Abstract group data - 352.106

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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': 220, 'aut_gen_orders': [10, 20, 20, 20, 10, 10], 'aut_gens': [[1, 2, 4], [177, 2, 60], [305, 90, 68], [17, 266, 324], [65, 90, 164], [81, 266, 188], [321, 266, 140]], 'aut_group': None, 'aut_hash': 4036028994375102156, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3520, 'aut_permdeg': 30, 'aut_perms': [21960359936056615192131874037979, 180678531365467730912835555355940, 40354592194452701358484855747467, 224354321548627836215777769880768, 251269366487593421864026859571175, 242022511267426713053936316144151], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 22, 1, 1], [2, 44, 1, 1], [4, 2, 1, 1], [4, 22, 1, 1], [4, 44, 1, 1], [8, 4, 1, 1], [8, 44, 1, 1], [11, 2, 5, 1], [22, 2, 5, 1], [22, 8, 5, 2], [44, 4, 5, 1], [88, 4, 10, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.(C_2^4\\times C_{10})', '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': 110, 'autcentquo_group': '440.42', 'autcentquo_hash': 42, 'autcentquo_nilpotent': False, 'autcentquo_order': 440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [2, 22, 1], [2, 44, 1], [4, 2, 1], [4, 22, 1], [4, 44, 1], [8, 4, 1], [8, 44, 1], [11, 2, 5], [22, 2, 5], [22, 8, 10], [44, 4, 5], [88, 4, 10]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '176.31', 'commutator_count': 1, 'commutator_label': '44.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 106, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 22, 1, 1], [2, 44, 1, 1], [4, 2, 1, 1], [4, 22, 1, 1], [4, 44, 1, 1], [8, 4, 1, 1], [8, 44, 1, 1], [11, 2, 5, 1], [22, 2, 5, 1], [22, 8, 5, 2], [44, 4, 5, 1], [88, 4, 10, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4032, 'exponent': 88, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 11], 'faithful_reps': [[4, 0, 10]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '88.11', 'hash': 106, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 44, 'inner_gen_orders': [2, 2, 44], 'inner_gens': [[1, 178, 84], [177, 2, 92], [273, 266, 4]], 'inner_hash': 31, 'inner_nilpotent': False, 'inner_order': 176, 'inner_split': True, 'inner_tex': 'D_4\\times D_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 22], [4, 16]], 'label': '352.106', 'linC_count': 10, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 20, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C8:D22', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 17, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 46, 'number_divisions': 17, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 68, 'number_subgroups': 506, 'old_label': None, 'order': 352, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 75], [4, 68], [8, 48], [11, 10], [22, 90], [44, 20], [88, 40]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 178, 260], [177, 2, 292]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [720, 40410], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 1], [10, 4], [20, 1], [40, 1]], 'representations': {'PC': {'code': 1400542845637078416380015939580000009, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -2, -11, 2137, 1514, 836, 50, 4035, 2217, 69, 10084, 88, 11525]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [59290859, 683409, 682177, 29306243, 45659637, 685345]}, 'Perm': {'d': 19, 'gens': [6405076233123247, 87881944550400, 13877053326259200, 20715131677363200, 6446835113241600, 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_8:D_{22}', 'transitive_degree': 88, '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: 109880370
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 106, 'group_order': 352, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109880381
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 106, 'group_order': 352, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 176, 'size': 1}
  • id: 109880392
    {'aut_label': '2B', 'centralizer': '4.i1.a1', 'counter': 3, 'group_counter': 106, 'group_order': 352, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2, 'size': 4}
  • id: 109880403
    {'aut_label': '2C', 'centralizer': '4.j1.a1', 'counter': 4, 'group_counter': 106, 'group_order': 352, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 134, 'size': 4}
  • id: 109880411
    {'aut_label': '2D', 'centralizer': '22.d1.a1', 'counter': 5, 'group_counter': 106, 'group_order': 352, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 241, 'size': 22}
  • id: 109880412
    {'aut_label': '2E', 'centralizer': '44.f1.a1', 'counter': 6, 'group_counter': 106, 'group_order': 352, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 231, 'size': 44}
  • id: 109880413
    {'aut_label': '4A', 'centralizer': '2.f1.a1', 'counter': 7, 'group_counter': 106, 'group_order': 352, 'label': '4A', 'order': 4, 'powers': [2, 7, 7], 'representative': 88, 'size': 2}
  • id: 109880414
    {'aut_label': '4B', 'centralizer': '22.b1.a1', 'counter': 8, 'group_counter': 106, 'group_order': 352, 'label': '4B', 'order': 4, 'powers': [2, 8, 8], 'representative': 249, 'size': 22}
  • id: 109880415
    {'aut_label': '4C', 'centralizer': '44.e1.a1', 'counter': 9, 'group_counter': 106, 'group_order': 352, 'label': '4C', 'order': 4, 'powers': [2, 9, 9], 'representative': 67, 'size': 44}
  • id: 109880371
    {'aut_label': '8A', 'centralizer': '4.f1.a1', 'counter': 10, 'group_counter': 106, 'group_order': 352, 'label': '8A', 'order': 8, 'powers': [7, 10, 10], 'representative': 44, 'size': 4}
  • id: 109880372
    {'aut_label': '8B', 'centralizer': '44.k1.a1', 'counter': 11, 'group_counter': 106, 'group_order': 352, 'label': '8B', 'order': 8, 'powers': [7, 11, 11], 'representative': 293, 'size': 44}
  • id: 109880373
    {'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 106, 'group_order': 352, 'label': '11A1', 'order': 11, 'powers': [13, 16, 1], 'representative': 64, 'size': 2}
  • id: 109880374
    {'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 106, 'group_order': 352, 'label': '11A2', 'order': 11, 'powers': [15, 12, 1], 'representative': 128, 'size': 2}
  • id: 109880375
    {'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 106, 'group_order': 352, 'label': '11A3', 'order': 11, 'powers': [16, 15, 1], 'representative': 192, 'size': 2}
  • id: 109880376
    {'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 106, 'group_order': 352, 'label': '11A4', 'order': 11, 'powers': [14, 13, 1], 'representative': 256, 'size': 2}
  • id: 109880377
    {'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 16, 'group_counter': 106, 'group_order': 352, 'label': '11A5', 'order': 11, 'powers': [12, 14, 1], 'representative': 320, 'size': 2}
  • id: 109880378
    {'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 17, 'group_counter': 106, 'group_order': 352, 'label': '22A1', 'order': 22, 'powers': [16, 19, 2], 'representative': 16, 'size': 2}
  • id: 109880379
    {'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 18, 'group_counter': 106, 'group_order': 352, 'label': '22A3', 'order': 22, 'powers': [15, 20, 2], 'representative': 48, 'size': 2}
  • id: 109880380
    {'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 19, 'group_counter': 106, 'group_order': 352, 'label': '22A5', 'order': 22, 'powers': [14, 18, 2], 'representative': 80, 'size': 2}
  • id: 109880382
    {'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 20, 'group_counter': 106, 'group_order': 352, 'label': '22A7', 'order': 22, 'powers': [13, 21, 2], 'representative': 112, 'size': 2}
  • id: 109880383
    {'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 21, 'group_counter': 106, 'group_order': 352, 'label': '22A9', 'order': 22, 'powers': [12, 17, 2], 'representative': 144, 'size': 2}
  • id: 109880384
    {'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 22, 'group_counter': 106, 'group_order': 352, 'label': '22B1', 'order': 22, 'powers': [12, 24, 3], 'representative': 34, 'size': 8}
  • id: 109880385
    {'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 23, 'group_counter': 106, 'group_order': 352, 'label': '22B3', 'order': 22, 'powers': [14, 25, 3], 'representative': 10, 'size': 8}
  • id: 109880386
    {'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 24, 'group_counter': 106, 'group_order': 352, 'label': '22B5', 'order': 22, 'powers': [16, 23, 3], 'representative': 18, 'size': 8}
  • id: 109880387
    {'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 25, 'group_counter': 106, 'group_order': 352, 'label': '22B7', 'order': 22, 'powers': [15, 26, 3], 'representative': 130, 'size': 8}
  • id: 109880388
    {'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 26, 'group_counter': 106, 'group_order': 352, 'label': '22B9', 'order': 22, 'powers': [13, 22, 3], 'representative': 66, 'size': 8}
