2, 18], [2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 24], [1, -24]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 30], [-1, -30]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]]]}
  • id: 8390343
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 82, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e7', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 24], [-1, -24]], [[-1, 12], [-1, -12]], [[2, 18], [2, -18]], [[-2, 24], [-2, -24]], [[2, 30], [2, -30]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 12], [1, -12]], [[1, 24], [1, -24]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]]]}
  • id: 8390344
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 83, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e8', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 30], [-2, -30]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 24], [2, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 24], [-1, -24]], [[-1, 12], [-1, -12]], [[2, 18], [2, -18]], [[-2, 24], [-2, -24]], [[2, 30], [2, -30]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 30], [-1, -30]], [[1, 12], [1, -12]], [[1, 24], [1, -24]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]]]}
  • id: 8390345
    {'center': '264.a1.a1', 'center_index': 264, 'center_order': 4, 'counter': 84, 'cyclotomic_n': 132, 'dim': 4, 'faithful': False, 'field': [1, -24, 66, 236, -265, -194, 142, 38, -22, -2, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '528.107', 'image_order': 528, 'indicator': 1, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.234.4e9', 'nt': [132, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 24], [2, -24]], [[-2, 6], [-2, -6]], [[-2, 30], [-2, -30]], [[-2, 18], [-2, -18]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[-2, 30], [-2, -30]], [[2, 24], [2, -24]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[-2, 11], [-2, -11]], [[2, 11], [2, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[1, 30], [1, -30]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[-2, 24], [-2, -24]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 30], [2, -30]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[-1, 24], [-1, -24]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 24], [1, -24]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[1, 24], [1, -24]], [[-1, 30], [-1, -30]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[1, 9], [1, 13], [-2, 31], [1, 35]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[-2, 5], [-2, 17], [1, 27], [1, 39]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-1, 1], [1, 7], [1, 9], [-1, 13], [-1, 15], [2, 19], [1, 21], [1, 23], [-2, 25], [-1, 27], [-1, 29], [1, 33], [1, 35], [-1, 39]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[2, 5], [2, 17], [-1, 27], [-1, 39]], [[1, 7], [1, 15], [1, 29], [-2, 37]], [[1, 1], [-2, 5], [-2, 7], [2, 11], [2, 13], [-2, 17], [-2, 19], [-1, 21], [-1, 23], [2, 25], [2, 27], [-2, 31], [-2, 33], [2, 37], [2, 39]], [[1, 1], [-1, 7], [-1, 9], [1, 13], [1, 15], [-2, 19], [-1, 21], [-1, 23], [2, 25], [1, 27], [1, 29], [-1, 33], [-1, 35], [1, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 1], [2, 5], [2, 7], [-2, 11], [-2, 13], [2, 17], [2, 19], [1, 21], [1, 23], [-2, 25], [-2, 27], [2, 31], [2, 33], [-2, 37], [-2, 39]], [[-1, 9], [-1, 13], [2, 31], [-1, 35]], [[-1, 7], [-1, 15], [-1, 29], [2, 37]], [[-2, 5], [-2, 17], [1, 27], [1, 39]]]}
  • id: 8390347
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  • id: 8390357
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 95, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f10', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 60], [-2, -60]], [[-2, 12], [-2, -12]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[2, 60], [2, -60]], 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  • id: 8390358
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  • id: 8390359
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 97, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f12', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 60], [-2, -60]], [[-2, 12], [-2, -12]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[2, 22], [2, -22]], [[-2, 22], [-2, -22]], [[0, 0]], [[0, 0]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[2, 60], [2, -60]], 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  • id: 8390360
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 98, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f13', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 11], [-2, 33], [-2, 55]], [[-2, 11], [2, 33], [2, 55]], [[0, 0]], [[0, 0]], [[2, 48], [2, -48]], [[-2, 36], [-2, -36]], [[2, 24], [2, -24]], [[-2, 12], [-2, -12]], [[-2, 60], [-2, -60]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[-2, 24], [-2, -24]], [[2, 60], [2, -60]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-2, 48], [-2, -48]], 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  • id: 8390361
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  • id: 8390259
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 100, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f15', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 11], [-2, 33], [-2, 55]], [[-2, 11], [2, 33], [2, 55]], [[0, 0]], [[0, 0]], [[2, 48], [2, -48]], [[-2, 36], [-2, -36]], [[2, 24], [2, -24]], [[-2, 12], [-2, -12]], [[-2, 60], [-2, -60]], [[2, 22], [2, -22]], [[-2, 22], [-2, -22]], [[0, 0]], [[0, 0]], [[-2, 24], [-2, -24]], [[2, 60], [2, -60]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-2, 48], [-2, -48]], 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  • id: 8390260
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  • id: 8390261
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 102, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f17', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 11], [-2, 33], [-2, 55]], [[-2, 11], [2, 33], [2, 55]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[2, 48], [2, -48]], [[-2, 12], [-2, -12]], [[-2, 60], [-2, -60]], [[-2, 36], [-2, -36]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[2, 60], [2, -60]], [[-2, 48], [-2, -48]], [[-2, 24], [-2, -24]], 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  • id: 8390262
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 103, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f18', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[2, 48], [2, -48]], [[-2, 12], [-2, -12]], [[-2, 60], [-2, -60]], [[-2, 36], [-2, -36]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[2, 60], [2, -60]], [[-2, 48], [-2, -48]], [[-2, 24], [-2, -24]], 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  • id: 8390263
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  • id: 8390348
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 87, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f2', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 24], [2, -24]], [[-2, 60], [-2, -60]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[2, 60], [2, -60]], [[-2, 48], [-2, -48]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[2, 12], [2, -12]], 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  • id: 8390264
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  • id: 8390349
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 88, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f3', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 11], [-2, 33], [-2, 55]], [[-2, 11], [2, 33], [2, 55]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 24], [2, -24]], [[-2, 60], [-2, -60]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[2, 22], [2, -22]], [[-2, 22], [-2, -22]], [[0, 0]], [[0, 0]], [[2, 60], [2, -60]], [[-2, 48], [-2, -48]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[2, 12], [2, -12]], 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  • id: 8390350
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 89, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f4', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 24], [2, -24]], [[-2, 60], [-2, -60]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[2, 22], [2, -22]], [[-2, 22], [-2, -22]], [[0, 0]], [[0, 0]], [[2, 60], [2, -60]], [[-2, 48], [-2, -48]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[2, 12], [2, -12]], 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  • id: 8390352
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  • id: 8390353
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 91, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f6', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 36], [-2, -36]], [[-2, 60], [-2, -60]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[-2, 12], [-2, -12]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[-2, 24], [-2, -24]], [[2, 60], [2, -60]], [[2, 36], [2, -36]], 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  • id: 8390354
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10], [2, 14], [-2, 22], [-2, 26], [2, 34], [2, 38], [1, 42], [1, 46], [-2, 50], [-2, 54], [2, 62], [2, 66], [-2, 74], [-2, 78]], [[1, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [-2, 38], [-1, 42], [-1, 46], [2, 50], [2, 54], [-2, 62], [-2, 66], [2, 74], [2, 78]], [[2, 10], [2, 34], [-1, 54], [-1, 78]], [[1, 18], [1, 26], [-2, 62], [1, 70]], [[-1, 14], [-1, 30], [-1, 58], [2, 74]], [[1, 13], [-1, 31], [-1, 53], [-1, 57], [-1, 79]], [[1, 9], [1, 13], [-1, 31], [-1, 35], [-1, 53], [1, 75]], [[1, 3], [1, 7], [-1, 15], [-1, 19], [1, 27], [1, 31], [-1, 39], [-1, 43], [-1, 47], [-1, 49], [1, 55], [1, 59], [1, 61], [-1, 67], [1, 79]], [[-1, 3], [-1, 7], [1, 15], [1, 19], [-1, 27], [-1, 31], [1, 39], [1, 43], [1, 47], [1, 49], [-1, 55], [-1, 59], [-1, 61], [1, 67], [-1, 79]], [[-1, 1], [-1, 5], [1, 7], [1, 13], [-1, 15], [1, 17], [-1, 25], [1, 41], [1, 45], [-1, 53], [-1, 57], [1, 59], [1, 65], [1, 69], [-1, 77]], [[1, 1], [-1, 43], [-1, 45], [-1, 65], [-1, 67]], [[1, 7], [-1, 37], [-1, 51], [1, 59], [1, 73]], [[-1, 1], [-1, 3], [1, 11], [1, 15], [-1, 21], [-1, 27], [1, 35], [1, 39], [1, 43], [-1, 51], [-1, 55], [1, 63], [1, 65], [1, 67], [-1, 75], [-1, 79]], [[-1, 13], [1, 31], [1, 53], [1, 57], [1, 79]], [[-1, 3], [1, 19], [-1, 25], [1, 41], [1, 47], [1, 69]], [[1, 1], [1, 5], [-1, 7], [-1, 13], [1, 15], [-1, 17], [1, 25], [-1, 41], [-1, 45], [1, 53], [1, 57], [-1, 59], [-1, 65], [-1, 69], [1, 77]], [[-1, 1], [1, 43], [1, 45], [1, 65], [1, 67]], [[1, 3], [-1, 19], [1, 25], [-1, 41], [-1, 47], [-1, 69]], [[-1, 9], [-1, 13], [1, 31], [1, 35], [1, 53], [-1, 75]], [[-1, 3], [1, 5], [-1, 7], [1, 15], [-1, 17], [1, 19], [-1, 31], [1, 43], [1, 47], [-1, 55], [-1, 59], [1, 67], [-1, 79]], [[1, 1], [-1, 9], [-1, 13], [1, 19], [1, 21], [-1, 33], [-1, 37], [1, 47], [1, 49], [1, 53], [-1, 61], [-1, 63], [-1, 65], [1, 73], [1, 77]], [[-1, 1], [1, 9], [1, 13], [-1, 19], [-1, 21], [1, 33], [1, 37], [-1, 47], [-1, 49], [-1, 53], [1, 61], [1, 63], [1, 65], [-1, 73], [-1, 77]], [[1, 3], [-1, 5], [1, 7], [-1, 15], [1, 17], [-1, 19], [1, 31], [-1, 43], [-1, 47], [1, 55], [1, 59], [-1, 67], [1, 79]], [[1, 1], [1, 3], [-1, 11], [-1, 15], [1, 21], [1, 27], [-1, 35], [-1, 39], [-1, 43], [1, 51], [1, 55], [-1, 63], [-1, 65], [-1, 67], [1, 75], [1, 79]], [[-1, 7], [1, 37], [1, 51], [-1, 59], [-1, 73]]]}
  • id: 8390355
