Abstract group data - 352.79

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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': 110, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 10, 11], 'aut_gens': [[1, 2, 8, 16], [5, 2, 8, 336], [9, 2, 8, 336], [1, 6, 8, 336], [1, 10, 8, 336], [1, 2, 8, 340], [1, 2, 8, 344], [1, 2, 8, 272], [33, 2, 8, 16]], 'aut_group': None, 'aut_hash': 3808563084807252545, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7040, 'aut_permdeg': 52, 'aut_perms': [71653880663568369996541902209749636654110551239381786481340409099495, 3680307797481668636109791225884737255851938896712413007878843598049, 487411756994668348988348660232110501337040392477292418228574426029, 487411734960255272093669653758272475340512892731984248234334426029, 487411723957669220781170735937480598837143993965977274343774426029, 487411723957669220780082655456883268612983789110303299395934426029, 821795792268220116958197934195016785159076215684372506490044500888, 63286760349739332569350205577461786641484629080164767693269477120006], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 22, 2, 1], [2, 44, 1, 1], [4, 2, 2, 1], [4, 4, 1, 1], [4, 22, 2, 1], [4, 44, 1, 1], [11, 2, 5, 1], [22, 2, 5, 3], [22, 4, 10, 1], [44, 4, 10, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{11}:C_5.C_2^6.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 22, 2], [2, 44, 1], [4, 2, 2], [4, 4, 1], [4, 22, 2], [4, 44, 1], [11, 2, 5], [22, 2, 15], [22, 4, 10], [44, 4, 20]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '88.11', 'commutator_count': 1, 'commutator_label': '44.4', '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': 79, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 22, 1, 2], [2, 44, 1, 1], [4, 2, 2, 1], [4, 4, 1, 1], [4, 22, 1, 2], [4, 44, 1, 1], [11, 2, 5, 1], [22, 2, 5, 3], [22, 4, 10, 1], [44, 4, 10, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2016, 'exponent': 44, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '88.11', 'hash': 79, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 2, 1, 22], 'inner_gens': [[1, 2, 8, 348], [1, 2, 8, 24], [1, 2, 8, 16], [45, 10, 8, 16]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 88, 'inner_split': True, 'inner_tex': 'C_2\\times D_{22}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 46], [4, 10]], 'label': '352.79', 'linC_count': 80, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 16, 'linQ_dim': 14, 'linQ_dim_count': 16, 'linR_count': 140, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D22:D4', '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': 18, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 64, 'number_divisions': 20, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 94, 'number_subgroups': 658, 'old_label': None, 'order': 352, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 95], [4, 96], [11, 10], [22, 70], [44, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 10], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[5, 2, 8, 336], [13, 2, 8, 16], [1, 6, 8, 336], [1, 2, 8, 272]], 'outer_group': '80.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 13, 'outer_perms': [3669840, 41040, 479001600, 753], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{10}', 'pc_rank': 4, '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, 4], [4, 1], [10, 4], [20, 2], [40, 1]], 'representations': {'PC': {'code': 354576364180869906000009, 'gens': [1, 2, 4, 5], 'pres': [6, -2, -2, -2, 2, 2, -11, 31, 10444, 370, 88, 11525]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [685345, 1024145, 14316699, 30666285, 45661573, 682177]}, 'Perm': {'d': 19, 'gens': [12933411247, 6778996856755200, 732385303372800, 13516122267648000, 13516309078272000, 4364893]}}, 'schur_multiplier': [2, 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': 'D_{22}:D_4', 'transitive_degree': 176, '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: 103902314
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 79, 'group_order': 352, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 103902325
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 79, 'group_order': 352, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8, 'size': 1}
  • id: 103902336
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 79, 'group_order': 352, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 4, 'size': 1}
  • id: 103902347
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 79, 'group_order': 352, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 12, 'size': 1}
  • id: 103902358
    {'aut_label': '2D', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 79, 'group_order': 352, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 176, 'size': 4}
  • id: 103902369
    {'aut_label': '2E', 'centralizer': '22.e1.a1', 'counter': 6, 'group_counter': 79, 'group_order': 352, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 165, 'size': 22}
  • id: 103902375
    {'aut_label': '2E', 'centralizer': '22.e1.a1', 'counter': 7, 'group_counter': 79, 'group_order': 352, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 205, 'size': 22}
  • id: 103902376
    {'aut_label': '2G', 'centralizer': '44.e1.a1', 'counter': 8, 'group_counter': 79, 'group_order': 352, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 59, 'size': 44}
  • id: 103902377
    {'aut_label': '4A1', 'centralizer': '2.e1.a1', 'counter': 9, 'group_counter': 79, 'group_order': 352, 'label': '4A1', 'order': 4, 'powers': [3, 9, 10], 'representative': 6, 'size': 2}
  • id: 103902315
    {'aut_label': '4A1', 'centralizer': '2.e1.a1', 'counter': 10, 'group_counter': 79, 'group_order': 352, 'label': '4A-1', 'order': 4, 'powers': [3, 10, 9], 'representative': 2, 'size': 2}
  • id: 103902316
    {'aut_label': '4B', 'centralizer': '4.e1.a1', 'counter': 11, 'group_counter': 79, 'group_order': 352, 'label': '4B', 'order': 4, 'powers': [4, 11, 11], 'representative': 190, 'size': 4}
  • id: 103902317
    {'aut_label': '4C', 'centralizer': '22.e1.a1', 'counter': 12, 'group_counter': 79, 'group_order': 352, 'label': '4C', 'order': 4, 'powers': [3, 12, 12], 'representative': 175, 'size': 22}
  • id: 103902318
    {'aut_label': '4C', 'centralizer': '22.e1.a1', 'counter': 13, 'group_counter': 79, 'group_order': 352, 'label': '4D', 'order': 4, 'powers': [3, 13, 13], 'representative': 195, 'size': 22}
  • id: 103902319
    {'aut_label': '4E', 'centralizer': '44.g1.a1', 'counter': 14, 'group_counter': 79, 'group_order': 352, 'label': '4E', 'order': 4, 'powers': [4, 14, 14], 'representative': 61, 'size': 44}
  • id: 103902320
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 79, 'group_order': 352, 'label': '11A1', 'order': 11, 'powers': [16, 19, 1], 'representative': 64, 'size': 2}
  • id: 103902321
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 79, 'group_order': 352, 'label': '11A2', 'order': 11, 'powers': [18, 15, 1], 'representative': 128, 'size': 2}
  • id: 103902322
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 17, 'group_counter': 79, 'group_order': 352, 'label': '11A3', 'order': 11, 'powers': [19, 18, 1], 'representative': 192, 'size': 2}
  • id: 103902323
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 18, 'group_counter': 79, 'group_order': 352, 'label': '11A4', 'order': 11, 'powers': [17, 16, 1], 'representative': 256, 'size': 2}
  • id: 103902324
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 79, 'group_order': 352, 'label': '11A5', 'order': 11, 'powers': [15, 17, 1], 'representative': 320, 'size': 2}
  • id: 103902326
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 79, 'group_order': 352, 'label': '22A1', 'order': 22, 'powers': [15, 22, 2], 'representative': 40, 'size': 2}
  • id: 103902327
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 79, 'group_order': 352, 'label': '22A3', 'order': 22, 'powers': [17, 23, 2], 'representative': 104, 'size': 2}
  • id: 103902328
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 22, 'group_counter': 79, 'group_order': 352, 'label': '22A5', 'order': 22, 'powers': [19, 21, 2], 'representative': 168, 'size': 2}
  • id: 103902329
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 79, 'group_order': 352, 'label': '22A7', 'order': 22, 'powers': [18, 24, 2], 'representative': 136, 'size': 2}
  • id: 103902330
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 24, 'group_counter': 79, 'group_order': 352, 'label': '22A9', 'order': 22, 'powers': [16, 20, 2], 'representative': 72, 'size': 2}
  • id: 103902331
    {'aut_label': '22B1', 'centralizer': '2.c1.a1', 'counter': 25, 'group_counter': 79, 'group_order': 352, 'label': '22B1', 'order': 22, 'powers': [16, 27, 3], 'representative': 68, 'size': 2}
  • id: 103902332
    {'aut_label': '22B1', 'centralizer': '2.c1.a1', 'counter': 26, 'group_counter': 79, 'group_order': 352, 'label': '22B3', 'order': 22, 'powers': [19, 28, 3], 'representative': 196, 'size': 2}
  • id: 103902333
    {'aut_label': '22B1', 'centralizer': '2.c1.a1', 'counter': 27, 'group_counter': 79, 'group_order': 352, 'label': '22B5', 'order': 22, 'powers': [15, 26, 3], 'representative': 324, 'size': 2}
  • id: 103902334
    {'aut_label': '22B1', 'centralizer': '2.c1.a1', 'counter': 28, 'group_counter': 79, 'group_order': 352, 'label': '22B7', 'order': 22, 'powers': [17, 29, 3], 'representative': 100, 'size': 2}
  • id: 103902335
    {'aut_label': '22B1', 'centralizer': '2.c1.a1', 'counter': 29, 'group_counter': 79, 'group_order': 352, 'label': '22B9', 'order': 22, 'powers': [18, 25, 3], 'representative': 228, 'size': 2}
  • id: 103902337
    {'aut_label': '22C1', 'centralizer': '2.c1.a1', 'counter': 30, 'group_counter': 79, 'group_order': 352, 'label': '22C1', 'order': 22, 'powers': [15, 32, 4], 'representative': 44, 'size': 2}
  • id: 103902338
    {'aut_label': '22C1', 'centralizer': '2.c1.a1', 'counter': 31, 'group_counter': 79, 'group_order': 352, 'label': '22C3', 'order': 22, 'powers': [17, 33, 4], 'representative': 108, 'size': 2}
  • id: 103902339
    {'aut_label': '22C1', 'centralizer': '2.c1.a1', 'counter': 32, 'group_counter': 79, 'group_order': 352, 'label': '22C5', 'order': 22, 'powers': [19, 31, 4], 'representative': 172, 'size': 2}
  • id: 103902340
    {'aut_label': '22C1', 'centralizer': '2.c1.a1', 'counter': 33, 'group_counter': 79, 'group_order': 352, 'label': '22C7', 'order': 22, 'powers': [18, 34, 4], 'representative': 236, 'size': 2}
  • id: 103902341
    {'aut_label': '22C1', 'centralizer': '2.c1.a1', 'counter': 34, 'group_counter': 79, 'group_order': 352, 'label': '22C9', 'order': 22, 'powers': [16, 30, 4], 'representative': 300, 'size': 2}
  • id: 103902342
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 35, 'group_counter': 79, 'group_order': 352, 'label': '22D1', 'order': 22, 'powers': [19, 39, 5], 'representative': 16, 'size': 4}
  • id: 103902343
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 36, 'group_counter': 79, 'group_order': 352, 'label': '22D-1', 'order': 22, 'powers': [19, 40, 5], 'representative': 20, 'size': 4}
  • id: 103902344
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 37, 'group_counter': 79, 'group_order': 352, 'label': '22D3', 'order': 22, 'powers': [18, 42, 5], 'representative': 48, 'size': 4}
  • id: 103902345
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 79, 'group_order': 352, 'label': '22D-3', 'order': 22, 'powers': [18, 41, 5], 'representative': 304, 'size': 4}