  • id: 109880389
    {'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 27, 'group_counter': 106, 'group_order': 352, 'label': '22C1', 'order': 22, 'powers': [15, 29, 4], 'representative': 6, 'size': 8}
  • id: 109880390
    {'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 28, 'group_counter': 106, 'group_order': 352, 'label': '22C3', 'order': 22, 'powers': [12, 30, 4], 'representative': 14, 'size': 8}
  • id: 109880391
    {'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 29, 'group_counter': 106, 'group_order': 352, 'label': '22C5', 'order': 22, 'powers': [13, 28, 4], 'representative': 22, 'size': 8}
  • id: 109880393
    {'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 30, 'group_counter': 106, 'group_order': 352, 'label': '22C7', 'order': 22, 'powers': [16, 31, 4], 'representative': 294, 'size': 8}
  • id: 109880394
    {'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 31, 'group_counter': 106, 'group_order': 352, 'label': '22C9', 'order': 22, 'powers': [14, 27, 4], 'representative': 38, 'size': 8}
  • id: 109880395
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 32, 'group_counter': 106, 'group_order': 352, 'label': '44A1', 'order': 44, 'powers': [17, 34, 7], 'representative': 8, 'size': 4}
  • id: 109880396
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 33, 'group_counter': 106, 'group_order': 352, 'label': '44A3', 'order': 44, 'powers': [18, 35, 7], 'representative': 24, 'size': 4}
  • id: 109880397
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 34, 'group_counter': 106, 'group_order': 352, 'label': '44A5', 'order': 44, 'powers': [19, 33, 7], 'representative': 40, 'size': 4}
  • id: 109880398
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 35, 'group_counter': 106, 'group_order': 352, 'label': '44A7', 'order': 44, 'powers': [20, 36, 7], 'representative': 56, 'size': 4}
  • id: 109880399
    {'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 36, 'group_counter': 106, 'group_order': 352, 'label': '44A9', 'order': 44, 'powers': [21, 32, 7], 'representative': 72, 'size': 4}
  • id: 109880400
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 37, 'group_counter': 106, 'group_order': 352, 'label': '88A1', 'order': 88, 'powers': [32, 41, 10], 'representative': 4, 'size': 4}
  • id: 109880401
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 38, 'group_counter': 106, 'group_order': 352, 'label': '88A-1', 'order': 88, 'powers': [32, 42, 10], 'representative': 260, 'size': 4}
  • id: 109880402
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 39, 'group_counter': 106, 'group_order': 352, 'label': '88A3', 'order': 88, 'powers': [33, 44, 10], 'representative': 12, 'size': 4}
  • id: 109880404
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 40, 'group_counter': 106, 'group_order': 352, 'label': '88A-3', 'order': 88, 'powers': [33, 43, 10], 'representative': 100, 'size': 4}
  • id: 109880405
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 41, 'group_counter': 106, 'group_order': 352, 'label': '88A5', 'order': 88, 'powers': [34, 40, 10], 'representative': 20, 'size': 4}
  • id: 109880406
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 42, 'group_counter': 106, 'group_order': 352, 'label': '88A-5', 'order': 88, 'powers': [34, 39, 10], 'representative': 196, 'size': 4}
  • id: 109880407
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 43, 'group_counter': 106, 'group_order': 352, 'label': '88A7', 'order': 88, 'powers': [35, 45, 10], 'representative': 292, 'size': 4}
  • id: 109880408
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 44, 'group_counter': 106, 'group_order': 352, 'label': '88A-7', 'order': 88, 'powers': [35, 46, 10], 'representative': 324, 'size': 4}
  • id: 109880409
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 45, 'group_counter': 106, 'group_order': 352, 'label': '88A9', 'order': 88, 'powers': [36, 38, 10], 'representative': 36, 'size': 4}
  • id: 109880410
    {'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 46, 'group_counter': 106, 'group_order': 352, 'label': '88A-9', 'order': 88, 'powers': [36, 37, 10], 'representative': 228, '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: 4429988
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1a', '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], 'schur_index': 1}
  • id: 4429997
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1b', '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], 'schur_index': 1}
  • id: 4429998
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1c', '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], 'schur_index': 1}
  • id: 4429999
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1d', '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], 'schur_index': 1}
  • id: 4430000
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1e', '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], 'schur_index': 1}
  • id: 4430001
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1f', '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], 'schur_index': 1}
  • id: 4430002
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1g', '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], 'schur_index': 1}
  • id: 4430003
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.1h', '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], 'schur_index': 1}
  • id: 4430004
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, -2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4429989
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4429994
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -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], 'schur_index': 1}
  • id: 4429990
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2c', 'multiplicity': 5, 'nt': [11, 2], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 0, 0, 10, 0, 0, 10, 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], 'schur_index': 1}
  • id: 4429991
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2d', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, -10, -10, 0, 0, 10, 0, 0, 10, 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], 'schur_index': 1}
  • id: 4429992
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2e', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, -10, 10, 0, 0, 10, 0, 0, -10, 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], 'schur_index': 1}
  • id: 4429993
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.2f', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 10, -10, 0, 0, 10, 0, 0, -10, 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], 'schur_index': 1}
  • id: 4429995
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.4b', 'multiplicity': 5, 'nt': [44, 12], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 0, 0, -20, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4429996
    {'cdim': 4, 'counter': 17, 'faithful': True, 'group': '352.106', 'group_order': 352, 'image': None, 'label': '352.106.4c', 'multiplicity': 10, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 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], '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: 6787829
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 352, 'label': '352.106.1a', '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]]]}
  • id: 6787840
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 176, 'label': '352.106.1b', '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]]]}
  • id: 6787851
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 176, 'label': '352.106.1c', '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]]]}
  • id: 6787862
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 176, 'label': '352.106.1d', '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]]]}
  • id: 6787870
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 176, 'label': '352.106.1e', '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]]]}
  • id: 6787871
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 176, 'label': '352.106.1f', '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]]]}
  • id: 6787872
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 176, 'label': '352.106.1g', '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]]]}
  • id: 6787873
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 176, 'label': '352.106.1h', '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]]]}
  • id: 6787874
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 88, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 44, 'label': '352.106.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6787830