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 93, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f8', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [2, 55]], [[2, 11], [-2, 33], [-2, 55]], [[0, 0]], [[0, 0]], [[-2, 36], [-2, -36]], [[-2, 60], [-2, -60]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[-2, 12], [-2, -12]], [[2, 22], [2, -22]], [[-2, 22], [-2, -22]], [[0, 0]], [[0, 0]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[-2, 24], [-2, -24]], [[2, 60], [2, -60]], [[2, 36], [2, -36]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 55], [-2, 77]], [[2, 11], [-2, 33], [2, 77]], [[2, 55], [2, 77]], [[-2, 11], [2, 33], [-2, 77]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 60], [1, -60]], [[1, 12], [1, -12]], [[-1, 24], [-1, -24]], [[1, 36], [1, -36]], [[-1, 48], [-1, -48]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 24], [1, -24]], [[1, 48], [1, -48]], [[-1, 36], [-1, -36]], [[-1, 60], [-1, -60]], [[-1, 12], [-1, -12]], [[-1, 9], [1, 35], [-1, 57], [-1, 75], [-1, 79]], [[1, 5], [-1, 17], [1, 27], [-1, 39], [-1, 49], [1, 61]], [[-1, 1], [-1, 5], [1, 13], [-1, 15], [1, 17], [-1, 25], [1, 37], [1, 41], [1, 45], [1, 51], [-1, 53], [-1, 57], [1, 65], [1, 69], [-1, 73], [-1, 77]], [[1, 1], [1, 3], [-1, 9], [-1, 13], [1, 21], [1, 25], [-1, 33], [-1, 37], [-1, 41], [1, 49], [1, 53], [-1, 61], [-1, 63], [-1, 65], [-1, 69], [1, 73], [1, 77]], [[1, 3], [-1, 11], [-1, 15], [1, 21], [1, 27], [-1, 35], [-1, 39], [1, 45], [1, 51], [1, 55], [-1, 63], [1, 75], [1, 79]], [[-1, 5], [1, 17], [-1, 27], [1, 39], [1, 49], [-1, 61]], [[1, 1], [1, 5], [-1, 13], [1, 15], [-1, 17], [1, 25], [-1, 37], [-1, 41], [-1, 45], [-1, 51], [1, 53], [1, 57], [-1, 65], [-1, 69], [1, 73], [1, 77]], [[-1, 1], [-1, 3], [1, 9], [1, 13], [-1, 21], [-1, 25], [1, 33], [1, 37], [1, 41], [-1, 49], [-1, 53], [1, 61], [1, 63], [1, 65], [1, 69], [-1, 73], [-1, 77]], [[-1, 3], [1, 11], [1, 15], [-1, 21], [-1, 27], [1, 35], [1, 39], [-1, 45], [-1, 51], [-1, 55], [1, 63], [-1, 75], [-1, 79]], [[1, 9], [-1, 35], [1, 57], [1, 75], [1, 79]], [[-1, 2], [1, 14], [1, 18], [-1, 26], [-1, 30], [2, 38], [1, 42], [1, 46], [-2, 50], [-1, 54], [-1, 58], [1, 66], [1, 70], [-1, 78]], [[1, 14], [1, 30], [1, 58], [-2, 74]], [[-1, 18], [-1, 26], [2, 62], [-1, 70]], [[-2, 10], [-2, 34], [1, 54], [1, 78]], [[1, 2], [-1, 14], [-1, 18], [1, 26], [1, 30], [-2, 38], [-1, 42], [-1, 46], [2, 50], [1, 54], [1, 58], [-1, 66], [-1, 70], [1, 78]], [[-1, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [2, 38], [1, 42], [1, 46], [-2, 50], [-2, 54], [2, 62], [2, 66], [-2, 74], [-2, 78]], [[1, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [-2, 38], [-1, 42], [-1, 46], [2, 50], [2, 54], [-2, 62], [-2, 66], [2, 74], [2, 78]], [[2, 10], [2, 34], [-1, 54], [-1, 78]], [[1, 18], [1, 26], [-2, 62], [1, 70]], [[-1, 14], [-1, 30], [-1, 58], [2, 74]], [[-1, 13], [1, 31], [1, 53], [1, 57], [1, 79]], [[-1, 9], [-1, 13], [1, 31], [1, 35], [1, 53], [-1, 75]], [[-1, 3], [-1, 7], [1, 15], [1, 19], [-1, 27], [-1, 31], [1, 39], [1, 43], [1, 47], [1, 49], [-1, 55], [-1, 59], [-1, 61], [1, 67], [-1, 79]], [[1, 3], [1, 7], [-1, 15], [-1, 19], [1, 27], [1, 31], [-1, 39], [-1, 43], [-1, 47], [-1, 49], [1, 55], [1, 59], [1, 61], [-1, 67], [1, 79]], [[1, 1], [1, 5], [-1, 7], [-1, 13], [1, 15], [-1, 17], [1, 25], [-1, 41], [-1, 45], [1, 53], [1, 57], [-1, 59], [-1, 65], [-1, 69], [1, 77]], [[-1, 1], [1, 43], [1, 45], [1, 65], [1, 67]], [[-1, 7], [1, 37], [1, 51], [-1, 59], [-1, 73]], [[1, 1], [1, 3], [-1, 11], [-1, 15], [1, 21], [1, 27], [-1, 35], [-1, 39], [-1, 43], [1, 51], [1, 55], [-1, 63], [-1, 65], [-1, 67], [1, 75], [1, 79]], [[1, 13], [-1, 31], [-1, 53], [-1, 57], [-1, 79]], [[1, 3], [-1, 19], [1, 25], [-1, 41], [-1, 47], [-1, 69]], [[-1, 1], [-1, 5], [1, 7], [1, 13], [-1, 15], [1, 17], [-1, 25], [1, 41], [1, 45], [-1, 53], [-1, 57], [1, 59], [1, 65], [1, 69], [-1, 77]], [[1, 1], [-1, 43], [-1, 45], [-1, 65], [-1, 67]], [[-1, 3], [1, 19], [-1, 25], [1, 41], [1, 47], [1, 69]], [[1, 9], [1, 13], [-1, 31], [-1, 35], [-1, 53], [1, 75]], [[1, 3], [-1, 5], [1, 7], [-1, 15], [1, 17], [-1, 19], [1, 31], [-1, 43], [-1, 47], [1, 55], [1, 59], [-1, 67], [1, 79]], [[-1, 1], [1, 9], [1, 13], [-1, 19], [-1, 21], [1, 33], [1, 37], [-1, 47], [-1, 49], [-1, 53], [1, 61], [1, 63], [1, 65], [-1, 73], [-1, 77]], [[1, 1], [-1, 9], [-1, 13], [1, 19], [1, 21], [-1, 33], [-1, 37], [1, 47], [1, 49], [1, 53], [-1, 61], [-1, 63], [-1, 65], [1, 73], [1, 77]], [[-1, 3], [1, 5], [-1, 7], [1, 15], [-1, 17], [1, 19], [-1, 31], [1, 43], [1, 47], [-1, 55], [-1, 59], [1, 67], [-1, 79]], [[-1, 1], [-1, 3], [1, 11], [1, 15], [-1, 21], [-1, 27], [1, 35], [1, 39], [1, 43], [-1, 51], [-1, 55], [1, 63], [1, 65], [1, 67], [-1, 75], [-1, 79]], [[1, 7], [-1, 37], [-1, 51], [1, 59], [1, 73]]]}
  • id: 8390356
    {'center': '528.a1.a1', 'center_index': 528, 'center_order': 2, 'counter': 94, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [1, 0, 60, 0, 715, 0, 3556, 0, 8851, 0, 11664, 0, 8104, 0, 2828, 0, 473, 0, 36, 0, 1], 'group': '1056.234', 'group_counter': 234, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.234', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.234.4f9', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 11], [-2, 33], [-2, 55]], [[-2, 11], [2, 33], [2, 55]], [[0, 0]], [[0, 0]], [[-2, 60], [-2, -60]], [[-2, 12], [-2, -12]], [[-2, 36], [-2, -36]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[-2, 22], [-2, -22]], [[2, 22], [2, -22]], [[0, 0]], [[0, 0]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[2, 60], [2, -60]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11], [2, 33], [-2, 77]], [[2, 55], [2, 77]], [[2, 11], [-2, 33], [2, 77]], [[-2, 55], [-2, 77]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[-1, 24], [-1, -24]], [[-1, 48], [-1, -48]], [[1, 60], [1, -60]], [[1, 36], [1, -36]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 48], [1, -48]], [[-1, 36], [-1, -36]], [[-1, 60], [-1, -60]], [[-1, 12], [-1, -12]], [[1, 24], [1, -24]], [[-1, 1], [-1, 5], [1, 13], [-1, 15], [1, 17], [-1, 25], [1, 37], [1, 41], [1, 45], [1, 51], [-1, 53], [-1, 57], [1, 65], [1, 69], [-1, 73], [-1, 77]], [[1, 3], [-1, 11], [-1, 15], [1, 21], [1, 27], [-1, 35], [-1, 39], [1, 45], [1, 51], [1, 55], [-1, 63], [1, 75], [1, 79]], [[-1, 1], [-1, 3], [1, 9], [1, 13], [-1, 21], [-1, 25], [1, 33], [1, 37], [1, 41], [-1, 49], [-1, 53], [1, 61], [1, 63], [1, 65], [1, 69], [-1, 73], [-1, 77]], [[-1, 5], [1, 17], [-1, 27], [1, 39], [1, 49], [-1, 61]], [[1, 9], [-1, 35], [1, 57], [1, 75], [1, 79]], [[-1, 3], [1, 11], [1, 15], [-1, 21], [-1, 27], [1, 35], [1, 39], [-1, 45], [-1, 51], [-1, 55], [1, 63], [-1, 75], [-1, 79]], [[1, 1], [1, 3], [-1, 9], [-1, 13], [1, 21], [1, 25], [-1, 33], [-1, 37], [-1, 41], [1, 49], [1, 53], [-1, 61], [-1, 63], [-1, 65], [-1, 69], [1, 73], [1, 77]], [[1, 5], [-1, 17], [1, 27], [-1, 39], [-1, 49], [1, 61]], [[-1, 9], [1, 35], [-1, 57], [-1, 75], [-1, 79]], [[1, 1], [1, 5], [-1, 13], [1, 15], [-1, 17], [1, 25], [-1, 37], [-1, 41], [-1, 45], [-1, 51], [1, 53], [1, 57], [-1, 65], [-1, 69], [1, 73], [1, 77]], [[-2, 10], [-2, 34], [1, 54], [1, 78]], [[1, 2], [-1, 14], [-1, 18], [1, 26], [1, 30], [-2, 38], [-1, 42], [-1, 46], [2, 50], [1, 54], [1, 58], [-1, 66], [-1, 70], [1, 78]], [[-1, 14], [-1, 30], [-1, 58], [2, 74]], [[1, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [-2, 38], [-1, 42], [-1, 46], [2, 50], [2, 54], [-2, 62], [-2, 66], [2, 74], [2, 78]], [[2, 10], [2, 34], [-1, 54], [-1, 78]], [[-1, 18], [-1, 26], [2, 62], [-1, 70]], [[1, 18], [1, 26], [-2, 62], [1, 70]], [[-1, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [2, 38], [1, 42], [1, 46], [-2, 50], [-2, 54], [2, 62], [2, 66], [-2, 74], [-2, 78]], [[1, 14], [1, 30], [1, 58], [-2, 74]], [[-1, 2], [1, 14], [1, 18], [-1, 26], [-1, 30], [2, 38], [1, 42], [1, 46], [-2, 50], [-1, 54], [-1, 58], [1, 66], [1, 70], [-1, 78]], [[1, 7], [-1, 37], [-1, 51], [1, 59], [1, 73]], [[-1, 1], [-1, 5], [1, 7], [1, 13], [-1, 15], [1, 17], [-1, 25], [1, 41], [1, 45], [-1, 53], [-1, 57], [1, 59], [1, 65], [1, 69], [-1, 77]], [[1, 1], [-1, 43], [-1, 45], [-1, 65], [-1, 67]], [[-1, 1], [1, 43], [1, 45], [1, 65], [1, 67]], [[1, 1], [-1, 9], [-1, 13], [1, 19], [1, 21], [-1, 33], [-1, 37], [1, 47], [1, 49], [1, 53], [-1, 61], [-1, 63], [-1, 65], [1, 73], [1, 77]], [[1, 9], [1, 13], [-1, 31], [-1, 35], [-1, 53], [1, 75]], [[-1, 3], [1, 19], [-1, 25], [1, 41], [1, 47], [1, 69]], [[-1, 13], [1, 31], [1, 53], [1, 57], [1, 79]], [[-1, 7], [1, 37], [1, 51], [-1, 59], [-1, 73]], [[-1, 3], [-1, 7], [1, 15], [1, 19], [-1, 27], [-1, 31], [1, 39], [1, 43], [1, 47], [1, 49], [-1, 55], [-1, 59], [-1, 61], [1, 67], [-1, 79]], [[-1, 1], [1, 9], [1, 13], [-1, 19], [-1, 21], [1, 33], [1, 37], [-1, 47], [-1, 49], [-1, 53], [1, 61], [1, 63], [1, 65], [-1, 73], [-1, 77]], [[-1, 9], [-1, 13], [1, 31], [1, 35], [1, 53], [-1, 75]], [[1, 3], [1, 7], [-1, 15], [-1, 19], [1, 27], [1, 31], [-1, 39], [-1, 43], [-1, 47], [-1, 49], [1, 55], [1, 59], [1, 61], [-1, 67], [1, 79]], [[1, 1], [1, 5], [-1, 7], [-1, 13], [1, 15], [-1, 17], [1, 25], [-1, 41], [-1, 45], [1, 53], [1, 57], [-1, 59], [-1, 65], [-1, 69], [1, 77]], [[-1, 1], [-1, 3], [1, 11], [1, 15], [-1, 21], [-1, 27], [1, 35], [1, 39], [1, 43], [-1, 51], [-1, 55], [1, 63], [1, 65], [1, 67], [-1, 75], [-1, 79]], [[-1, 3], [1, 5], [-1, 7], [1, 15], [-1, 17], [1, 19], [-1, 31], [1, 43], [1, 47], [-1, 55], [-1, 59], [1, 67], [-1, 79]], [[1, 3], [-1, 5], [1, 7], [-1, 15], [1, 17], [-1, 19], [1, 31], [-1, 43], [-1, 47], [1, 55], [1, 59], [-1, 67], [1, 79]], [[1, 1], [1, 3], [-1, 11], [-1, 15], [1, 21], [1, 27], [-1, 35], [-1, 39], [-1, 43], [1, 51], [1, 55], [-1, 63], [-1, 65], [-1, 67], [1, 75], [1, 79]], [[1, 13], [-1, 31], [-1, 53], [-1, 57], [-1, 79]], [[1, 3], [-1, 19], [1, 25], [-1, 41], [-1, 47], [-1, 69]]]}
• 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: 69521967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1056, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 66, 'label': '1056.234.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '1056.234', 'subgroup_hash': 234, 'subgroup_order': 1056, 'subgroup_tex': 'C_{24}:D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 528, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '528.107', 'subgroup_hash': 107, 'subgroup_order': 528, 'subgroup_tex': 'D_{11}\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 528, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.96', 'subgroup_hash': 96, 'subgroup_order': 528, 'subgroup_tex': 'C_{12}.D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 528, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.31', 'subgroup_hash': 31, 'subgroup_order': 528, 'subgroup_tex': 'D_{11}\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 69522048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 528, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.49', 'subgroup_hash': 49, 'subgroup_order': 528, 'subgroup_tex': 'C_{24}:C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 528, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.18', 'subgroup_hash': 18, 'subgroup_order': 528, 'subgroup_tex': 'C_{33}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 528, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.19', 'subgroup_hash': 19, 'subgroup_order': 528, 'subgroup_tex': 'C_{33}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 528, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.65', 'subgroup_hash': 65, 'subgroup_order': 528, 'subgroup_tex': 'C_{264}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 176, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 22, 'label': '1056.234.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '352.108', 'subgroup_hash': 108, 'subgroup_order': 352, 'subgroup_tex': '\\SD_{16}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69521968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 264, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.14', 'subgroup_hash': 14, 'subgroup_order': 264, 'subgroup_tex': 'C_{12}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69521979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 264, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.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': '264.20', 'subgroup_hash': 20, 'subgroup_order': 264, 'subgroup_tex': 'C_{11}\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69521990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 264, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.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': '264.25', 'subgroup_hash': 25, 'subgroup_order': 264, 'subgroup_tex': 'D_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 69522001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 264, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.18', 'subgroup_hash': 18, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 264, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.23', 'subgroup_hash': 23, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 264, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.4', 'subgroup_hash': 4, 'subgroup_order': 264, 'subgroup_tex': 'C_{264}', 'supersolvable': True, 'sylow': 0}
  • id: 69522011