  • id: 103902346
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 39, 'group_counter': 79, 'group_order': 352, 'label': '22D5', 'order': 22, 'powers': [17, 37, 5], 'representative': 80, 'size': 4}
  • id: 103902348
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 40, 'group_counter': 79, 'group_order': 352, 'label': '22D-5', 'order': 22, 'powers': [17, 38, 5], 'representative': 272, 'size': 4}
  • id: 103902349
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 41, 'group_counter': 79, 'group_order': 352, 'label': '22D7', 'order': 22, 'powers': [16, 44, 5], 'representative': 112, 'size': 4}
  • id: 103902350
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 42, 'group_counter': 79, 'group_order': 352, 'label': '22D-7', 'order': 22, 'powers': [16, 43, 5], 'representative': 240, 'size': 4}
  • id: 103902351
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 43, 'group_counter': 79, 'group_order': 352, 'label': '22D9', 'order': 22, 'powers': [15, 35, 5], 'representative': 144, 'size': 4}
  • id: 103902352
    {'aut_label': '22D1', 'centralizer': '4.a1.a1', 'counter': 44, 'group_counter': 79, 'group_order': 352, 'label': '22D-9', 'order': 22, 'powers': [15, 36, 5], 'representative': 208, 'size': 4}
  • id: 103902353
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 45, 'group_counter': 79, 'group_order': 352, 'label': '44A1', 'order': 44, 'powers': [25, 49, 9], 'representative': 34, 'size': 4}
  • id: 103902354
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 46, 'group_counter': 79, 'group_order': 352, 'label': '44A-1', 'order': 44, 'powers': [25, 50, 10], 'representative': 38, 'size': 4}
  • id: 103902355
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 47, 'group_counter': 79, 'group_order': 352, 'label': '44A3', 'order': 44, 'powers': [26, 51, 10], 'representative': 102, 'size': 4}
  • id: 103902356
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 48, 'group_counter': 79, 'group_order': 352, 'label': '44A-3', 'order': 44, 'powers': [26, 52, 9], 'representative': 98, 'size': 4}
  • id: 103902357
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 49, 'group_counter': 79, 'group_order': 352, 'label': '44A5', 'order': 44, 'powers': [27, 48, 9], 'representative': 162, 'size': 4}
  • id: 103902359
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 50, 'group_counter': 79, 'group_order': 352, 'label': '44A-5', 'order': 44, 'powers': [27, 47, 10], 'representative': 166, 'size': 4}
  • id: 103902360
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 51, 'group_counter': 79, 'group_order': 352, 'label': '44A7', 'order': 44, 'powers': [28, 54, 10], 'representative': 134, 'size': 4}
  • id: 103902361
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 52, 'group_counter': 79, 'group_order': 352, 'label': '44A-7', 'order': 44, 'powers': [28, 53, 9], 'representative': 130, 'size': 4}
  • id: 103902362
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 53, 'group_counter': 79, 'group_order': 352, 'label': '44A9', 'order': 44, 'powers': [29, 45, 9], 'representative': 66, 'size': 4}
  • id: 103902363
    {'aut_label': '44A1', 'centralizer': '4.d1.a1', 'counter': 54, 'group_counter': 79, 'group_order': 352, 'label': '44A-9', 'order': 44, 'powers': [29, 46, 10], 'representative': 70, 'size': 4}
  • id: 103902364
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 55, 'group_counter': 79, 'group_order': 352, 'label': '44B1', 'order': 44, 'powers': [30, 57, 11], 'representative': 18, 'size': 4}
  • id: 103902365
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 56, 'group_counter': 79, 'group_order': 352, 'label': '44B3', 'order': 44, 'powers': [31, 61, 11], 'representative': 306, 'size': 4}
  • id: 103902366
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 57, 'group_counter': 79, 'group_order': 352, 'label': '44B5', 'order': 44, 'powers': [32, 63, 11], 'representative': 82, 'size': 4}
  • id: 103902367
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 58, 'group_counter': 79, 'group_order': 352, 'label': '44B7', 'order': 44, 'powers': [33, 59, 11], 'representative': 242, 'size': 4}
  • id: 103902368
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 59, 'group_counter': 79, 'group_order': 352, 'label': '44B9', 'order': 44, 'powers': [34, 55, 11], 'representative': 146, 'size': 4}
  • id: 103902370
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 60, 'group_counter': 79, 'group_order': 352, 'label': '44B13', 'order': 44, 'powers': [34, 64, 11], 'representative': 210, 'size': 4}
  • id: 103902371
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 61, 'group_counter': 79, 'group_order': 352, 'label': '44B15', 'order': 44, 'powers': [33, 60, 11], 'representative': 114, 'size': 4}
  • id: 103902372
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 62, 'group_counter': 79, 'group_order': 352, 'label': '44B17', 'order': 44, 'powers': [32, 56, 11], 'representative': 274, 'size': 4}
  • id: 103902373
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 63, 'group_counter': 79, 'group_order': 352, 'label': '44B19', 'order': 44, 'powers': [31, 58, 11], 'representative': 50, 'size': 4}
  • id: 103902374
    {'aut_label': '44B1', 'centralizer': '4.e1.a1', 'counter': 64, 'group_counter': 79, 'group_order': 352, 'label': '44B21', 'order': 44, 'powers': [30, 62, 11], 'representative': 22, '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: 2517831
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2517842
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2517844
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2517845
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2517846
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2517847
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2517848
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2517849
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2517850
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517832
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517833
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517834
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517835
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, -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, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517836
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2f', 'multiplicity': 5, 'nt': [11, 2], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 10, 0, 0, 0, 10, 10, 10, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2517837
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2g', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 10, 10, -10, 0, 0, 0, -10, -10, 10, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2517838
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2h', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 10, 10, -10, 0, 0, 0, 10, 10, -10, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2517839
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2i', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 10, 0, 0, 0, -10, -10, -10, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2517841
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.4a', 'multiplicity': 5, 'nt': [44, 12], 'qdim': 20, 'qvalues': [20, -20, 20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517843
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.4b', 'multiplicity': 5, 'nt': [44, 12], 'qdim': 20, 'qvalues': [20, 20, -20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2517840
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '352.79', 'group_order': 352, 'image': None, 'label': '352.79.2j', 'multiplicity': 20, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, -40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, -4, 4, 4, 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, 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: 3308412
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 352, 'label': '352.79.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3308423
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 176, 'label': '352.79.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 3308434
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 176, 'label': '352.79.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 3308445
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 176, 'label': '352.79.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 3308456
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 176, 'label': '352.79.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 3308467
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 176, 'label': '352.79.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3308473
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 176, 'label': '352.79.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3308474
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 352, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 176, 'label': '352.79.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3308475
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 88, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.b1', 'kernel_order': 44, 'label': '352.79.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308413
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 88, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 44, 'label': '352.79.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308414
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 88, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 44, 'label': '352.79.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 3308415
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 88, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 44, 'label': '352.79.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 3308416
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 88, 'counter': 13, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 22, 'label': '352.79.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]]]}
  • id: 3308417
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 88, 'counter': 14, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 22, 'label': '352.79.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]]]}
  • id: 3308418
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.79.2f1', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]]]}
  • id: 3308419
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.79.2f2', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]]]}
  • id: 3308420
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.79.2f3', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 3308421
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.79.2f4', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]]]}
  • id: 3308422
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 16, 'label': '352.79.2f5', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 3308424
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.79.2g1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]]]}
  • id: 3308425
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.79.2g2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]]]}
  • id: 3308426