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 88, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 44, 'label': '352.106.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6787831
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 11, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.106.2c1', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]]]}
  • id: 6787832
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 12, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.106.2c2', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[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, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]]]}
  • id: 6787833
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 13, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.106.2c3', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6787834
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 14, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.106.2c4', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]]]}
  • id: 6787835
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.106.2c5', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[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, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]]]}
  • id: 6787836
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.106.2d1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[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, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]]]}
  • id: 6787837
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.106.2d2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[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, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]]]}
  • id: 6787838
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.106.2d3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6787839
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.106.2d4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]]]}
  • id: 6787841
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.106.2d5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[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, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]]]}
  • id: 6787842
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.106.2e1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]]]}
  • id: 6787843
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.106.2e2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[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, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]]]}
  • id: 6787844
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.106.2e3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6787845
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.106.2e4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]]]}
  • id: 6787846
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.106.2e5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[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, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]]]}
  • id: 6787847
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.106.2f1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[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, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]]]}
  • id: 6787848
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.106.2f2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[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, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]]]}
  • id: 6787849
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.106.2f3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6787850
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.106.2f4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]]]}
  • id: 6787852
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.106.2f5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[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, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]]]}
  • id: 6787853
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 22, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 11, 'label': '352.106.4a', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6787854
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 32, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.106.4b1', 'nt': [44, 12], '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]], [[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, 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]], [[-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]]]}
  • id: 6787855
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.106.4b2', 'nt': [44, 12], '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]], [[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, 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]], [[-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]]]}
  • id: 6787856
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.106.4b3', 'nt': [44, 12], '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]], [[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, 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]], [[-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]]]}
  • id: 6787857
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.106.4b4', 'nt': [44, 12], '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]], [[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, 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]], [[-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]]]}
  • id: 6787858
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.106.4b5', 'nt': [44, 12], '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]], [[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, 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]], [[-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]]]}
  • id: 6787859
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c1', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 12], [-2, -12]], [[2, 16], [2, -16]], [[-2, 20], [-2, -20]], [[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]], [[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], [-2, 23], [1, 27], [-1, 31], [1, 35], [-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], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [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, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 21], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]]]}
  • id: 6787869
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 46, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c10', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[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]], [[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, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 21], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[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], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 9], [-1, 13], [-1, 31], [-1, 35]]]}
  • id: 6787860
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c2', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 12], [-2, -12]], [[2, 16], [2, -16]], [[-2, 20], [-2, -20]], [[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]], [[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], [2, 23], [-1, 27], [1, 31], [-1, 35], [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], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-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, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 21], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]]]}
  • id: 6787861
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c3', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 16], [2, -16]], [[-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]], [[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], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 21], [-2, 23], [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], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[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, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]]]}
  • id: 6787863
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c4', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 8], [2, -8]], [[-2, 4], [-2, -4]], [[2, 16], [2, -16]], [[-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]], [[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], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 21], [2, 23], [-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], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-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, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]]]}