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 264, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.2', 'subgroup_hash': 2, 'subgroup_order': 264, 'subgroup_tex': 'C_{11}:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 69522012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 132, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.34', 'subgroup_hash': 34, 'subgroup_order': 264, 'subgroup_tex': 'S_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 132, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.5', 'subgroup_hash': 5, 'subgroup_order': 264, 'subgroup_tex': 'C_6.D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 132, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.10', 'subgroup_hash': 10, 'subgroup_order': 264, 'subgroup_tex': 'C_{11}:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 132, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.11', 'subgroup_hash': 11, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 176, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.3', 'subgroup_hash': 3, 'subgroup_order': 176, 'subgroup_tex': 'C_8\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '176.31', 'subgroup_hash': 31, 'subgroup_order': 176, 'subgroup_tex': 'D_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '176.33', 'subgroup_hash': 33, 'subgroup_order': 176, 'subgroup_tex': 'Q_8\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 88, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '176.25', 'subgroup_hash': 25, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '176.15', 'subgroup_hash': 15, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '176.16', 'subgroup_hash': 16, 'subgroup_order': 176, 'subgroup_tex': 'Q_8:D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '176.5', 'subgroup_hash': 5, 'subgroup_order': 176, 'subgroup_tex': 'C_{88}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 132, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 132, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 69522027
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 132, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 66, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.8', 'subgroup_hash': 8, 'subgroup_order': 132, 'subgroup_tex': 'S_3\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 66, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.9', 'subgroup_hash': 9, 'subgroup_order': 132, 'subgroup_tex': 'D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 69522030
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 66, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.1', 'subgroup_hash': 1, 'subgroup_order': 132, 'subgroup_tex': 'C_3:C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 69522031
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 66, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.3', 'subgroup_hash': 3, 'subgroup_order': 132, 'subgroup_tex': 'C_{33}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 66, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.5', 'subgroup_hash': 5, 'subgroup_order': 132, 'subgroup_tex': 'S_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 66, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.5', 'subgroup_hash': 5, 'subgroup_order': 132, 'subgroup_tex': 'S_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1056.234.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69522035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 88, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 88, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.12.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': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.2', 'subgroup_hash': 2, 'subgroup_order': 88, 'subgroup_tex': 'C_{88}', 'supersolvable': True, 'sylow': 0}
  • id: 69522038
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 88, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.1', 'subgroup_hash': 1, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '88.11', 'subgroup_hash': 11, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 44, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '88.9', 'subgroup_hash': 9, 'subgroup_order': 88, 'subgroup_tex': 'D_4\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 69522044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 44, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.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': '88.10', 'subgroup_hash': 10, 'subgroup_order': 88, 'subgroup_tex': 'Q_8\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.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': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.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': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522047
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 66, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 69522049
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 66, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522050
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 66, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522051
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 33, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522052
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 33, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.3', 'subgroup_hash': 3, 'subgroup_order': 66, 'subgroup_tex': 'D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 69522053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': True, 'centralizer_order': 44, 'characteristic': True, 'core_order': 48, 'counter': 54, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1056.234.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 69522057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.22.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 44, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522062
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 44, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.24.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': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 69522063
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 44, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 22, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522066
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 22, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 69522067
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.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': 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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522071
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 33, 'counter': 70, 'cyclic': True, 'direct': False, 'hall': 33, 'label': '1056.234.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 69522072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1056.234.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 69522073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 24, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.234.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '44.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 69522075
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 24, 'counter': 74, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 69522076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69522077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 69522082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.i1.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': 44, 'quotient_simple': 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: 69522083
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.44.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.j1.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 69522084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.44.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.k1.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': 44, 'quotient_simple': 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: 69522085
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 22, 'counter': 83, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522086
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 22, 'counter': 84, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1056.234.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522087
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 22, 'counter': 85, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1056.234.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522088
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 11, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 69522089
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 11, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 69522090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 69522091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 69522094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.66.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 69522098
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 12, 'counter': 95, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{22}', '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: 69522099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 69522100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69522101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69522102
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69521969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.88.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69521970
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69521971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69521972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.88.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.h1.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 69521973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 11, 'counter': 104, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '1056.234.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.109', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 69521974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 8, 'counter': 105, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 69521975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 69521976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69521977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 69521978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 69521980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 69521981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 69521982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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': 0}
  • id: 69521983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.i1.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': 132, 'quotient_simple': 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': 0}
  • id: 69521984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.132.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.j1.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 69521985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.132.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.k1.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': 132, 'quotient_simple': 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': 0}
  • id: 69521986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 6, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '176.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_{11}', '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: 69521987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69521988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.176.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69521989
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 69521991
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.176.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 69521992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 4, 'counter': 121, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.34', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], '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: 69521993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.264.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 69521994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.264.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 69521995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.264.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 69521996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.264.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69521997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.264.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69521998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.264.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69521999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.264.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 69522000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.234.264.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.h1.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 69522002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 3, 'counter': 130, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1056.234.352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '352.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '352.108', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 108, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}\\times D_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 69522003