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.79.2g3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]]]}
  • id: 3308427
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.79.2g4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]]]}
  • id: 3308428
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 8, 'label': '352.79.2g5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
  • id: 3308429
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.79.2h1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]]]}
  • id: 3308430
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.79.2h2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 3308431
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.79.2h3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 3308432
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.79.2h4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]]]}
  • id: 3308433
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 8, 'label': '352.79.2h5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 3308435
    {'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': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.79.2i1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]]]}
  • id: 3308436
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.79.2i2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 3308437
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.79.2i3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 3308438
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.79.2i4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]]]}
  • id: 3308439
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 8, 'label': '352.79.2i5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 3308440
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j1', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 4], [-1, 18]], [[-1, 6], [-1, 16]], [[1, 6], [1, 16]], [[1, 4], [1, 18]], [[-1, 8], [-1, 14]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[-1, 10], [-1, 12]], [[1, 8], [1, 14]], [[1, 10], [1, 12]], [[-1, 3], [-1, 19]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, 17]], [[-1, 9], [-1, -9]], [[1, 3], [1, 19]], [[1, 7], [1, 15]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 9], [-1, 13]], [[1, 3], [1, -3]], [[-1, 5], [-1, 17]], [[-1, 7], [-1, -7]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 9], [1, -9]], [[-1, 7], [-1, 15]], [[1, 9], [1, 13]], [[-1, 5], [-1, -5]]]}
  • id: 3308450
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 44, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j10', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[1, 10], [1, 12]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[-1, 8], [-1, 14]], [[1, 8], [1, 14]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 4], [-1, 18]], [[-1, 10], [-1, 12]], [[1, 6], [1, 16]], [[1, 4], [1, 18]], [[-1, 6], [-1, 16]], [[1, 7], [1, 15]], [[-1, 5], [-1, -5]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[1, 3], [1, 19]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, 15]], [[1, 9], [1, 13]], [[1, 5], [1, 17]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, 19]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, 17]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 9], [-1, 13]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[1, 3], [1, -3]]]}
  • id: 3308451
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 45, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j11', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[1, 10], [1, 12]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[-1, 8], [-1, 14]], [[1, 8], [1, 14]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 4], [-1, 18]], [[-1, 10], [-1, 12]], [[1, 6], [1, 16]], [[1, 4], [1, 18]], [[-1, 6], [-1, 16]], [[-1, 7], [-1, 15]], [[1, 5], [1, -5]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, 19]], [[1, 1], [1, -1]], [[1, 7], [1, 15]], [[-1, 9], [-1, 13]], [[-1, 5], [-1, 17]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[1, 7], [1, -7]], [[1, 3], [1, 19]], [[1, 9], [1, -9]], [[1, 5], [1, 17]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 9], [1, 13]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 3], [-1, -3]]]}
  • id: 3308452
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 46, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j12', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 10], [-1, 12]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[1, 8], [1, 14]], [[-1, 8], [-1, 14]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 4], [1, 18]], [[1, 10], [1, 12]], [[-1, 6], [-1, 16]], [[-1, 4], [-1, 18]], [[1, 6], [1, 16]], [[1, 7], [1, 15]], [[1, 5], [1, -5]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[1, 3], [1, 19]], [[1, 1], [1, -1]], [[-1, 7], [-1, 15]], [[1, 9], [1, 13]], [[1, 5], [1, 17]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 7], [1, -7]], [[-1, 3], [-1, 19]], [[1, 9], [1, -9]], [[-1, 5], [-1, 17]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, 13]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 3], [-1, -3]]]}
  • id: 3308453
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j13', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, 14]], [[1, 6], [1, 16]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 6], [-1, 16]], [[-1, 10], [-1, 12]], [[1, 8], [1, 14]], [[1, 4], [1, 18]], [[1, 10], [1, 12]], [[-1, 4], [-1, 18]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[1, 9], [1, 13]], [[-1, 3], [-1, -3]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 5], [-1, 17]], [[1, 7], [1, 15]], [[1, 3], [1, 19]], [[1, 1], [1, -1]], [[-1, 9], [-1, 13]], [[1, 5], [1, -5]], [[-1, 7], [-1, 15]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[1, 5], [1, 17]], [[-1, 3], [-1, 19]], [[1, 9], [1, -9]]]}
  • id: 3308454
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j14', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 8], [1, 14]], [[-1, 6], [-1, 16]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 6], [1, 16]], [[1, 10], [1, 12]], [[-1, 8], [-1, 14]], [[-1, 4], [-1, 18]], [[-1, 10], [-1, 12]], [[1, 4], [1, 18]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 9], [-1, 13]], [[-1, 3], [-1, -3]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 5], [1, 17]], [[-1, 7], [-1, 15]], [[-1, 3], [-1, 19]], [[1, 1], [1, -1]], [[1, 9], [1, 13]], [[1, 5], [1, -5]], [[1, 7], [1, 15]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[-1, 5], [-1, 17]], [[1, 3], [1, 19]], [[1, 9], [1, -9]]]}
  • id: 3308455
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j15', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 8], [1, 14]], [[-1, 6], [-1, 16]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 6], [1, 16]], [[1, 10], [1, 12]], [[-1, 8], [-1, 14]], [[-1, 4], [-1, 18]], [[-1, 10], [-1, 12]], [[1, 4], [1, 18]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[1, 9], [1, 13]], [[1, 3], [1, -3]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 5], [-1, 17]], [[1, 7], [1, 15]], [[1, 3], [1, 19]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, 13]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, 15]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 5], [1, 17]], [[-1, 3], [-1, 19]], [[-1, 9], [-1, -9]]]}
  • id: 3308457
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j16', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, 14]], [[1, 6], [1, 16]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 6], [-1, 16]], [[-1, 10], [-1, 12]], [[1, 8], [1, 14]], [[1, 4], [1, 18]], [[1, 10], [1, 12]], [[-1, 4], [-1, 18]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[-1, 9], [-1, 13]], [[1, 3], [1, -3]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 5], [1, 17]], [[-1, 7], [-1, 15]], [[-1, 3], [-1, 19]], [[-1, 1], [-1, -1]], [[1, 9], [1, 13]], [[-1, 5], [-1, -5]], [[1, 7], [1, 15]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, 17]], [[1, 3], [1, 19]], [[-1, 9], [-1, -9]]]}
  • id: 3308458
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j17', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 4], [-1, 18]], [[1, 8], [1, 14]], [[-1, 10], [-1, 12]], [[1, 10], [1, 12]], [[-1, 8], [-1, 14]], [[1, 6], [1, 16]], [[1, 4], [1, 18]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 6], [-1, 16]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 5], [1, 17]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, 17]], [[1, 3], [1, 19]], [[-1, 9], [-1, 13]], [[1, 7], [1, 15]], [[-1, 5], [-1, -5]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[1, 3], [1, -3]], [[1, 9], [1, 13]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[-1, 3], [-1, 19]], [[-1, 7], [-1, 15]], [[-1, 1], [-1, -1]]]}
  • id: 3308459
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j18', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[1, 4], [1, 18]], [[-1, 8], [-1, 14]], [[1, 10], [1, 12]], [[-1, 10], [-1, 12]], [[1, 8], [1, 14]], [[-1, 6], [-1, 16]], [[-1, 4], [-1, 18]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 6], [1, 16]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 5], [-1, 17]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 7], [-1, -7]], [[1, 5], [1, 17]], [[-1, 3], [-1, 19]], [[1, 9], [1, 13]], [[-1, 7], [-1, 15]], [[-1, 5], [-1, -5]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 3], [1, -3]], [[-1, 9], [-1, 13]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, 19]], [[1, 7], [1, 15]], [[-1, 1], [-1, -1]]]}
  • id: 3308460
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j19', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[1, 4], [1, 18]], [[-1, 8], [-1, 14]], [[1, 10], [1, 12]], [[-1, 10], [-1, 12]], [[1, 8], [1, 14]], [[-1, 6], [-1, 16]], [[-1, 4], [-1, 18]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 6], [1, 16]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[1, 5], [1, 17]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 7], [1, -7]], [[-1, 5], [-1, 17]], [[1, 3], [1, 19]], [[-1, 9], [-1, 13]], [[1, 7], [1, 15]], [[1, 5], [1, -5]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 3], [-1, -3]], [[1, 9], [1, 13]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, 19]], [[-1, 7], [-1, 15]], [[1, 1], [1, -1]]]}
  • id: 3308441
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j2', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 4], [1, 18]], [[1, 6], [1, 16]], [[-1, 6], [-1, 16]], [[-1, 4], [-1, 18]], [[1, 8], [1, 14]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[1, 10], [1, 12]], [[-1, 8], [-1, 14]], [[-1, 10], [-1, 12]], [[1, 3], [1, 19]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 5], [-1, 17]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, 19]], [[-1, 7], [-1, 15]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 9], [1, 13]], [[1, 3], [1, -3]], [[1, 5], [1, 17]], [[-1, 7], [-1, -7]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 9], [1, -9]], [[1, 7], [1, 15]], [[-1, 9], [-1, 13]], [[-1, 5], [-1, -5]]]}
  • id: 3308461