  • id: 6787864
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c5', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 16], [2, -16]], [[2, 8], [2, -8]], [[-2, 12], [-2, -12]], [[-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]], [[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, 9], [1, 13], [1, 31], [1, 35]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[-1, 9], [-1, 13], [-1, 31], [-1, 35]], [[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], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 21], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[1, 5], [1, 17], [1, 27], [1, 39]]]}
  • id: 6787865
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c6', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 16], [2, -16]], [[2, 8], [2, -8]], [[-2, 12], [-2, -12]], [[-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]], [[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, 9], [-1, 13], [-1, 31], [-1, 35]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[1, 9], [1, 13], [1, 31], [1, 35]], [[-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], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 21], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[-1, 5], [-1, 17], [-1, 27], [-1, 39]]]}
  • id: 6787866
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c7', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[2, 8], [2, -8]], [[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]], [[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, 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], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 21], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[1, 9], [1, 13], [1, 31], [1, 35]], [[-1, 7], [1, 15], [1, 29], [-1, 37]]]}
  • id: 6787867
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c8', 'nt': [88, 10], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 4], [-2, -4]], [[-2, 20], [-2, -20]], [[2, 8], [2, -8]], [[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]], [[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, 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], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 21], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[-1, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[-1, 9], [-1, 13], [-1, 31], [-1, 35]], [[1, 7], [-1, 15], [-1, 29], [1, 37]]]}
  • id: 6787868
    {'center': '176.a1.a1', 'center_index': 176, 'center_order': 2, 'counter': 45, 'cyclotomic_n': 88, 'dim': 4, 'faithful': True, 'field': [352, 0, 880, 0, 616, 0, 176, 0, 22, 0, 1], 'group': '352.106', 'group_counter': 106, 'group_order': 352, 'image': None, 'image_isoclass': '352.106', 'image_order': 352, 'indicator': 0, 'kernel': '352.a1.a1', 'kernel_order': 1, 'label': '352.106.4c9', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 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, 20], [-2, -20]], [[-2, 12], [-2, -12]], [[-2, 4], [-2, -4]], [[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]], [[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, 1], [1, 3], [1, 5], [-1, 9], [1, 13], [-1, 17], [-1, 19], [1, 21], [-2, 25], [1, 29], [-1, 33], [1, 37]], [[-1, 1], [1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 21], [-2, 23], [1, 27], [-1, 31], [1, 35], [-1, 39]], [[1, 1], [-1, 3], [-1, 5], [1, 9], [-1, 13], [1, 17], [1, 19], [-1, 21], [2, 25], [-1, 29], [1, 33], [-1, 37]], [[-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], [2, 23], [-1, 27], [1, 31], [-1, 35], [1, 39]], [[1, 9], [1, 13], [1, 31], [1, 35]]]}
• 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: 65710020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 352, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 22, 'label': '352.106.1.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': '352.106', 'subgroup_hash': 106, 'subgroup_order': 352, 'subgroup_tex': 'C_8:D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 176, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.24', 'subgroup_hash': 24, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.32', 'subgroup_hash': 32, 'subgroup_order': 176, 'subgroup_tex': 'D_4:D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 65710053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.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': '176.14', 'subgroup_hash': 14, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': '176.31', 'subgroup_hash': 31, 'subgroup_order': 176, 'subgroup_tex': 'D_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 65710075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.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': '176.15', 'subgroup_hash': 15, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 65710085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.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': '176.4', 'subgroup_hash': 4, 'subgroup_order': 176, 'subgroup_tex': 'C_{88}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 65710086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.2.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': '176.5', 'subgroup_hash': 5, 'subgroup_order': 176, 'subgroup_tex': 'C_{88}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 65710087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 88, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 65710021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 88, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '88.9', 'subgroup_hash': 9, 'subgroup_order': 88, 'subgroup_tex': 'D_4\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 65710022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 88, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.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': ['C2'], '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: 65710023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 88, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 65710024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 88, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.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': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 88, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.4.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': [], '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: 65710026
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 88, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.4.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': '88.1', 'subgroup_hash': 1, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.4.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': '88.6', 'subgroup_hash': 6, 'subgroup_order': 88, 'subgroup_tex': 'C_{22}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '88.11', 'subgroup_hash': 11, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 44, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.4.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': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 44, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.8.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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710033
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 44, 'counter': 21, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.8.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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 65710034
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 44, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.8.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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 22, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 22, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710038
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 11, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 11, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.8.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a2', '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '352.106.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 65710043
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 22, 'counter': 30, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.16.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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710044