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 2, 'counter': 131, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.234.528.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '528.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.107', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 107, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}\\times D_{12}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], '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: 69522004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.528.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.528.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.528.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.234.528.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 69522008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.234', 'ambient_counter': 234, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1056.234.1056.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1056.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1056.234', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 234, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1056, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', '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: 69521980
    {'ambient': '1056.234', 'aut_centralizer_order': 880, 'aut_label': '132.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '44.a1.a1', '66.a1.a1', '66.d1.a1', '66.e1.a1'], 'contains': ['264.a1.a1', '264.c1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6866, -1, 3045, -1, 5956, -1, 6317, -1], 'generators': [2, 792], 'label': '1056.234.132.f1.a1', 'mobius_quo': None, 'mobius_sub': 22, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '132.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522052
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '660.15', 'aut_weyl_index': 32, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '48.d1.a1', '176.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [85, -1, 9802, -1, 395, -1, 239, -1], 'generators': [3, 96, 704], 'label': '1056.234.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.d1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '132.5'}
  • id: 69521967
    {'ambient': '1056.234', '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': '528.a1.a1', 'complements': ['1056.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8580, 4981, 1454, 5110, 6905, 4586, 7268, 5731], 'generators': [1, 704, 132, 264, 2, 96, 528], 'label': '1056.234.1.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.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '528.107', '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': '528.107'}
  • id: 69521968
    {'ambient': '1056.234', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '44.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '44.e1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5156, 1467, 4940, 1750, 3900, 8551, 4083, 2006], 'generators': [1, 704, 528, 792, 96], 'label': '1056.234.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '528.107', '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': '44.3'}
  • id: 69521969
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.e1.a1', '44.g1.a1', '44.k1.a1'], 'contains': ['176.a1.a1', '264.f1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3521, -1, 6074, -1, 2964, -1, 3689, -1], 'generators': [793, 704, 528], 'label': '1056.234.88.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521970
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '88.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1760, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '44.f1.a1', '44.i1.a1', '44.k1.a1'], 'contains': ['176.a1.a1', '264.g1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [3735, -1, 5332, -1, 3704, -1, 4699, -1], 'generators': [103, 528, 704], 'label': '1056.234.88.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '88.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69521971
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3520, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '44.d1.a1'], 'contains': ['176.b1.a1', '176.c1.a1', '176.d1.a1', '264.h1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [1002, -1, 9633, -1, 235, -1, 1645, -1], 'generators': [1, 2, 704], 'label': '1056.234.88.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '88.h1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 69521972
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3520, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '44.d1.a1'], 'contains': ['176.b1.b1', '176.c1.a1', '176.d1.a1', '264.h1.b1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [1002, -1, 8234, -1, 235, -1, 1507, -1], 'generators': [529, 2, 704], 'label': '1056.234.88.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '88.h1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 69521973
    {'ambient': '1056.234', 'aut_centralizer_order': 2112, 'aut_label': '96.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '2.d1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.c1.a1', '48.d1.a1'], 'contains': ['1056.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [441, 2423, 9018, 2199, 1641, 7793, 1067, 2260], 'generators': [96], 'label': '1056.234.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.b1', '48.b1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '1056.234', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521974
    {'ambient': '1056.234', 'aut_centralizer_order': 5280, 'aut_label': '132.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.c1.a1', 'complements': ['8.h1.a1', '8.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '44.c1.a1', '66.c1.a1', '66.d1.a1', '66.g1.a1'], 'contains': ['264.a1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9405, 5474, 1598, 8801, 7835, 5458, 7978, 4868], 'generators': [132], 'label': '1056.234.132.a1.a1', 'mobius_quo': 0, 'mobius_sub': 66, 'normal_closure': '132.a1.a1', 'normal_contained_in': ['12.b1.a1', '44.c1.a1'], 'normal_contains': ['264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.2', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521975
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '44.d1.a1', '66.a1.a1'], 'contains': ['264.b1.a1', '264.c1.a1', '264.d1.a1', '264.h1.a1', '264.h1.b1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1865, -1, 7685, -1, 1944, -1, 2450, -1], 'generators': [1, 2, 528], 'label': '1056.234.132.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521976
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '132.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.e1.a1', '66.a1.a1', '66.b1.a1', '66.c1.a1'], 'contains': ['264.a1.a1', '264.b1.a1', '264.f1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5553, -1, 4170, -1, 5592, -1, 5950, -1], 'generators': [1, 792], 'label': '1056.234.132.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521977
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.d1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '132.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '44.f1.a1', '66.b1.a1'], 'contains': ['264.b1.a1', '264.e1.a1', '264.g1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [4624, -1, 5299, -1, 3930, -1, 4304, -1], 'generators': [1, 1014], 'label': '1056.234.132.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.b1.a1', 'old_label': '132.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521978
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.e1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '44.g1.a1', '66.a1.a1'], 'contains': ['264.c1.a1', '264.d1.a1', '264.f1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [3497, -1, 6110, -1, 3122, -1, 3535, -1], 'generators': [793, 2], 'label': '1056.234.132.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69521979
    {'ambient': '1056.234', 'aut_centralizer_order': 44, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '480.1154', 'aut_weyl_index': 44, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '12.g1.a1', '44.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6486, 5305, 3430, 7617, 4475, 2754, 4640, 6762], 'generators': [2, 96, 528, 792, 704], 'label': '1056.234.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 69521981
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.g1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '44.h1.a1', '66.a1.a1', '66.f1.a1', '66.g1.a1'], 'contains': ['264.a1.a1', '264.d1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [6508, -1, 3399, -1, 5813, -1, 6178, -1], 'generators': [3, 792], 'label': '1056.234.132.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69521982
    {'ambient': '1056.234', 'aut_centralizer_order': 880, 'aut_label': '132.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '44.b1.a1', '66.b1.a1', '66.d1.a1', '66.f1.a1'], 'contains': ['264.a1.a1', '264.e1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7318, -1, 2023, -1, 6697, -1, 7066, -1], 'generators': [1014, 792], 'label': '1056.234.132.h1.a1', 'mobius_quo': None, 'mobius_sub': 22, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '132.h1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69521983
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.i1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '44.i1.a1', '66.b1.a1', '66.e1.a1', '66.g1.a1'], 'contains': ['264.a1.a1', '264.g1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [7861, -1, 2449, -1, 6839, -1, 7204, -1], 'generators': [103, 792], 'label': '1056.234.132.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.i1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69521984
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '132.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '44.j1.a1', '66.c1.a1', '66.e1.a1', '66.f1.a1'], 'contains': ['264.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8445, -1, 672, -1, 8572, -1, 8754, -1], 'generators': [13], 'label': '1056.234.132.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.j1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521985
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '132.k1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '44.k1.a1', '66.b1.a1'], 'contains': ['264.e1.a1', '264.f1.a1', '264.g1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [5040, -1, 4822, -1, 4548, -1, 4857, -1], 'generators': [793, 1014], 'label': '1056.234.132.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.b1.a1', 'old_label': '132.k1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69521986
    {'ambient': '1056.234', 'aut_centralizer_order': 10560, 'aut_label': '176.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1', '88.d1.a1', '88.e1.a1', '88.f1.a1', '88.g1.a1'], 'contains': ['352.a1.a1', '528.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2952, 4239, 6617, 3787, 2124, 6679, 3234, 3310], 'generators': [528, 704], 'label': '1056.234.176.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '176.a1.a1', 'normal_contained_in': ['16.a1.a1', '88.a1.a1'], 'normal_contains': ['352.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '88.4', 'quotient_action_kernel_order': 88, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521987
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '176.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '88.b1.a1', '88.h1.a1'], 'contains': ['352.a1.a1', '528.b1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1182, -1, 9330, -1, 967, -1, 2123, -1], 'generators': [1, 704], 'label': '1056.234.176.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '176.b1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521988