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j20', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 8], [1, -8]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 10], [-1, -10]], [[-1, 4], [-1, 18]], [[1, 8], [1, 14]], [[-1, 10], [-1, 12]], [[1, 10], [1, 12]], [[-1, 8], [-1, 14]], [[1, 6], [1, 16]], [[1, 4], [1, 18]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 6], [-1, 16]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[-1, 5], [-1, 17]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[1, 7], [1, -7]], [[1, 5], [1, 17]], [[-1, 3], [-1, 19]], [[1, 9], [1, 13]], [[-1, 7], [-1, 15]], [[1, 5], [1, -5]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, 13]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[1, 3], [1, 19]], [[1, 7], [1, 15]], [[1, 1], [1, -1]]]}
  • id: 3308442
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  • id: 3308443
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  • id: 3308444
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  • id: 3308446
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  • id: 3308447
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  • id: 3308448
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 42, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j8', 'nt': [88, 20], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 11]], [[-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, 16]], [[-1, 10], [-1, 12]], [[-1, 4], [-1, 18]], [[1, 4], [1, 18]], [[1, 10], [1, 12]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 6], [1, 16]], [[1, 8], [1, 14]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[-1, 8], [-1, 14]], [[-1, 9], [-1, 13]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 7], [1, 15]], [[1, 5], [1, -5]], [[1, 9], [1, 13]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[-1, 3], [-1, 19]], [[1, 5], [1, 17]], [[1, 9], [1, -9]], [[-1, 7], [-1, 15]], [[1, 1], [1, -1]], [[1, 3], [1, 19]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 5], [-1, 17]], [[1, 7], [1, -7]]]}
  • id: 3308449
    {'center': '44.b1.a1', 'center_index': 44, 'center_order': 8, 'counter': 43, 'cyclotomic_n': 44, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.30', 'image_order': 176, 'indicator': 0, 'kernel': '176.a1.a1', 'kernel_order': 2, 'label': '352.79.2j9', 'nt': [88, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 11]], [[2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 8], [1, -8]], [[-1, 10], [-1, 12]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18]], [[1, 8], [1, 14]], [[-1, 8], [-1, 14]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10], [-1, 12], [1, 14], [-1, 16], [1, 18]], [[1, 4], [1, 18]], [[1, 10], [1, 12]], [[-1, 6], [-1, 16]], [[-1, 4], [-1, 18]], [[1, 6], [1, 16]], [[-1, 7], [-1, 15]], [[-1, 5], [-1, -5]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[-1, 3], [-1, 19]], [[-1, 1], [-1, -1]], [[1, 7], [1, 15]], [[-1, 9], [-1, 13]], [[-1, 5], [-1, 17]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19]], [[-1, 7], [-1, -7]], [[1, 3], [1, 19]], [[-1, 9], [-1, -9]], [[1, 5], [1, 17]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 9], [1, 13]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19]], [[1, 3], [1, -3]]]}
  • id: 3308462
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.c1.a1', 'kernel_order': 2, 'label': '352.79.4a1', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308463
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.c1.a1', 'kernel_order': 2, 'label': '352.79.4a2', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 5], [2, -5]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308464
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 57, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.c1.a1', 'kernel_order': 2, 'label': '352.79.4a3', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308465
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 58, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.c1.a1', 'kernel_order': 2, 'label': '352.79.4a4', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308466
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 59, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.c1.a1', 'kernel_order': 2, 'label': '352.79.4a5', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[2, 4], [2, -4]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308468
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 60, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.b1.a1', 'kernel_order': 2, 'label': '352.79.4b1', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308469
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 61, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.b1.a1', 'kernel_order': 2, 'label': '352.79.4b2', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 5], [-2, -5]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308470
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 62, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.b1.a1', 'kernel_order': 2, 'label': '352.79.4b3', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 4], [-2, -4]], [[2, 4], [2, -4]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308471
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 63, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.b1.a1', 'kernel_order': 2, 'label': '352.79.4b4', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3308472
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 4, 'counter': 64, 'cyclotomic_n': 11, 'dim': 4, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '352.79', 'group_counter': 79, 'group_order': 352, 'image': None, 'image_isoclass': '176.31', 'image_order': 176, 'indicator': 1, 'kernel': '176.b1.a1', 'kernel_order': 2, 'label': '352.79.4b5', 'nt': [44, 12], 'q_character': None, 'values': [[[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]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 3], [2, -3]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 4], [-2, -4]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 51888330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 352, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 22, 'label': '352.79.1.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': '352.79', 'subgroup_hash': 79, 'subgroup_order': 352, 'subgroup_tex': 'D_{22}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.36', 'subgroup_hash': 36, 'subgroup_order': 176, 'subgroup_tex': 'C_{22}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.36', 'subgroup_hash': 36, 'subgroup_order': 176, 'subgroup_tex': 'C_{22}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 176, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.20', 'subgroup_hash': 20, 'subgroup_order': 176, 'subgroup_tex': 'C_2^2:C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.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': '176.29', 'subgroup_hash': 29, 'subgroup_order': 176, 'subgroup_tex': 'C_2\\times D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 176, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.28', 'subgroup_hash': 28, 'subgroup_order': 176, 'subgroup_tex': 'C_4\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.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': '176.13', 'subgroup_hash': 13, 'subgroup_order': 176, 'subgroup_tex': 'D_{22}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 176, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.2.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': '176.11', 'subgroup_hash': 11, 'subgroup_order': 176, 'subgroup_tex': 'C_{22}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 88, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.12', 'subgroup_hash': 12, 'subgroup_order': 88, 'subgroup_tex': 'C_2^2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 88, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, '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: 51888332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 88, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.11', 'subgroup_hash': 11, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 88, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '88.8', 'subgroup_hash': 8, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 88, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.8', 'subgroup_hash': 8, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 88, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, '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: 51888336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 88, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': False, '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: 51888337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.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: 51888338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.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': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 51888340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 51888342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.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': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 44, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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', 'S', 'L1', 'D1', 'C3'], 'split': False, '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: 51888347
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.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': True, '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: 51888348
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', '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': True, '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: 51888349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 44, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 22, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.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: 51888353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 22, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.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: 51888355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 22, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 22, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.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: 51888357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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: 51888358
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 22, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 22, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 51888360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.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: 51888361
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 22, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 51888362
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 22, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.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: 51888364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '352.79.11.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 51888365
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 22, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.16.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': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 22, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.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': ['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: 51888367