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 11, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 11, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 65710046
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 11, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.16.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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 65710047
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 11, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 65710048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 65710050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 65710054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 65710055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.22.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 65710056
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 11, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '352.106.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C5'], '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: 65710057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.106.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710059
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 8, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.44.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 65710063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.44.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710068
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.44.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 65710069
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 4, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.88.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': ['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: 65710070
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710071
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710074
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.88.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710076
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.88.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65710077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710078
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.106.88.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.h1.a2', '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 65710079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.106.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, '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': 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: 65710080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 65710081
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 65710082
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.176.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 65710083
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.106.176.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, '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: 65710084
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.106', 'ambient_counter': 106, 'ambient_order': 352, 'ambient_tex': 'C_8:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '352.106.352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '352.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '352.106', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 106, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 65710044
    {'ambient': '352.106', 'aut_centralizer_order': 88, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '10.2', 'aut_weyl_index': 352, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.a1.a1', '176.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6659, -1, 3535, -1, 2802, -1, 6869, -1], 'generators': [2, 32], 'label': '352.106.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.b1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65710020
    {'ambient': '352.106', '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': '176.a1.a1', 'complements': ['352.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', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2570, 5552, 7586, 4647, 6179, 5290, 3213, 4302], 'generators': [1, 32, 44, 264, 2, 176], 'label': '352.106.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.d1.a1', '2.e1.a1', '2.b1.a1', '2.c1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710021
    {'ambient': '352.106', 'aut_centralizer_order': 44, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.46', 'aut_weyl_index': 44, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '44.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4477, 3983, 6218, 7806, 3590, 4916, 6544, 8618], 'generators': [134, 32, 176, 88], 'label': '352.106.4.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.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '176.31', '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': '16.11'}
  • id: 65710022
    {'ambient': '352.106', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '88.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '44.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7109, 1052, 3308, 1876, 4342, 1249, 5427, 1520], 'generators': [1, 176, 32, 88], 'label': '352.106.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.d1.a1', '2.b1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '176.31', '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': '88.11'}
  • id: 65710023
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '44.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3223, 6521, 5644, 4391, 3008, 3668, 5986, 5846], 'generators': [7, 176, 32, 88], 'label': '352.106.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.d1.a1', '2.c1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
  • id: 65710024
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '44.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3754, 2518, 6859, 5455, 6376, 2645, 3476, 2873], 'generators': [3, 176, 32, 88], 'label': '352.106.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.e1.a1', '2.b1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710025
    {'ambient': '352.106', 'aut_centralizer_order': 88, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 88, 'centralizer': '4.f1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '44.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [699, 9133, 8955, 6519, 7824, 8948, 2615, 4998], 'generators': [44, 88, 176, 32], 'label': '352.106.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '176.31', '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: 65710026
    {'ambient': '352.106', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '88.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '44.k1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1657, 5448, 8485, 3329, 7347, 6313, 1411, 4007], 'generators': [5, 176, 32, 88], 'label': '352.106.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.e1.a1', '2.c1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '176.31', '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': '88.11'}
  • id: 65710027
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.g1.a1', '44.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6384, -1, 4122, -1, 1638, -1, 8020, -1], 'generators': [1, 176, 32, 2], 'label': '352.106.4.h1.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.h1.a1', 'projective_image': '176.31', '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': '88.11'}
  • id: 65710028
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.g1.a1', '44.e1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5584, -1, 4831, -1, 2357, -1, 7330, -1], 'generators': [89, 176, 32, 2], 'label': '352.106.4.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': '176.31', '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': '44.3'}
  • id: 65710029
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.f1.a1', '8.h1.a1', '8.h1.a2', '44.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8949, -1, 1452, -1, 396, -1, 9211, -1], 'generators': [1, 176, 32, 134], 'label': '352.106.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.a1', 'projective_image': '176.31', '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': '44.3'}
  • id: 65710030
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '44.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8078, -1, 2478, -1, 1093, -1, 8543, -1], 'generators': [89, 176, 32, 134], 'label': '352.106.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.k1.a1', 'projective_image': '176.31', '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': '88.11'}
  • id: 65710031