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '176.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '88.b1.a1', '88.h1.b1'], 'contains': ['352.a1.a1', '528.b1.b1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1182, -1, 8319, -1, 967, -1, 1847, -1], 'generators': [529, 704], 'label': '1056.234.176.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '176.b1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521989
    {'ambient': '1056.234', 'aut_centralizer_order': 880, 'aut_label': '176.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3520, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '88.c1.a1', '88.h1.a1', '88.h1.b1'], 'contains': ['352.a1.a1', '528.c1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [771, -1, 9496, -1, 825, -1, 1985, -1], 'generators': [2, 704], 'label': '1056.234.176.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '176.c1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 69521990
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '528.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '12.h1.a1', '44.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5681, 4239, 4022, 2816, 4188, 5176, 4361, 7662], 'generators': [3, 528, 704, 792, 96], 'label': '1056.234.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69521991
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '176.d1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3520, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '88.d1.a1', '88.h1.a1', '88.h1.b1'], 'contains': ['352.a1.a1', '528.d1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [550, -1, 9018, -1, 682, -1, 1551, -1], 'generators': [3, 704], 'label': '1056.234.176.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '176.d1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 69521992
    {'ambient': '1056.234', 'aut_centralizer_order': 10560, 'aut_label': '264.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.a1.a1', '132.a1.a1', '132.c1.a1', '132.f1.a1', '132.g1.a1', '132.h1.a1', '132.i1.a1', '132.j1.a1'], 'contains': ['528.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7048, 5202, 2768, 5499, 6035, 5767, 6394, 4582], 'generators': [792], 'label': '1056.234.264.a1.a1', 'mobius_quo': 0, 'mobius_sub': -264, 'normal_closure': '264.a1.a1', 'normal_contained_in': ['24.b1.a1', '88.a1.a1', '132.a1.a1'], 'normal_contains': ['528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '132.7', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521993
    {'ambient': '1056.234', 'aut_centralizer_order': 960, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.b1.a1', '132.b1.a1', '132.c1.a1', '132.d1.a1'], 'contains': ['528.a1.a1', '528.b1.a1', '528.b1.b1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2798, -1, 7009, -1, 2659, -1, 2928, -1], 'generators': [1, 528], 'label': '1056.234.264.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '264.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69521994
    {'ambient': '1056.234', 'aut_centralizer_order': 1760, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '88.c1.a1', '132.b1.a1', '132.e1.a1', '132.f1.a1'], 'contains': ['528.a1.a1', '528.c1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2437, -1, 7551, -1, 2496, -1, 3086, -1], 'generators': [2, 528], 'label': '1056.234.264.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '264.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521995
    {'ambient': '1056.234', 'aut_centralizer_order': 160, 'aut_label': '264.d1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '88.d1.a1', '132.b1.a1', '132.e1.a1', '132.g1.a1'], 'contains': ['528.a1.a1', '528.d1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2076, -1, 7343, -1, 2288, -1, 2771, -1], 'generators': [3, 528], 'label': '1056.234.264.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '264.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521996
    {'ambient': '1056.234', 'aut_centralizer_order': 1760, 'aut_label': '264.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '88.e1.a1', '132.d1.a1', '132.h1.a1', '132.k1.a1'], 'contains': ['528.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4999, -1, 5521, -1, 4001, -1, 4413, -1], 'generators': [1014], 'label': '1056.234.264.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '264.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521997
    {'ambient': '1056.234', 'aut_centralizer_order': 960, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.f1.a1', '132.c1.a1', '132.e1.a1', '132.k1.a1'], 'contains': ['528.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3817, -1, 5944, -1, 3217, -1, 3612, -1], 'generators': [793], 'label': '1056.234.264.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '264.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521998
    {'ambient': '1056.234', 'aut_centralizer_order': 160, 'aut_label': '264.g1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '132.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '88.g1.a1', '132.d1.a1', '132.i1.a1', '132.k1.a1'], 'contains': ['528.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [4688, -1, 4882, -1, 4215, -1, 4680, -1], 'generators': [103], 'label': '1056.234.264.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.b1.a1', 'old_label': '264.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69521999
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 264, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '88.h1.a1', '132.b1.a1'], 'contains': ['528.b1.a1', '528.c1.a1', '528.d1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 132, 'diagramx': [1024, -1, 9518, -1, 1120, -1, 1699, -1], 'generators': [1, 2], 'label': '1056.234.264.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '132.b1.a1', 'old_label': '264.h1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522000
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 264, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '88.h1.b1', '132.b1.a1'], 'contains': ['528.b1.b1', '528.c1.a1', '528.d1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 132, 'diagramx': [1024, -1, 8515, -1, 1120, -1, 1403, -1], 'generators': [529, 2], 'label': '1056.234.264.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '132.b1.a1', 'old_label': '264.h1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522001
    {'ambient': '1056.234', 'aut_centralizer_order': 44, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '480.1154', 'aut_weyl_index': 44, 'centralizer': '48.a1.a1', 'complements': ['264.h1.a1', '264.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '12.i1.a1', '44.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6028, 8305, 2913, 4772, 5512, 1459, 5641, 8569], 'generators': [1014, 96, 528, 792, 704], 'label': '1056.234.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '44.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 69522002
    {'ambient': '1056.234', 'aut_centralizer_order': 10560, 'aut_label': '352.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.c1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '176.a1.a1', '176.b1.a1', '176.b1.b1', '176.c1.a1', '176.d1.a1'], 'contains': ['1056.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [550, 3217, 9216, 2765, 1011, 7243, 1906, 2807], 'generators': [704], 'label': '1056.234.352.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '352.a1.a1', 'normal_contained_in': ['32.a1.a1', '176.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '352.a1.a1', 'projective_image': '1056.234', 'quotient_action_image': '2.1', 'quotient_action_kernel': '176.3', 'quotient_action_kernel_order': 176, 'quotient_fusion': None, 'short_label': '352.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522003
    {'ambient': '1056.234', 'aut_centralizer_order': 21120, 'aut_label': '528.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1', '264.d1.a1', '264.e1.a1', '264.f1.a1', '264.g1.a1'], 'contains': ['1056.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3217, 3849, 6460, 3508, 2742, 6733, 3159, 3278], 'generators': [528], 'label': '1056.234.528.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '528.a1.a1', 'normal_contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '1.1', 'quotient_action_kernel': '528.107', 'quotient_action_kernel_order': 528, 'quotient_fusion': None, 'short_label': '528.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522004
    {'ambient': '1056.234', 'aut_centralizer_order': 960, 'aut_label': '528.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '176.b1.a1', '264.b1.a1', '264.h1.a1'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1222, -1, 8862, -1, 1482, -1, 2045, -1], 'generators': [1], 'label': '1056.234.528.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '528.b1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522005
    {'ambient': '1056.234', 'aut_centralizer_order': 960, 'aut_label': '528.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '176.b1.b1', '264.b1.a1', '264.h1.b1'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1222, -1, 8319, -1, 1482, -1, 1630, -1], 'generators': [529], 'label': '1056.234.528.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '528.b1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522006
    {'ambient': '1056.234', 'aut_centralizer_order': 1760, 'aut_label': '528.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '176.c1.a1', '264.c1.a1', '264.h1.a1', '264.h1.b1'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [816, -1, 9462, -1, 1340, -1, 1768, -1], 'generators': [2], 'label': '1056.234.528.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '528.c1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522007
    {'ambient': '1056.234', 'aut_centralizer_order': 160, 'aut_label': '528.d1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '176.d1.a1', '264.d1.a1', '264.h1.a1', '264.h1.b1'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 132, 'diagramx': [555, -1, 9023, -1, 1197, -1, 1492, -1], 'generators': [3], 'label': '1056.234.528.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '132.b1.a1', 'old_label': '528.d1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522008
    {'ambient': '1056.234', 'aut_centralizer_order': None, 'aut_label': '1056.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': ['96.a1.a1', '352.a1.a1', '528.a1.a1', '528.b1.a1', '528.b1.b1', '528.c1.a1', '528.d1.a1'], 'contains': [], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [752, 3217, 9023, 2765, 1411, 7243, 1768, 2807], 'generators': [], 'label': '1056.234.1056.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1056.a1.a1', 'normal_contained_in': ['96.a1.a1', '352.a1.a1', '528.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1056.a1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1056.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 69522009
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '528.a1.a1', 'complements': ['264.h1.a1', '264.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '12.j1.a1', '44.i1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6854, 6445, 3777, 3617, 5823, 3794, 5942, 5197], 'generators': [103, 528, 704, 792, 96], 'label': '1056.234.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69522010
    {'ambient': '1056.234', 'aut_centralizer_order': 264, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 264, 'centralizer': '4.f1.a1', 'complements': ['264.h1.a1', '264.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.b1.a1', '44.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9769, 7239, 1933, 8964, 6724, 4519, 7175, 5868], 'generators': [132, 96, 264, 704, 528], 'label': '1056.234.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.b1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522011
    {'ambient': '1056.234', 'aut_centralizer_order': 24, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '44.c1.a1', 'complements': ['264.h1.a1', '264.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.c1.a1', '44.j1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8074, 3165, 198, 6198, 8859, 6156, 9167, 4222], 'generators': [13, 792, 528, 704, 96], 'label': '1056.234.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522012
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.h1.a1', '8.h1.b1', '12.d1.a1', '44.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1313, -1, 8127, -1, 954, -1, 1240, -1], 'generators': [1, 528, 704, 2, 96], 'label': '1056.234.4.h1.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': '4.h1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522013