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 22, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.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': [], '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: 51888368
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 11, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 51888369
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 11, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.16.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: 51888370
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 11, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888371
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 11, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 51888372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.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: 51888377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.22.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888380
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 11, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '352.79.32.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': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', '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: 51888381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51888382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.44.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.44.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': False, '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: 51888384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51888386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51888387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.44.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '352.79.88.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': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51888399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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: 51888400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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: 51888401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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: 51888402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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: 51888403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51888404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51888405
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 176, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.88.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888406
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.88.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 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: 51888408
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.88.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51888409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 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: 51888410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 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: 51888411
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51888412
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '352.79.88.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.l1.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: 51888413
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.88.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.m1.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: 51888414
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.88.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.n1.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: 51888415
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 2, 'counter': 87, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.176.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': '176.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51888416
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 2, 'counter': 88, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '176.b1.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': [], '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: 51888417
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 2, 'counter': 89, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '352.79.176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '176.c1.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': [], '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: 51888419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.176.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: 51888420
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.176.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: 51888421
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.176.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 51888422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '352.79.176.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 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: 51888423
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '352.79', 'ambient_counter': 79, 'ambient_order': 352, 'ambient_tex': 'D_{22}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 352, 'characteristic': True, 'core_order': 1, 'counter': 94, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '352.79.352.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': '352.79', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 79, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}:D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', '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: 51888353
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.e1.b1', '88.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3958, -1, 2925, -1, 3169, -1, 6659, -1], 'generators': [1, 32, 8], 'label': '352.79.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.e1.a1', 'projective_image': '176.30', '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': '22.1'}
  • id: 51888330
    {'ambient': '352.79', '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': '88.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': [3199, 4833, 5245, 5119, 4885, 5225, 5030, 5284], 'generators': [1, 32, 176, 4, 2, 8], 'label': '352.79.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 51888331
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.e1.a1', '8.h1.a1', '44.d1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3023, 3580, 3202, 662, 2543, 3993, 6978, 7968], 'generators': [1, 8, 32, 4], 'label': '352.79.4.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.a1.a1', '8.c1.a1', '8.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '88.11', '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': '44.3'}
  • id: 51888332
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, '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.f1.a1', '8.i1.a1', '8.l1.a1', '44.e1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4165, 7774, 5888, 6666, 6158, 6546, 4320, 3993], 'generators': [19, 8, 32, 4], 'label': '352.79.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '88.11', '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: 51888333
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '44.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5743, 4927, 6672, 9338, 8584, 5269, 1239, 5269], 'generators': [2, 32, 4, 8], 'label': '352.79.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '44.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '88.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51888334
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '44.c1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2258, 802, 3986, 8045, 3681, 1360, 6033, 2717], 'generators': [190, 32, 12, 8], 'label': '352.79.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '88.11', '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': '4.2'}
  • id: 51888335
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '44.f1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6696, 9237, 8352, 2161, 7355, 9354, 2260, 9354], 'generators': [3, 4, 32, 8], 'label': '352.79.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888336
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.n1.a1', '44.g1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [386, 6312, 2503, 3699, 1851, 7932, 7552, 6582], 'generators': [17, 12, 32, 8], 'label': '352.79.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
  • id: 51888337
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.i1.a1', '44.h1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8567, -1, 7771, -1, 9100, -1, 3099, -1], 'generators': [335, 4, 32, 176], 'label': '352.79.4.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': '44.3'}
  • id: 51888338
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.b1', '8.g1.a1', '8.i1.a1', '44.h1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8567, -1, 7330, -1, 9100, -1, 2737, -1], 'generators': [7, 4, 32, 176], 'label': '352.79.4.h1.b1', '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.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888339
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.j1.a1', '44.i1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 9761, -1, 9620, -1, 741, -1], 'generators': [1, 4, 32, 14], 'label': '352.79.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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': '22.1'}
  • id: 51888340
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.b1.b1', '8.h1.a1', '8.j1.a1', '44.i1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 9155, -1, 9620, -1, 243, -1], 'generators': [1, 4, 32, 2], 'label': '352.79.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.i1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 51888341
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1', '4.j1.a1', '4.j1.b1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1322, 3619, 2503, 742, 2199, 3641, 7552, 6436], 'generators': [1, 176, 12, 8, 32], 'label': '352.79.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 51888342
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '8.n1.a1', '44.j1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1076, -1, 1182, -1, 450, -1, 8985, -1], 'generators': [329, 12, 32, 176], 'label': '352.79.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '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: 51888343
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.b1', '8.k1.a1', '8.n1.a1', '44.j1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1076, -1, 716, -1, 450, -1, 9347, -1], 'generators': [1, 12, 32, 176], 'label': '352.79.4.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.j1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888344
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.l1.a1', '8.m1.a1', '44.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1704, -1, 1977, -1, 831, -1, 8399, -1], 'generators': [329, 12, 32, 190], 'label': '352.79.4.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': '44.3'}
  • id: 51888345