    {'ambient': '352.106', 'aut_centralizer_order': 22, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.229', 'aut_weyl_index': 22, 'centralizer': '16.a1.a1', 'complements': ['176.d1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '22.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [933, 9473, 9127, 9392, 5757, 9027, 4100, 8762], 'generators': [2, 32, 264, 44, 176], 'label': '352.106.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.a1.a1', '4.f1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 65710032
    {'ambient': '352.106', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '88.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7751, 2394, 2767, 2245, 1725, 3599, 7954, 3740], 'generators': [1, 32, 176], 'label': '352.106.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '176.31', '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: 65710033
    {'ambient': '352.106', 'aut_centralizer_order': 176, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 176, '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', '88.a1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3366, 5448, 6863, 5455, 5638, 4916, 4201, 4998], 'generators': [88, 176, 32], 'label': '352.106.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1', '4.a1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '176.31', '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: 65710034
    {'ambient': '352.106', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 16, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '88.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7221, 1146, 3237, 4033, 2582, 1691, 7133, 1930], 'generators': [89, 32, 176], 'label': '352.106.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '176.31', '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: 65710035
    {'ambient': '352.106', 'aut_centralizer_order': 88, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 176, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '88.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5308, -1, 4930, -1, 3228, -1, 6513, -1], 'generators': [2, 32, 176], 'label': '352.106.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '176.31', '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': '4.2'}
  • id: 65710036
    {'ambient': '352.106', 'aut_centralizer_order': 88, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 176, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '88.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9046, -1, 2021, -1, 1148, -1, 8899, -1], 'generators': [134, 32, 176], 'label': '352.106.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.e1.a1', 'projective_image': '176.31', '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': '4.2'}
  • id: 65710037
    {'ambient': '352.106', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 16, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '88.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8404, -1, 1452, -1, 570, -1, 8345, -1], 'generators': [7, 32, 176], 'label': '352.106.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.f1.a1', 'projective_image': '176.31', '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': '44.3'}
  • id: 65710038
    {'ambient': '352.106', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 16, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '88.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6028, -1, 4294, -1, 4209, -1, 5572, -1], 'generators': [3, 32, 176], 'label': '352.106.8.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': '176.31', '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': '44.3'}
  • id: 65710039
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '110.1', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '88.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9689, -1, 160, -1, 163, -1, 9453, -1], 'generators': [1, 32, 134], 'label': '352.106.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.h1.a1', 'projective_image': '352.106', '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': '22.1'}
  • id: 65710040
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '110.1', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '88.h1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9689, -1, 874, -1, 163, -1, 9844, -1], 'generators': [177, 32, 134], 'label': '352.106.8.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.h1.a2', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a2', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 65710041
    {'ambient': '352.106', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 110, 'centralizer': '176.a1.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'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1203, -1, 8815, -1, 8483, -1, 1028, -1], 'generators': [1, 2, 44], 'label': '352.106.11.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': '176.31', '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': '16.11'}
  • id: 65710042
    {'ambient': '352.106', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['176.c1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.h1.a1', '4.i1.a1', '22.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4992, 527, 5355, 3420, 4557, 2114, 4724, 1625], 'generators': [1, 88, 176, 2, 32], 'label': '352.106.2.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.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710043
    {'ambient': '352.106', 'aut_centralizer_order': 352, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 352, 'centralizer': '2.a1.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', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7302, 2735, 2966, 4944, 2399, 4258, 7256, 4369], 'generators': [176, 32], 'label': '352.106.16.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', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65710045
    {'ambient': '352.106', 'aut_centralizer_order': 88, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '10.2', 'aut_weyl_index': 352, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '176.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9862, -1, 617, -1, 1175, -1, 9150, -1], 'generators': [134, 32], 'label': '352.106.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.c1.a1', 'projective_image': '352.106', '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': '2.1'}
  • id: 65710046
    {'ambient': '352.106', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '176.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8955, -1, 1018, -1, 1615, -1, 8367, -1], 'generators': [1, 32], 'label': '352.106.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.d1.a1', 'projective_image': '352.106', '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': '22.1'}
  • id: 65710047
    {'ambient': '352.106', 'aut_centralizer_order': 8, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '176.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9408, -1, 215, -1, 685, -1, 8759, -1], 'generators': [7, 32], 'label': '352.106.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.e1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 65710048
    {'ambient': '352.106', 'aut_centralizer_order': 220, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '16.a1.a1', 'complements': ['16.d1.a1', '16.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [179, 9112, 9840, 9248, 8520, 9735, 2263, 9743], 'generators': [2, 44], 'label': '352.106.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['44.b1.a1', '44.a1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 65710049
    {'ambient': '352.106', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.a1', '44.e1.a1', '44.h1.a1', '44.j1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4207, -1, 6064, -1, 6862, -1, 3010, -1], 'generators': [1, 2, 88], 'label': '352.106.22.b1.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.b1.a1', 'projective_image': '176.31', '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': '8.3'}
  • id: 65710050
    {'ambient': '352.106', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.i1.a1', '44.k1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1102, -1, 9064, -1, 8190, -1, 989, -1], 'generators': [5, 2], 'label': '352.106.22.c1.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.c1.a1', 'projective_image': '176.31', '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': '16.11'}
  • id: 65710051
    {'ambient': '352.106', 'aut_centralizer_order': 20, 'aut_label': '22.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.f1.a1', '44.g1.a1', '44.h1.a1', '44.i1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5308, -1, 5088, -1, 5033, -1, 4764, -1], 'generators': [1, 134, 88], 'label': '352.106.22.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.d1.a1', 'projective_image': '176.31', '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': '8.3'}