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '12.e1.a1', '44.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3671, -1, 6005, -1, 2956, -1, 3167, -1], 'generators': [1, 528, 704, 1014, 96], 'label': '1056.234.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522014
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '12.f1.a1', '44.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2313, -1, 6877, -1, 2035, -1, 2394, -1], 'generators': [793, 528, 704, 2, 96], 'label': '1056.234.4.j1.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': '4.j1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522015
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '528.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.j1.a1', '6.b1.a1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5327, 2041, 4564, 2169, 4043, 7270, 4223, 4533], 'generators': [1, 96, 792, 528, 2, 704], 'label': '1056.234.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '528.107', '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': '528.107'}
  • id: 69522016
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.g1.a1', '12.k1.a1', '44.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4381, -1, 4593, -1, 3267, -1, 3468, -1], 'generators': [793, 528, 704, 1014, 96], 'label': '1056.234.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522017
    {'ambient': '1056.234', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '44.c1.a1', 'complements': ['176.c1.a1', '176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '66.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9915, 3055, 334, 7220, 9855, 7357, 8399, 3111], 'generators': [1, 264, 528, 132, 96], 'label': '1056.234.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522018
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '66.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5624, -1, 4482, -1, 4827, -1, 3741, -1], 'generators': [1, 792, 528, 2, 96], 'label': '1056.234.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 69522019
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '66.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7188, -1, 2921, -1, 6104, -1, 5297, -1], 'generators': [1, 792, 528, 1014, 96], 'label': '1056.234.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '528.107', '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': '176.31'}
  • id: 69522020
    {'ambient': '1056.234', 'aut_centralizer_order': 44, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.229', 'aut_weyl_index': 132, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.i1.a1', '66.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9141, -1, 1605, -1, 7065, -1, 6614, -1], 'generators': [2, 96, 264, 132, 528], 'label': '1056.234.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '528.107', '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': '16.11'}
  • id: 69522021
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.j1.a1', '66.e1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8426, -1, 746, -1, 9491, -1, 8046, -1], 'generators': [13, 792, 528, 2, 96], 'label': '1056.234.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '528.107', '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': '176.31'}
  • id: 69522022
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.i1.a1', '66.f1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7705, -1, 1107, -1, 9170, -1, 7734, -1], 'generators': [13, 792, 528, 1014, 96], 'label': '1056.234.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 69522023
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.h1.a1', '12.j1.a1', '66.g1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9579, -1, 2271, -1, 7429, -1, 6968, -1], 'generators': [3, 264, 528, 132, 96], 'label': '1056.234.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 69522024
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '44.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.a1.a1', '88.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2261, 1151, 7267, 1743, 1276, 9511, 1361, 1118], 'generators': [1, 704, 96, 528], 'label': '1056.234.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.b1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522025
    {'ambient': '1056.234', 'aut_centralizer_order': 528, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '88.a1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6292, 4981, 3659, 5059, 5342, 4834, 5710, 5446], 'generators': [792, 96, 528, 704], 'label': '1056.234.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522026
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '528.a1.a1', 'complements': ['528.c1.a1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.k1.a1', '6.c1.a1', '22.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5807, 6445, 4004, 750, 5334, 3251, 5468, 5731], 'generators': [1, 96, 792, 528, 1014, 704], 'label': '1056.234.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69522027
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '44.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '88.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3604, 3026, 6404, 3059, 2175, 8309, 2546, 2229], 'generators': [793, 528, 96, 704], 'label': '1056.234.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522028
    {'ambient': '1056.234', 'aut_centralizer_order': 88, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.45', 'aut_weyl_index': 176, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '24.d1.a1', '88.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1643, -1, 7958, -1, 954, -1, 1674, -1], 'generators': [2, 96, 704, 528], 'label': '1056.234.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 69522029
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 16, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '24.e1.a1', '88.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1254, -1, 7587, -1, 704, -1, 1117, -1], 'generators': [3, 704, 96, 528], 'label': '1056.234.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522030
    {'ambient': '1056.234', 'aut_centralizer_order': 88, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.45', 'aut_weyl_index': 176, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.f1.a1', '88.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4155, -1, 5969, -1, 3126, -1, 3407, -1], 'generators': [1014, 528, 704, 96], 'label': '1056.234.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 69522031
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 16, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.g1.a1', '88.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3231, -1, 5447, -1, 3437, -1, 3708, -1], 'generators': [103, 704, 96, 528], 'label': '1056.234.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '264.34'}
  • id: 69522032
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '660.15', 'aut_weyl_index': 32, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '24.h1.a1', '88.h1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [666, -1, 9575, -1, 144, -1, 520, -1], 'generators': [1, 704, 96, 2], 'label': '1056.234.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.h1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '132.5'}
  • id: 69522033
    {'ambient': '1056.234', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '660.15', 'aut_weyl_index': 32, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.b1', '16.c1.a1', '16.d1.a1', '24.h1.b1', '88.h1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [666, -1, 8952, -1, 144, -1, 206, -1], 'generators': [529, 704, 96, 2], 'label': '1056.234.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.h1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '132.5'}
  • id: 69522034
    {'ambient': '1056.234', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 110, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.c1.a1', '22.d1.a1', '22.e1.a1', '22.f1.a1', '22.g1.a1', '33.a1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8682, -1, 943, -1, 6905, -1, 8768, -1], 'generators': [1, 704, 528, 2, 132, 264], 'label': '1056.234.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522035
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '44.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '132.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5755, 2172, 4272, 4346, 5602, 7108, 4707, 3341], 'generators': [1, 528, 96, 792], 'label': '1056.234.12.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', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522036
    {'ambient': '1056.234', 'aut_centralizer_order': 528, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '4.f1.a1', 'complements': ['88.h1.a1', '88.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '132.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9887, 5379, 1588, 7456, 8117, 5458, 7705, 4868], 'generators': [132, 264, 528, 96], 'label': '1056.234.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522037
    {'ambient': '1056.234', 'aut_centralizer_order': 12, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 12, 'centralizer': '44.c1.a1', 'complements': ['528.c1.a1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.a1.a1', '22.d1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9885, 636, 269, 8051, 8063, 8551, 8424, 2086], 'generators': [1, 96, 704, 264, 132, 528], 'label': '1056.234.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522038
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '44.c1.a1', 'complements': ['88.h1.a1', '88.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.a1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '132.j1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9098, 4055, 285, 6228, 9162, 6156, 8451, 4222], 'generators': [13, 528, 96, 792], 'label': '1056.234.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.g1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522039
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '264.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '24.h1.a1', '24.h1.b1', '132.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1997, -1, 7764, -1, 1623, -1, 854, -1], 'generators': [1, 528, 96, 2], 'label': '1056.234.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522040
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '264.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '132.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4129, -1, 5229, -1, 3900, -1, 3063, -1], 'generators': [1, 528, 96, 1014], 'label': '1056.234.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522041
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1', '132.e1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3172, -1, 6316, -1, 2486, -1, 2244, -1], 'generators': [793, 528, 96, 2], 'label': '1056.234.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
  • id: 69522042
    {'ambient': '1056.234', 'aut_centralizer_order': 88, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.46', 'aut_weyl_index': 264, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '132.f1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7000, -1, 2762, -1, 6104, -1, 5195, -1], 'generators': [2, 96, 528, 792], 'label': '1056.234.12.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 69522043
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 24, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '132.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6237, -1, 3218, -1, 5853, -1, 4951, -1], 'generators': [3, 528, 96, 792], 'label': '1056.234.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 69522044
    {'ambient': '1056.234', 'aut_centralizer_order': 88, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.46', 'aut_weyl_index': 264, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '132.h1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7480, -1, 2127, -1, 7067, -1, 6616, -1], 'generators': [1014, 96, 528, 792], 'label': '1056.234.12.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 69522045
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 24, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '132.i1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7817, -1, 2444, -1, 7348, -1, 6889, -1], 'generators': [103, 528, 96, 792], 'label': '1056.234.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 69522046
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.c1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.g1.a1', '132.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4618, -1, 4827, -1, 4182, -1, 3937, -1], 'generators': [793, 528, 96, 1014], 'label': '1056.234.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