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.b1', '8.l1.a1', '8.m1.a1', '44.k1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1704, -1, 1648, -1, 831, -1, 8670, -1], 'generators': [1, 12, 32, 190], 'label': '352.79.4.k1.b1', '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.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888346
    {'ambient': '352.79', 'aut_centralizer_order': 704, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.c1.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', '16.b1.a1', '16.c1.a1', '88.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4846, 4833, 3986, 4254, 5331, 5049, 4863, 6142], 'generators': [4, 32, 8], 'label': '352.79.8.a1.a1', 'mobius_quo': -2, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.c1.a1', '16.b1.a1', '16.a1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888347
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': ['44.j1.a1', '44.j1.b1', '44.k1.a1', '44.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.b1.a1', '88.i1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9614, 7581, 8955, 2193, 8994, 7785, 1610, 9354], 'generators': [331, 32, 4], 'label': '352.79.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.b1.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': '44.3'}
  • id: 51888348
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': ['44.j1.b1', '44.j1.a1', '44.k1.b1', '44.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.b1', '4.i1.b1'], 'contains': ['16.b1.a1', '88.i1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9614, 7581, 8515, 3136, 8994, 7785, 1248, 8481], 'generators': [3, 32, 4], 'label': '352.79.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', '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.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888349
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': ['44.h1.a1', '44.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '88.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1929, 3750, 1977, 662, 831, 4125, 8323, 7719], 'generators': [329, 32, 12], 'label': '352.79.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.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.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888350
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': ['44.h1.b1', '44.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.b1', '4.k1.b1'], 'contains': ['16.c1.a1', '16.e1.b1', '88.k1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1929, 3750, 716, 1368, 831, 4125, 9089, 7066], 'generators': [1, 32, 12], 'label': '352.79.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', '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.c1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888351
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '88.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7324, -1, 4590, -1, 4431, -1, 5611, -1], 'generators': [8, 32, 176], 'label': '352.79.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.d1.a1', 'projective_image': '176.30', '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': '2.1'}
  • id: 51888352
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.e1.b1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.f1.a1', '4.h1.a1', '4.h1.b1', '22.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5299, 8819, 7330, 5119, 6608, 6817, 3487, 4133], 'generators': [3, 176, 4, 8, 32], 'label': '352.79.2.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.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 51888354
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '88.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6380, -1, 6050, -1, 6096, -1, 4481, -1], 'generators': [19, 32, 8], 'label': '352.79.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.f1.a1', 'projective_image': '176.30', '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: 51888355
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.b1.a1', '16.d1.a1', '88.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8603, -1, 7045, -1, 7384, -1, 3575, -1], 'generators': [4, 32, 176], 'label': '352.79.8.g1.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.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': '2.1'}
  • id: 51888356
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.e1.b1', '88.f1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6771, -1, 8130, -1, 6422, -1, 3958, -1], 'generators': [1, 32, 4], 'label': '352.79.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.h1.a1', 'projective_image': '176.31', '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: 51888357
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.b1.a1', '16.f1.a1', '88.g1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8050, -1, 7656, -1, 8346, -1, 3193, -1], 'generators': [19, 32, 4], 'label': '352.79.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.i1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888358
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.b1.a1', '88.h1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9157, -1, 9761, -1, 9872, -1, 106, -1], 'generators': [2, 4, 32], 'label': '352.79.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.j1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888359
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '88.j1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3067, -1, 1182, -1, 1881, -1, 8706, -1], 'generators': [12, 32, 176], 'label': '352.79.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888360
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.c1.a1', '16.f1.a1', '88.l1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2342, -1, 2451, -1, 2843, -1, 7345, -1], 'generators': [19, 32, 12], 'label': '352.79.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.l1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888361
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.c1.a1', '88.m1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1345, -1, 1648, -1, 1420, -1, 7834, -1], 'generators': [190, 12, 32], 'label': '352.79.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.m1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888362
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.c1.a1', '88.n1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [386, -1, 187, -1, 450, -1, 9626, -1], 'generators': [17, 32, 12], 'label': '352.79.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 51888363
    {'ambient': '352.79', 'aut_centralizer_order': 44, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.238', 'aut_weyl_index': 44, 'centralizer': '8.a1.a1', 'complements': ['176.e1.b1', '176.e1.a1', '176.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '22.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4244, 763, 5007, 8989, 5185, 935, 4781, 1426], 'generators': [2, 32, 4, 176, 8], 'label': '352.79.2.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.e1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '88.11', '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': '8.5'}
  • id: 51888364
    {'ambient': '352.79', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '64.267', 'aut_weyl_index': 110, 'centralizer': '88.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': [1507, -1, 5625, -1, 4585, -1, 5280, -1], 'generators': [1, 2, 176], 'label': '352.79.11.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': '88.11', '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': '8.5'}
  • id: 51888365
    {'ambient': '352.79', 'aut_centralizer_order': 704, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6713, 4833, 3982, 4239, 5020, 4771, 5349, 6142], 'generators': [8, 32], 'label': '352.79.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '176.30', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888366
    {'ambient': '352.79', 'aut_centralizer_order': 704, 'aut_label': '16.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '176.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8678, 5515, 8193, 3517, 7208, 5416, 3132, 7528], 'generators': [4, 32], 'label': '352.79.16.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.a1.a1', '176.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.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.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888367
    {'ambient': '352.79', 'aut_centralizer_order': 704, 'aut_label': '16.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.a1.a1', '176.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2285, 4152, 1082, 2819, 2192, 4125, 8071, 6883], 'generators': [12, 32], 'label': '352.79.16.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normal_contains': ['32.a1.a1', '176.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.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.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888368
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.g1.a1', '8.k1.a1'], 'contains': ['32.a1.a1', '176.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7944, -1, 4308, -1, 4398, -1, 5866, -1], 'generators': [176, 32], 'label': '352.79.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '352.79', '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': '1.1'}
  • id: 51888369
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '176.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5566, -1, 2920, -1, 3473, -1, 6136, -1], 'generators': [329, 32], 'label': '352.79.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.e1.a1', 'projective_image': '352.79', '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: 51888370
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.e1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '176.e1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5566, -1, 2591, -1, 3473, -1, 6659, -1], 'generators': [1, 32], 'label': '352.79.16.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.e1.b1', 'projective_image': '352.79', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 51888371
    {'ambient': '352.79', 'aut_centralizer_order': 16, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.i1.a1', '8.l1.a1'], 'contains': ['32.a1.a1', '176.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7105, -1, 6184, -1, 6023, -1, 5079, -1], 'generators': [19, 32], 'label': '352.79.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.f1.a1', 'projective_image': '352.79', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 51888372
    {'ambient': '352.79', 'aut_centralizer_order': 440, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '8.a1.a1', 'complements': ['16.e1.b1', '16.e1.a1', '16.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.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': [3726, 1498, 5865, 7943, 5199, 348, 4772, 348], 'generators': [2, 176], 'label': '352.79.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '88.11', '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': '8.5'}
  • id: 51888392
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.i1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '22.e1.a1'], 'contains': ['88.f1.a1', '88.h1.a1', '88.i1.b1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [9245, -1, 9170, -1, 9462, -1, 447, -1], 'generators': [1, 2], 'label': '352.79.44.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.a1', 'old_label': '44.i1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888373