  • id: 65710052
    {'ambient': '352.106', 'aut_centralizer_order': 20, 'aut_label': '22.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.j1.a1', '44.k1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2228, -1, 8508, -1, 8910, -1, 615, -1], 'generators': [5, 134], 'label': '352.106.22.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': '176.31', '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': '16.11'}
  • id: 65710053
    {'ambient': '352.106', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['176.c1.a1', '176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.g1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2264, 6780, 7948, 4647, 5107, 7630, 2953, 7409], 'generators': [5, 88, 176, 2, 32], 'label': '352.106.2.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.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710054
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '22.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.h1.a1', '44.k1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [617, -1, 9451, -1, 9812, -1, 180, -1], 'generators': [1, 44], 'label': '352.106.22.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': '176.31', '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': '8.5'}
  • id: 65710055
    {'ambient': '352.106', 'aut_centralizer_order': 20, 'aut_label': '22.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.i1.a1', '44.j1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1535, -1, 8066, -1, 9359, -1, 1890, -1], 'generators': [3, 44], 'label': '352.106.22.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': '176.31', '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': '16.11'}
  • id: 65710056
    {'ambient': '352.106', 'aut_centralizer_order': 352, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 352, 'centralizer': '2.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1'], 'contains': ['352.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9184, 3385, 810, 4944, 1615, 4258, 8354, 4369], 'generators': [32], 'label': '352.106.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '352.106', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65710057
    {'ambient': '352.106', 'aut_centralizer_order': 440, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 440, 'centralizer': '8.c1.a1', 'complements': ['8.h1.a1', '8.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.c1.a1'], 'contains': ['88.a1.a1', '88.b1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2514, 7502, 7794, 8574, 7288, 7709, 2619, 7056], 'generators': [2, 88], 'label': '352.106.44.a1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.a1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 65710058
    {'ambient': '352.106', 'aut_centralizer_order': 440, 'aut_label': '44.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 440, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.a1.a1', '22.d1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '88.c1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4155, 6687, 6503, 7797, 6334, 6352, 3850, 8618], 'generators': [134, 88], 'label': '352.106.44.b1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.b1.a1', 'normal_contained_in': ['4.b1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 65710059
    {'ambient': '352.106', 'aut_centralizer_order': 880, 'aut_label': '44.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '4.f1.a1', 'complements': ['8.h1.a1', '8.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '22.a1.a1', '22.f1.a1', '22.g1.a1'], 'contains': ['88.a1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [138, 8245, 8906, 7060, 8520, 8948, 1986, 5760], 'generators': [44], 'label': '352.106.44.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'], 'normalizer': '1.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65710060
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.d1.a1', '88.g1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6231, -1, 3584, -1, 4648, -1, 5151, -1], 'generators': [1, 2], 'label': '352.106.44.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.d1.a1', 'projective_image': '176.31', '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': '4.2'}
  • id: 65710061
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.f1.a1', '88.g1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4813, -1, 4225, -1, 5125, -1, 4693, -1], 'generators': [89, 2], 'label': '352.106.44.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.e1.a1', 'projective_image': '176.31', '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: 65710062
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '22.d1.a1'], 'contains': ['88.c1.a1', '88.d1.a1', '88.e1.a1', '88.h1.a1', '88.h1.a2'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8327, -1, 1972, -1, 2119, -1, 7576, -1], 'generators': [1, 134, 176], 'label': '352.106.44.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '44.f1.a1', 'projective_image': '176.31', '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': '2.1'}
  • id: 65710063
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '22.d1.a1'], 'contains': ['88.c1.a1', '88.e1.a1', '88.f1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7741, -1, 2491, -1, 3769, -1, 5994, -1], 'generators': [89, 134], 'label': '352.106.44.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '44.g1.a1', 'projective_image': '176.31', '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': '4.2'}
  • id: 65710064
    {'ambient': '352.106', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.j1.a1', '4.k1.a1', '22.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7109, 1992, 3764, 1969, 3590, 718, 5986, 6055], 'generators': [1, 88, 176, 134, 32], 'label': '352.106.2.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.c1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710065
    {'ambient': '352.106', 'aut_centralizer_order': 80, 'aut_label': '44.h1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '44.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1', '22.d1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '88.d1.a1', '88.f1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5508, -1, 5504, -1, 6811, -1, 3076, -1], 'generators': [1, 88], 'label': '352.106.44.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': '176.31', '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': '4.2'}
  • id: 65710066
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 440, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.c1.a1', '22.d1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.e1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3131, -1, 5034, -1, 6005, -1, 3533, -1], 'generators': [7, 88], 'label': '352.106.44.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.i1.a1', 'projective_image': '176.31', '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': '8.3'}
  • id: 65710067
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '44.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 440, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.b1.a1', '22.e1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.g1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3661, -1, 7307, -1, 7617, -1, 2303, -1], 'generators': [3, 88], 'label': '352.106.44.j1.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.j1.a1', 'projective_image': '176.31', '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': '8.3'}
  • id: 65710068
    {'ambient': '352.106', 'aut_centralizer_order': 80, 'aut_label': '44.k1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 880, 'centralizer': '44.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '22.c1.a1', '22.e1.a1', '22.f1.a1'], 'contains': ['88.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1881, -1, 9230, -1, 8190, -1, 989, -1], 'generators': [5], 'label': '352.106.44.k1.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.k1.a1', 'projective_image': '176.31', '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': '4.2'}
  • id: 65710069
    {'ambient': '352.106', 'aut_centralizer_order': 1760, 'aut_label': '88.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1', '44.h1.a1', '44.i1.a1', '44.j1.a1', '44.k1.a1'], 'contains': ['176.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3131, 6687, 6750, 7060, 6811, 6352, 3076, 5760], 'generators': [88], 'label': '352.106.88.a1.a1', 'mobius_quo': 0, 'mobius_sub': 88, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.b1.a1', '44.b1.a1', '44.a1.a1', '44.c1.a1'], 'normal_contains': ['176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '176.31', '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: 65710070