  • id: 69522047
    {'ambient': '1056.234', 'aut_centralizer_order': 1056, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2532, 3944, 6935, 3044, 2112, 7806, 2613, 2813], 'generators': [528, 96, 704], 'label': '1056.234.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522048
    {'ambient': '1056.234', 'aut_centralizer_order': 22, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11312', 'aut_weyl_index': 22, 'centralizer': '48.a1.a1', 'complements': ['528.b1.a1', '528.b1.b1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.d1.a1', '22.a1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8856, 9364, 1997, 9463, 6146, 587, 6499, 9457], 'generators': [2, 704, 96, 264, 132, 528], 'label': '1056.234.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 69522049
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '44.c1.a1', 'complements': ['66.d1.a1', '66.g1.a1', '66.e1.a1', '66.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '176.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [952, 835, 8964, 1743, 967, 9256, 1280, 453], 'generators': [1, 96, 704], 'label': '1056.234.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '1056.234', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522050
    {'ambient': '1056.234', 'aut_centralizer_order': 48, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '44.c1.a1', 'complements': ['66.d1.a1', '66.g1.a1', '66.e1.a1', '66.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '48.b1.b1', '176.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [952, 835, 8426, 537, 967, 9256, 654, 1472], 'generators': [529, 96, 704], 'label': '1056.234.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '1056.234', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522051
    {'ambient': '1056.234', 'aut_centralizer_order': 88, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '60.11', 'aut_weyl_index': 352, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '48.c1.a1', '176.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [474, -1, 9521, -1, 645, -1, 967, -1], 'generators': [2, 704, 96], 'label': '1056.234.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.c1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522053
    {'ambient': '1056.234', 'aut_centralizer_order': 220, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '24.a1.a1', 'complements': ['48.b1.a1', '48.b1.b1', '48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1', '66.d1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8576, 7937, 1642, 8566, 6358, 500, 7356, 9457], 'generators': [2, 704, 132, 264, 528], 'label': '1056.234.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '1.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522054
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.a1', '44.e1.a1', '44.g1.a1', '44.h1.a1', '66.a1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5122, -1, 4210, -1, 3548, -1, 4982, -1], 'generators': [1, 704, 2, 792, 528], 'label': '1056.234.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522055
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.e1.a1', '44.f1.a1', '44.i1.a1', '44.k1.a1', '66.b1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5785, -1, 3414, -1, 5156, -1, 6217, -1], 'generators': [1, 704, 1014, 792, 528], 'label': '1056.234.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522056
    {'ambient': '1056.234', 'aut_centralizer_order': 120, 'aut_label': '22.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1320, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.e1.a1', '44.j1.a1', '66.c1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9588, -1, 423, -1, 8069, -1, 9861, -1], 'generators': [1, 528, 132, 704, 264], 'label': '1056.234.22.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522057
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '22.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.i1.a1', '44.j1.a1', '66.e1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7993, -1, 710, -1, 7818, -1, 9617, -1], 'generators': [13, 704, 2, 792, 528], 'label': '1056.234.22.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522058
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '22.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.h1.a1', '44.j1.a1', '66.f1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6634, -1, 1172, -1, 7637, -1, 9442, -1], 'generators': [13, 704, 1014, 792, 528], 'label': '1056.234.22.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522059
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '528.a1.a1', 'complements': ['528.b1.a1', '528.b1.b1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.e1.a1', '22.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7953, 4981, 788, 6602, 7673, 1916, 8046, 3310], 'generators': [13, 96, 792, 528, 2, 704], 'label': '1056.234.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69522060
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '22.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 220, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.h1.a1', '44.i1.a1', '66.g1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8884, -1, 3125, -1, 6538, -1, 7531, -1], 'generators': [3, 704, 132, 264, 528], 'label': '1056.234.22.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522061
    {'ambient': '1056.234', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '22.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '264.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2668, 1856, 6821, 2757, 2787, 8403, 1972, 2260], 'generators': [1, 96, 528], 'label': '1056.234.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.b1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522062
    {'ambient': '1056.234', 'aut_centralizer_order': 1056, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '264.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7290, 4856, 2370, 5551, 6114, 6075, 5717, 4297], 'generators': [792, 528, 96], 'label': '1056.234.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '528.107', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522063
    {'ambient': '1056.234', 'aut_centralizer_order': 96, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '44.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.f1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '264.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3680, 2621, 6034, 4088, 3312, 7108, 3351, 3459], 'generators': [793, 96, 528], 'label': '1056.234.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '528.107', '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': '44.3'}
  • id: 69522064
    {'ambient': '1056.234', 'aut_centralizer_order': 176, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '264.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2368, -1, 7627, -1, 2538, -1, 2214, -1], 'generators': [2, 96, 528], 'label': '1056.234.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522065
    {'ambient': '1056.234', 'aut_centralizer_order': 16, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '264.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.d1.a1', '12.f1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '264.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1977, -1, 7246, -1, 2288, -1, 1801, -1], 'generators': [3, 96, 528], 'label': '1056.234.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522066
    {'ambient': '1056.234', 'aut_centralizer_order': 176, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.e1.a1', '12.i1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '264.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4414, -1, 5443, -1, 4152, -1, 3858, -1], 'generators': [1014, 528, 96], 'label': '1056.234.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522067
    {'ambient': '1056.234', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '264.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.e1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '264.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4167, -1, 5039, -1, 4358, -1, 4058, -1], 'generators': [103, 96, 528], 'label': '1056.234.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 69522068
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '264.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.d1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.d1.a1', '264.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [950, -1, 8962, -1, 1219, -1, 410, -1], 'generators': [1, 96, 2], 'label': '1056.234.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.h1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522069
    {'ambient': '1056.234', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '264.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.d1.a1'], 'contains': ['48.b1.b1', '48.c1.a1', '48.d1.a1', '264.h1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [950, -1, 8663, -1, 1219, -1, 68, -1], 'generators': [529, 96, 2], 'label': '1056.234.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.h1.b1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522070
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '528.a1.a1', 'complements': ['528.c1.a1', '528.b1.a1', '528.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '6.f1.a1', '22.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7428, 3489, 1454, 5110, 7271, 5948, 7656, 8227], 'generators': [13, 96, 792, 528, 1014, 704], 'label': '1056.234.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69522071
    {'ambient': '1056.234', 'aut_centralizer_order': 1056, 'aut_label': '32.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '4.f1.a1', 'complements': ['33.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.c1.a1', '16.d1.a1'], 'contains': ['96.a1.a1', '352.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [319, 2562, 9556, 1647, 1288, 7806, 1067, 1708], 'generators': [704, 96], 'label': '1056.234.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normal_contains': ['96.a1.a1', '352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '1056.234', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 69522072
    {'ambient': '1056.234', 'aut_centralizer_order': 20, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '32.46', 'aut_weyl_index': 660, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '66.b1.a1', '66.c1.a1', '66.d1.a1', '66.e1.a1', '66.f1.a1', '66.g1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [8978, -1, 881, -1, 8449, -1, 8770, -1], 'generators': [1, 2, 132], 'label': '1056.234.33.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522073
    {'ambient': '1056.234', 'aut_centralizer_order': 440, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 440, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.a1.a1', '22.b1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '88.c1.a1', '132.f1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6688, 6312, 3482, 7963, 4887, 2754, 6372, 6762], 'generators': [2, 792, 528, 704], 'label': '1056.234.44.a1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.b1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522074
    {'ambient': '1056.234', 'aut_centralizer_order': 440, 'aut_label': '44.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 440, 'centralizer': '24.a1.a1', 'complements': ['24.h1.a1', '24.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.a1.a1', '22.c1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '88.e1.a1', '132.h1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6147, 8077, 2902, 6125, 6358, 1459, 7356, 8569], 'generators': [1014, 792, 528, 704], 'label': '1056.234.44.b1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.b1.a1', 'normal_contained_in': ['4.d1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522075
    {'ambient': '1056.234', 'aut_centralizer_order': 2640, 'aut_label': '44.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '2.c1.a1', 'complements': ['24.h1.a1', '24.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '22.a1.a1', '22.d1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '132.a1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9588, 7151, 1824, 8801, 7554, 4210, 8251, 6023], 'generators': [132, 704, 264, 528], 'label': '1056.234.44.c1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.c1.a1', 'normal_contained_in': ['4.f1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522076