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.a1', '44.g1.a1', '44.j1.a1', '44.j1.b1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [936, -1, 2439, -1, 1244, -1, 8056, -1], 'generators': [1, 8, 176], 'label': '352.79.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '88.11', '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': '8.5'}
  • id: 51888374
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.k1.a1', '4.k1.b1', '22.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2882, 2233, 3613, 6539, 3414, 2328, 6489, 2820], 'generators': [1, 8, 12, 190, 32], 'label': '352.79.2.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.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 51888375
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.e1.a1', '44.f1.a1', '44.h1.a1', '44.h1.b1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4970, -1, 7456, -1, 6747, -1, 3487, -1], 'generators': [3, 8, 176], 'label': '352.79.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '88.11', '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': '8.5'}
  • id: 51888376
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.d1.a1', '44.e1.a1', '44.k1.a1', '44.k1.b1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2113, -1, 3372, -1, 3132, -1, 6489, -1], 'generators': [1, 190, 8], 'label': '352.79.22.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': '88.11', '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': '8.5'}
  • id: 51888377
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.d1.a1', '44.f1.a1', '44.i1.a1', '44.i1.b1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5954, -1, 8425, -1, 7999, -1, 1725, -1], 'generators': [1, 2, 8], 'label': '352.79.22.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': '88.11', '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': '2.1'}
  • id: 51888378
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.e1.a1', '44.g1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3229, -1, 6428, -1, 5613, -1, 3867, -1], 'generators': [17, 2], 'label': '352.79.22.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': '88.11', '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: 51888379
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '22.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.f1.a1', '44.g1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1441, -1, 5485, -1, 4149, -1, 5644, -1], 'generators': [17, 190], 'label': '352.79.22.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': '88.11', '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': '8.5'}
  • id: 51888380
    {'ambient': '352.79', 'aut_centralizer_order': 704, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1'], 'contains': ['352.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7662, 4934, 4012, 3549, 4727, 5042, 5623, 6978], 'generators': [32], 'label': '352.79.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.c1.a1', '16.b1.a1', '16.a1.a1'], 'normal_contains': ['352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '352.79', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888381
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '4.a1.a1', 'complements': [], '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', '88.e1.a1', '88.j1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4732, 2148, 5251, 5214, 4881, 2497, 5237, 1441], 'generators': [12, 8, 176], 'label': '352.79.44.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': '88.11', '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': '4.2'}
  • id: 51888382
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '44.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.a1.a1', '22.e1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '88.h1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5211, 2992, 6609, 8108, 7933, 3297, 1999, 5042], 'generators': [2, 8], 'label': '352.79.44.b1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.b1.a1', 'normal_contained_in': ['4.d1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888383
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '44.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.a1.a1', '22.d1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.m1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2109, 1304, 4567, 7030, 3882, 1360, 6066, 2717], 'generators': [190, 8], 'label': '352.79.44.c1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.c1.a1', 'normal_contained_in': ['4.e1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '88.11', '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: 51888384
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.b1.a1', '22.d1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '88.c1.a1', '88.f1.a1', '88.k1.a1', '88.k1.b1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3278, -1, 2573, -1, 3483, -1, 6397, -1], 'generators': [1, 4, 8], 'label': '352.79.44.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.d1.a1', 'projective_image': '88.11', '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': '2.1'}
  • id: 51888385
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '44.b1.a1', 'complements': ['176.d1.a1', '176.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.i1.a1', '4.i1.b1', '22.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6397, 6219, 8352, 2454, 7494, 5225, 1725, 8900], 'generators': [1, 8, 4, 2, 32], 'label': '352.79.2.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.d1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '88.11', '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': '44.3'}
  • id: 51888386
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.c1.a1', '22.d1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '88.d1.a1', '88.g1.a1', '88.l1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4205, -1, 6187, -1, 5781, -1, 4219, -1], 'generators': [19, 4, 8], 'label': '352.79.44.e1.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.e1.a1', 'projective_image': '88.11', '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': '4.2'}
  • id: 51888387
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '44.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '22.c1.a1', '22.e1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.i1.a1', '88.i1.b1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5808, -1, 8384, -1, 6835, -1, 2412, -1], 'generators': [3, 8], 'label': '352.79.44.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.f1.a1', 'projective_image': '88.11', '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: 51888388
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '44.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '22.b1.a1', '22.f1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.n1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1512, -1, 3924, -1, 2430, -1, 7002, -1], 'generators': [17, 8], 'label': '352.79.44.g1.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.g1.a1', 'projective_image': '88.11', '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: 51888389
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '22.c1.a1'], 'contains': ['88.e1.a1', '88.g1.a1', '88.i1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8621, -1, 7823, -1, 8643, -1, 2947, -1], 'generators': [335, 176], 'label': '352.79.44.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '44.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: 51888390
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '22.c1.a1'], 'contains': ['88.e1.a1', '88.g1.a1', '88.i1.b1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8621, -1, 7556, -1, 8643, -1, 2728, -1], 'generators': [7, 176], 'label': '352.79.44.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '44.h1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51888391
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.i1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '22.e1.a1'], 'contains': ['88.f1.a1', '88.h1.a1', '88.i1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [9245, -1, 9813, -1, 9462, -1, 860, -1], 'generators': [1, 14], 'label': '352.79.44.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.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': '1.1'}
  • id: 51888393
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.j1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '22.b1.a1'], 'contains': ['88.j1.a1', '88.k1.a1', '88.n1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [738, -1, 723, -1, 99, -1, 9335, -1], 'generators': [329, 176], 'label': '352.79.44.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.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': '4.2'}
  • id: 51888394
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.j1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '22.b1.a1'], 'contains': ['88.j1.a1', '88.k1.b1', '88.n1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [738, -1, 316, -1, 99, -1, 9918, -1], 'generators': [1, 176], 'label': '352.79.44.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.j1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51888395
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.k1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '22.d1.a1'], 'contains': ['88.k1.a1', '88.l1.a1', '88.m1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1055, -1, 1537, -1, 1127, -1, 7591, -1], 'generators': [329, 190], 'label': '352.79.44.k1.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.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: 51888396
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.d1.a1', '176.e1.b1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '22.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3510, 7605, 5888, 7664, 5796, 7968, 4274, 5284], 'generators': [17, 12, 8, 2, 32], 'label': '352.79.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '88.11', '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: 51888397
    {'ambient': '352.79', 'aut_centralizer_order': 40, 'aut_label': '44.k1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '22.d1.a1'], 'contains': ['88.k1.b1', '88.l1.a1', '88.m1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1055, -1, 1270, -1, 1127, -1, 8077, -1], 'generators': [1, 190], 'label': '352.79.44.k1.b1', '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.k1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51888398
    {'ambient': '352.79', 'aut_centralizer_order': 7040, 'aut_label': '88.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1', '44.d1.a1', '44.e1.a1', '44.f1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '176.b1.a1', '176.c1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4469, 3541, 4726, 4873, 5331, 3399, 4818, 5335], 'generators': [4, 8], 'label': '352.79.88.a1.a1', 'mobius_quo': 2, 'mobius_sub': 88, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1'], 'normal_contains': ['176.c1.a1', '176.b1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '88.11', 'quotient_action_kernel_order': 88, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888399
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '44.a1.a1'], 'contains': ['176.a1.a1', '176.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7149, -1, 5030, -1, 4709, -1, 5608, -1], 'generators': [8, 176], 'label': '352.79.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '88.b1.a1', 'projective_image': '176.30', '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: 51888400