    {'ambient': '352.106', 'aut_centralizer_order': 880, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '44.a1.a1', '44.d1.a1', '44.e1.a1'], 'contains': ['176.a1.a1', '176.b1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5951, -1, 3719, -1, 4648, -1, 5098, -1], 'generators': [2, 176], 'label': '352.106.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.b1.a1', 'projective_image': '176.31', '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: 65710071
    {'ambient': '352.106', 'aut_centralizer_order': 880, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '44.b1.a1', '44.f1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '176.c1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8409, -1, 2360, -1, 3567, -1, 6495, -1], 'generators': [134, 176], 'label': '352.106.88.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '88.c1.a1', 'projective_image': '176.31', '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': '2.1'}
  • id: 65710072
    {'ambient': '352.106', 'aut_centralizer_order': 160, 'aut_label': '88.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.d1.a1', '44.f1.a1', '44.h1.a1'], 'contains': ['176.a1.a1', '176.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7572, -1, 2739, -1, 3943, -1, 5775, -1], 'generators': [1, 176], 'label': '352.106.88.d1.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.d1.a1', 'projective_image': '176.31', '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': '2.1'}
  • id: 65710073
    {'ambient': '352.106', 'aut_centralizer_order': 80, 'aut_label': '88.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '44.f1.a1', '44.g1.a1', '44.i1.a1'], 'contains': ['176.a1.a1', '176.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7991, -1, 1986, -1, 3191, -1, 6135, -1], 'generators': [7, 176], 'label': '352.106.88.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '88.e1.a1', 'projective_image': '176.31', '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': '2.1'}
  • id: 65710074
    {'ambient': '352.106', 'aut_centralizer_order': 160, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.e1.a1', '44.g1.a1', '44.h1.a1'], 'contains': ['176.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6986, -1, 3087, -1, 4296, -1, 5436, -1], 'generators': [89], 'label': '352.106.88.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': '176.31', '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: 65710075
    {'ambient': '352.106', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1', '176.d1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '22.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3692, 3890, 7220, 6294, 6600, 3707, 2246, 4302], 'generators': [5, 88, 176, 134, 32], 'label': '352.106.2.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': '176.31', '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': '176.31'}
  • id: 65710076
    {'ambient': '352.106', 'aut_centralizer_order': 80, 'aut_label': '88.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1760, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '44.d1.a1', '44.e1.a1', '44.j1.a1'], 'contains': ['176.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6344, -1, 4225, -1, 5001, -1, 4760, -1], 'generators': [3], 'label': '352.106.88.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.g1.a1', 'projective_image': '176.31', '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': '2.1'}
  • id: 65710077
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '44.f1.a1'], 'contains': ['176.c1.a1', '176.d1.a1', '176.e1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9327, -1, 793, -1, 2009, -1, 7629, -1], 'generators': [1, 134], 'label': '352.106.88.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '88.h1.a1', 'projective_image': '352.106', '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': '1.1'}
  • id: 65710078
    {'ambient': '352.106', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a2', '44.f1.a1'], 'contains': ['176.c1.a1', '176.d1.a1', '176.e1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9327, -1, 1164, -1, 2009, -1, 7989, -1], 'generators': [177, 134], 'label': '352.106.88.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '88.h1.a2', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.h1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65710079
    {'ambient': '352.106', 'aut_centralizer_order': 3520, 'aut_label': '176.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '1.a1.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'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7267, 3952, 2739, 5588, 3943, 5044, 5775, 5131], 'generators': [176], 'label': '352.106.176.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'], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '1.1', 'quotient_action_kernel': '176.31', 'quotient_action_kernel_order': 176, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65710080
    {'ambient': '352.106', 'aut_centralizer_order': 880, 'aut_label': '176.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '88.b1.a1'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6706, -1, 3336, -1, 2971, -1, 6869, -1], 'generators': [2], 'label': '352.106.176.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '176.b1.a1', 'projective_image': '352.106', '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': '1.1'}
  • id: 65710081
    {'ambient': '352.106', 'aut_centralizer_order': 880, 'aut_label': '176.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '88.c1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9669, -1, 1118, -1, 2312, -1, 7989, -1], 'generators': [134], 'label': '352.106.176.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '176.c1.a1', 'projective_image': '352.106', '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': '1.1'}
  • id: 65710082
    {'ambient': '352.106', 'aut_centralizer_order': 160, 'aut_label': '176.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '88.d1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8740, -1, 1443, -1, 2641, -1, 7357, -1], 'generators': [1], 'label': '352.106.176.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '176.d1.a1', 'projective_image': '352.106', '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': '1.1'}
  • id: 65710083
    {'ambient': '352.106', 'aut_centralizer_order': 80, 'aut_label': '176.e1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '88.e1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9301, -1, 793, -1, 1982, -1, 7673, -1], 'generators': [7], 'label': '352.106.176.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '176.e1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65710084
    {'ambient': '352.106', 'aut_centralizer_order': None, 'aut_label': '352.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': ['32.a1.a1', '176.a1.a1', '176.b1.a1', '176.c1.a1', '176.d1.a1', '176.e1.a1'], 'contains': [], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8883, 3673, 1281, 5291, 2477, 4651, 7515, 4750], 'generators': [], 'label': '352.106.352.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '352.a1.a1', 'normal_contained_in': ['32.a1.a1', '176.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '352.a1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '352.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65710085
    {'ambient': '352.106', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.b1.a1', '176.c1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '22.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1657, 5552, 8485, 516, 7883, 6460, 1538, 481], 'generators': [1, 88, 176, 44, 32], 'label': '352.106.2.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.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '176.31', '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': '88.11'}
  • id: 65710086
    {'ambient': '352.106', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1', '176.c1.a1', '176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '22.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2870, 8008, 6493, 7940, 7338, 5290, 3476, 2768], 'generators': [3, 88, 176, 44, 32], 'label': '352.106.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '176.31', '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': '176.31'}
  • id: 65710087
    {'ambient': '352.106', 'aut_centralizer_order': 44, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.46', 'aut_weyl_index': 44, 'centralizer': '16.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2576, 7833, 7501, 9484, 5725, 7709, 4100, 7056], 'generators': [2, 32, 176, 88], 'label': '352.106.4.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.b1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}