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 880, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.c1.a1', '88.d1.a1', '88.h1.a1', '88.h1.b1', '132.b1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1935, -1, 7580, -1, 460, -1, 1979, -1], 'generators': [1, 2, 528, 704], 'label': '1056.234.44.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522077
    {'ambient': '1056.234', 'aut_centralizer_order': 240, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.b1.a1', '22.c1.a1', '22.d1.a1'], 'contains': ['88.a1.a1', '88.b1.a1', '88.f1.a1', '132.c1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5184, -1, 4291, -1, 4461, -1, 5959, -1], 'generators': [1, 792, 704, 528], 'label': '1056.234.44.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522078
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 880, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '22.c1.a1'], 'contains': ['88.b1.a1', '88.e1.a1', '88.g1.a1', '132.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [3977, -1, 5497, -1, 2770, -1, 4211, -1], 'generators': [1, 1014, 528, 704], 'label': '1056.234.44.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '44.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522079
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 880, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '22.b1.a1'], 'contains': ['88.c1.a1', '88.d1.a1', '88.f1.a1', '132.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [2499, -1, 6964, -1, 1894, -1, 2819, -1], 'generators': [793, 2, 528, 704], 'label': '1056.234.44.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522080
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.h1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.38', 'aut_weyl_index': 440, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1', '22.f1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.d1.a1', '132.g1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5721, -1, 3919, -1, 4710, -1, 6201, -1], 'generators': [3, 792, 528, 704], 'label': '1056.234.44.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.h1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522081
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '528.a1.a1', 'complements': ['528.c1.a1', '528.b1.a1', '528.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1', '22.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9417, 7908, 2552, 3617, 6538, 4586, 6880, 6967], 'generators': [3, 96, 264, 528, 132, 704], 'label': '1056.234.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '528.107'}
  • id: 69522082
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.38', 'aut_weyl_index': 440, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.c1.a1', '22.e1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.g1.a1', '132.i1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6960, -1, 3278, -1, 6540, -1, 7533, -1], 'generators': [103, 792, 528, 704], 'label': '1056.234.44.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.i1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 69522083
    {'ambient': '1056.234', 'aut_centralizer_order': 240, 'aut_label': '44.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '22.d1.a1', '22.e1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '132.j1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7977, -1, 363, -1, 8291, -1, 9365, -1], 'generators': [13, 704, 792, 528], 'label': '1056.234.44.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.j1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522084
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '44.k1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 880, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '22.c1.a1'], 'contains': ['88.e1.a1', '88.f1.a1', '88.g1.a1', '132.k1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4286, -1, 5122, -1, 3647, -1, 4461, -1], 'generators': [793, 1014, 528, 704], 'label': '1056.234.44.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '44.k1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522085
    {'ambient': '1056.234', 'aut_centralizer_order': 2112, 'aut_label': '48.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['96.a1.a1', '528.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3044, 3628, 6471, 3227, 2827, 7216, 2608, 2813], 'generators': [528, 96], 'label': '1056.234.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.6', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522086
    {'ambient': '1056.234', 'aut_centralizer_order': 96, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '22.a1.a1', 'complements': ['22.a1.a1', '22.g1.a1', '22.e1.a1', '22.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.h1.a1'], 'contains': ['96.a1.a1', '528.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1134, 1856, 8790, 2199, 1817, 8403, 1238, 1155], 'generators': [1, 96], 'label': '1056.234.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '1056.234', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522087
    {'ambient': '1056.234', 'aut_centralizer_order': 96, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '22.a1.a1', 'complements': ['22.a1.a1', '22.g1.a1', '22.e1.a1', '22.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.a1', '24.h1.b1'], 'contains': ['96.a1.a1', '528.b1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1134, 1856, 8164, 1258, 1817, 8403, 727, 2260], 'generators': [529, 96], 'label': '1056.234.48.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.b1', 'projective_image': '1056.234', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522088
    {'ambient': '1056.234', 'aut_centralizer_order': 176, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.d1.a1', '24.h1.a1', '24.h1.b1'], 'contains': ['96.a1.a1', '528.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [728, -1, 8989, -1, 1641, -1, 898, -1], 'generators': [2, 96], 'label': '1056.234.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.c1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522089
    {'ambient': '1056.234', 'aut_centralizer_order': 16, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '264.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.e1.a1', '24.h1.a1', '24.h1.b1'], 'contains': ['96.a1.a1', '528.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [427, -1, 9274, -1, 1465, -1, 462, -1], 'generators': [3, 96], 'label': '1056.234.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.d1.a1', 'projective_image': '1056.234', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 69522090
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '22.b1.a1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.c1.a1', '132.e1.a1', '132.f1.a1', '132.g1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [5415, -1, 4344, -1, 5110, -1, 5485, -1], 'generators': [1, 2, 792], 'label': '1056.234.66.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522091
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '66.b1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '22.c1.a1', '33.a1.a1'], 'contains': ['132.c1.a1', '132.d1.a1', '132.h1.a1', '132.i1.a1', '132.k1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [6988, -1, 2673, -1, 6768, -1, 7135, -1], 'generators': [1, 1014, 792], 'label': '1056.234.66.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522092
    {'ambient': '1056.234', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '528.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '33.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9177, -1, 1015, -1, 8451, -1, 7268, -1], 'generators': [1, 96, 132, 264, 2, 528], 'label': '1056.234.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '528.107', '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': '176.31'}
  • id: 69522093
    {'ambient': '1056.234', 'aut_centralizer_order': 240, 'aut_label': '66.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.d1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.c1.a1', '132.j1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9439, -1, 563, -1, 8901, -1, 9073, -1], 'generators': [1, 132], 'label': '1056.234.66.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522094
    {'ambient': '1056.234', 'aut_centralizer_order': 440, 'aut_label': '66.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.f1.a1', '132.h1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8826, -1, 1141, -1, 7738, -1, 7884, -1], 'generators': [2, 132], 'label': '1056.234.66.d1.a1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '66.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522095
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '66.e1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '22.e1.a1', '33.a1.a1'], 'contains': ['132.f1.a1', '132.i1.a1', '132.j1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [8526, -1, 827, -1, 8669, -1, 8848, -1], 'generators': [13, 2], 'label': '1056.234.66.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522096
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '66.f1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '22.f1.a1', '33.a1.a1'], 'contains': ['132.g1.a1', '132.h1.a1', '132.j1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [7847, -1, 1360, -1, 8475, -1, 8660, -1], 'generators': [13, 1014], 'label': '1056.234.66.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.f1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522097
    {'ambient': '1056.234', 'aut_centralizer_order': 40, 'aut_label': '66.g1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '22.g1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.g1.a1', '132.i1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [9160, -1, 2052, -1, 7932, -1, 8072, -1], 'generators': [3, 132], 'label': '1056.234.66.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.g1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 69522098
    {'ambient': '1056.234', 'aut_centralizer_order': 5280, 'aut_label': '88.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1', '44.e1.a1', '44.h1.a1', '44.i1.a1', '44.j1.a1'], 'contains': ['176.a1.a1', '264.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5993, 6356, 3567, 5184, 5350, 4525, 6470, 5731], 'generators': [792, 704, 528], 'label': '1056.234.88.a1.a1', 'mobius_quo': 0, 'mobius_sub': 88, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.b1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1'], 'normal_contains': ['176.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '528.107', 'quotient_action_image': '2.1', 'quotient_action_kernel': '44.3', 'quotient_action_kernel_order': 44, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522099
    {'ambient': '1056.234', 'aut_centralizer_order': 480, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.d1.a1', '44.e1.a1', '44.f1.a1'], 'contains': ['176.a1.a1', '176.b1.a1', '176.b1.b1', '264.b1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2862, -1, 7110, -1, 1728, -1, 2967, -1], 'generators': [1, 528, 704], 'label': '1056.234.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.b1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 69522100
    {'ambient': '1056.234', 'aut_centralizer_order': 880, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1760, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '44.a1.a1', '44.d1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '176.c1.a1', '264.c1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2347, -1, 7589, -1, 1522, -1, 3167, -1], 'generators': [2, 528, 704], 'label': '1056.234.88.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '88.c1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522101
    {'ambient': '1056.234', 'aut_centralizer_order': 80, 'aut_label': '88.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1760, 'centralizer': '264.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '44.d1.a1', '44.g1.a1', '44.h1.a1'], 'contains': ['176.a1.a1', '176.d1.a1', '264.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [2097, -1, 7343, -1, 1379, -1, 2767, -1], 'generators': [3, 528, 704], 'label': '1056.234.88.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.d1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 69522102
    {'ambient': '1056.234', 'aut_centralizer_order': 880, 'aut_label': '88.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1760, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '44.b1.a1', '44.f1.a1', '44.k1.a1'], 'contains': ['176.a1.a1', '264.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3953, -1, 5635, -1, 3522, -1, 4523, -1], 'generators': [1014, 528, 704], 'label': '1056.234.88.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.e1.a1', 'projective_image': '528.107', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}