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '44.d1.a1'], 'contains': ['176.a1.a1', '176.e1.a1', '176.e1.b1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4002, -1, 2573, -1, 3787, -1, 6397, -1], 'generators': [1, 8], 'label': '352.79.88.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.a1', 'old_label': '88.c1.a1', 'projective_image': '176.30', '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': '1.1'}
  • id: 51888401
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '44.e1.a1'], 'contains': ['176.a1.a1', '176.f1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6454, -1, 6180, -1, 5708, -1, 4526, -1], 'generators': [19, 8], 'label': '352.79.88.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.f1.a1', 'old_label': '88.d1.a1', 'projective_image': '176.30', '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: 51888402
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '88.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '44.a1.a1', '44.h1.a1', '44.h1.b1'], 'contains': ['176.b1.a1', '176.d1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8621, -1, 7283, -1, 6897, -1, 3639, -1], 'generators': [4, 176], 'label': '352.79.88.e1.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.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: 51888403
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '44.d1.a1', '44.i1.a1', '44.i1.b1'], 'contains': ['176.b1.a1', '176.e1.a1', '176.e1.b1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7509, -1, 8792, -1, 6422, -1, 3958, -1], 'generators': [1, 4], 'label': '352.79.88.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.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': '1.1'}
  • id: 51888404
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '44.e1.a1', '44.h1.a1', '44.h1.b1'], 'contains': ['176.b1.a1', '176.f1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8260, -1, 7756, -1, 7519, -1, 3390, -1], 'generators': [19, 4], 'label': '352.79.88.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.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: 51888405
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '2.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '44.b1.a1', '44.i1.a1', '44.i1.b1'], 'contains': ['176.b1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8959, -1, 9170, -1, 9184, -1, 860, -1], 'generators': [2], 'label': '352.79.88.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '88.h1.a1', 'projective_image': '176.31', '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: 51888406
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.f1.a1', '44.h1.a1', '44.i1.a1'], 'contains': ['176.b1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9275, -1, 8507, -1, 8643, -1, 2521, -1], 'generators': [331], 'label': '352.79.88.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.i1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888407
    {'ambient': '352.79', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['176.d1.a1', '176.e1.b1', '176.e1.a1', '176.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1', '22.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2258, 4833, 4390, 3874, 4149, 8841, 5644, 7587], 'generators': [17, 12, 8, 190, 32], 'label': '352.79.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 51888408
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '44.f1.a1', '44.h1.b1', '44.i1.b1'], 'contains': ['176.b1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9275, -1, 8241, -1, 8643, -1, 2303, -1], 'generators': [3], 'label': '352.79.88.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.i1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888409
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '88.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '44.a1.a1', '44.j1.a1', '44.j1.b1'], 'contains': ['176.c1.a1', '176.d1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2826, -1, 905, -1, 1881, -1, 8329, -1], 'generators': [12, 176], 'label': '352.79.88.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '88.j1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888410
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.k1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.d1.a1', '44.j1.a1', '44.k1.a1'], 'contains': ['176.c1.a1', '176.e1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1679, -1, 1208, -1, 1222, -1, 7813, -1], 'generators': [329, 12], 'label': '352.79.88.k1.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.k1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888411
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.k1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '44.d1.a1', '44.j1.b1', '44.k1.b1'], 'contains': ['176.c1.a1', '176.e1.b1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1679, -1, 601, -1, 1222, -1, 8578, -1], 'generators': [1, 12], 'label': '352.79.88.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.k1.b1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888412
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.l1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '44.e1.a1', '44.k1.a1', '44.k1.b1'], 'contains': ['176.c1.a1', '176.f1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [2465, -1, 1778, -1, 2843, -1, 7345, -1], 'generators': [19, 12], 'label': '352.79.88.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '88.l1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888413
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '88.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '44.c1.a1', '44.k1.a1', '44.k1.b1'], 'contains': ['176.c1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1270, -1, 1493, -1, 1508, -1, 7579, -1], 'generators': [190], 'label': '352.79.88.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '88.m1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888414
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '88.n1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '44.g1.a1', '44.j1.a1', '44.j1.b1'], 'contains': ['176.c1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [844, -1, 316, -1, 739, -1, 9335, -1], 'generators': [17], 'label': '352.79.88.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.n1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51888415
    {'ambient': '352.79', 'aut_centralizer_order': 7040, 'aut_label': '176.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, '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'], 'contains': ['352.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6511, 4199, 3820, 4667, 5020, 3927, 5365, 5335], 'generators': [8], 'label': '352.79.176.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': '176.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '176.30', 'quotient_action_kernel_order': 176, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888416
    {'ambient': '352.79', 'aut_centralizer_order': 7040, 'aut_label': '176.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '88.a1.a1', '88.e1.a1', '88.f1.a1', '88.g1.a1', '88.h1.a1', '88.i1.a1', '88.i1.b1'], 'contains': ['352.a1.a1'], 'core': '176.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8440, 4756, 8241, 4096, 7051, 4455, 3390, 6391], 'generators': [4], 'label': '352.79.176.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '176.b1.a1', 'normal_contained_in': ['16.b1.a1', '88.a1.a1'], 'normal_contains': ['352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.b1.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.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888417
    {'ambient': '352.79', 'aut_centralizer_order': 7040, 'aut_label': '176.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '88.a1.a1', '88.j1.a1', '88.k1.a1', '88.k1.b1', '88.l1.a1', '88.m1.a1', '88.n1.a1'], 'contains': ['352.a1.a1'], 'core': '176.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2285, 3641, 1208, 3224, 2038, 3399, 7813, 5863], 'generators': [12], 'label': '352.79.176.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '176.c1.a1', 'normal_contained_in': ['16.c1.a1', '88.a1.a1'], 'normal_contains': ['352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.c1.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.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888418
    {'ambient': '352.79', 'aut_centralizer_order': 176, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.g1.a1', '8.k1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4978, 2148, 4663, 5198, 4654, 2637, 5225, 1441], 'generators': [12, 176, 32, 8], 'label': '352.79.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '88.11', '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': '4.2'}
  • id: 51888419
    {'ambient': '352.79', 'aut_centralizer_order': 1760, 'aut_label': '176.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '88.b1.a1', '88.e1.a1', '88.j1.a1'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7149, -1, 4245, -1, 4435, -1, 5866, -1], 'generators': [176], 'label': '352.79.176.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '176.d1.a1', 'projective_image': '352.79', '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: 51888420
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '176.e1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '88.c1.a1', '88.f1.a1', '88.k1.a1'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6190, -1, 2828, -1, 3787, -1, 6136, -1], 'generators': [329], 'label': '352.79.176.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.a1', 'old_label': '176.e1.a1', 'projective_image': '352.79', '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: 51888421
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '176.e1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '22.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '88.c1.a1', '88.f1.a1', '88.k1.b1'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6190, -1, 2562, -1, 3787, -1, 6397, -1], 'generators': [1], 'label': '352.79.176.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.e1.a1', 'old_label': '176.e1.b1', 'projective_image': '352.79', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888422
    {'ambient': '352.79', 'aut_centralizer_order': 160, 'aut_label': '176.f1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '88.d1.a1', '88.g1.a1', '88.l1.a1'], 'contains': ['352.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6832, -1, 5947, -1, 5708, -1, 5079, -1], 'generators': [19], 'label': '352.79.176.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.e1.a1', 'old_label': '176.f1.a1', 'projective_image': '352.79', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51888423
    {'ambient': '352.79', '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', '176.e1.b1', '176.f1.a1'], 'contains': [], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6832, 4478, 3719, 3881, 4727, 4191, 5744, 6127], 'generators': [], 'label': '352.79.352.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '352.a1.a1', 'normal_contained_in': ['32.a1.a1', '176.c1.a1', '176.b1.a1', '176.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '352.a1.a1', 'projective_image': '352.79', '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'}