Abstract group data - 128.217

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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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 2, 2, 4, 2, 4, 2], 'aut_gens': [[1, 2, 16, 64], [57, 82, 24, 104], [69, 78, 56, 64], [9, 86, 56, 104], [49, 46, 48, 96], [57, 110, 56, 96], [17, 38, 48, 104], [85, 82, 56, 96], [1, 50, 48, 104]], 'aut_group': None, 'aut_hash': 8830010913410235833, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 48, 'aut_perms': [11789244359710144429756304118894303084096372351734775457641867, 3750078660926371333893929343393132487909983860575042317784253, 8717648959835615809165130893833215289093482081603989662505191, 4823424803011944836284656013163069555206768142176528845222959, 11651883453542244427237172627159420768521807520223590331943390, 7755319895719984662963600054721880328840092731387804162892675, 9920213331606899555747125658826056358717961484801713250222744, 101249072222887993574513173097786195904948075580444097428722], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [4, 1, 4, 1], [4, 2, 2, 4], [4, 4, 1, 1], [4, 8, 2, 2], [8, 4, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^8.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [4, 1, 4], [4, 2, 8], [4, 4, 1], [4, 8, 4], [8, 4, 16]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '16.11', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 217, '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], [4, 1, 2, 2], [4, 2, 1, 4], [4, 2, 2, 2], [4, 4, 1, 1], [4, 8, 1, 4], [8, 4, 2, 4], [8, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 336, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '8.5', 'hash': 217, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[1, 50, 48, 72], [17, 2, 48, 96], [33, 34, 16, 64], [9, 34, 16, 64]], 'inner_hash': 11, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2\\times D_4', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 2]], 'label': '128.217', 'linC_count': 64, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.D4', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 38, 'number_divisions': 24, 'number_normal_subgroups': 48, 'number_subgroup_autclasses': 73, 'number_subgroup_classes': 109, 'number_subgroups': 188, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 48, 0, 0, 0, 0, 0], 'outer_gens': [[9, 14, 16, 104], [69, 102, 56, 64], [69, 14, 48, 64], [1, 2, 16, 104], [9, 14, 16, 96], [9, 10, 16, 64], [9, 2, 16, 64]], 'outer_group': '128.2194', 'outer_hash': 2194, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 32, 'outer_perms': [137632127810995941549762385006763929, 229854548259398317446549684061744100, 75242497006393820885691830135221626, 28585563715509001071424212177686727, 139223645424615107953891343991728676, 86832561722268333525542040460586394, 43081420235675201171892249853382809], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 6], [8, 2]], 'representations': {'PC': {'code': 19498660647894401341803095, 'gens': [1, 2, 5, 7], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 224, 701, 36, 58, 1684, 851, 102, 3534, 2365]}, 'GLZN': {'d': 2, 'p': 85, 'gens': [21420476, 49744146, 9826016, 44344198, 23336788, 15848785, 42374694]}, 'Perm': {'d': 24, 'gens': [28260981050123881752812, 309139368049984964154, 56215244266503074745821, 20140, 83541765400471104274702, 26815, 110475688193783288033215]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.D_4', 'transitive_degree': 64, '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: 43427226
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 217, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 43427237
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 217, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 43427248
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 217, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 40, 'size': 1}
  • id: 43427258
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 217, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 8, 'size': 1}
  • id: 43427259
    {'aut_label': '2D', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 217, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 64, 'size': 4}
  • id: 43427260
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 217, 'group_order': 128, 'label': '4A1', 'order': 4, 'powers': [4], 'representative': 4, 'size': 1}
  • id: 43427261
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 217, 'group_order': 128, 'label': '4A-1', 'order': 4, 'powers': [4], 'representative': 12, 'size': 1}
  • id: 43427262
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 217, 'group_order': 128, 'label': '4B1', 'order': 4, 'powers': [4], 'representative': 36, 'size': 1}
  • id: 43427263
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 217, 'group_order': 128, 'label': '4B-1', 'order': 4, 'powers': [4], 'representative': 44, 'size': 1}
  • id: 43427227
    {'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 217, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 16, 'size': 2}
  • id: 43427228
    {'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 217, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 24, 'size': 2}
  • id: 43427229
    {'aut_label': '4E', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 217, 'group_order': 128, 'label': '4E', 'order': 4, 'powers': [3], 'representative': 84, 'size': 2}
  • id: 43427230
    {'aut_label': '4E', 'centralizer': '2.c1.a1', 'counter': 13, 'group_counter': 217, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 116, 'size': 2}
  • id: 43427231
    {'aut_label': '4G1', 'centralizer': '2.c1.a1', 'counter': 14, 'group_counter': 217, 'group_order': 128, 'label': '4G1', 'order': 4, 'powers': [2], 'representative': 80, 'size': 2}
  • id: 43427232
    {'aut_label': '4G1', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 217, 'group_order': 128, 'label': '4G-1', 'order': 4, 'powers': [2], 'representative': 112, 'size': 2}
  • id: 43427233
    {'aut_label': '4H1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 217, 'group_order': 128, 'label': '4H1', 'order': 4, 'powers': [3], 'representative': 52, 'size': 2}
  • id: 43427234
    {'aut_label': '4H1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 217, 'group_order': 128, 'label': '4H-1', 'order': 4, 'powers': [3], 'representative': 28, 'size': 2}
  • id: 43427235
    {'aut_label': '4I', 'centralizer': '4.a1.a1', 'counter': 18, 'group_counter': 217, 'group_order': 128, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 68, 'size': 4}
  • id: 43427236
    {'aut_label': '4J', 'centralizer': '8.k1.a1', 'counter': 19, 'group_counter': 217, 'group_order': 128, 'label': '4J', 'order': 4, 'powers': [2], 'representative': 1, 'size': 8}
  • id: 43427238
    {'aut_label': '4K', 'centralizer': '8.k1.b1', 'counter': 20, 'group_counter': 217, 'group_order': 128, 'label': '4K', 'order': 4, 'powers': [3], 'representative': 65, 'size': 8}
  • id: 43427239
    {'aut_label': '4K', 'centralizer': '8.k1.a1', 'counter': 21, 'group_counter': 217, 'group_order': 128, 'label': '4L', 'order': 4, 'powers': [3], 'representative': 5, 'size': 8}
  • id: 43427240
    {'aut_label': '4J', 'centralizer': '8.k1.b1', 'counter': 22, 'group_counter': 217, 'group_order': 128, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 69, 'size': 8}
  • id: 43427241
    {'aut_label': '8A1', 'centralizer': '4.d1.a1', 'counter': 23, 'group_counter': 217, 'group_order': 128, 'label': '8A1', 'order': 8, 'powers': [16], 'representative': 3, 'size': 4}
  • id: 43427242
    {'aut_label': '8A1', 'centralizer': '4.d1.a1', 'counter': 24, 'group_counter': 217, 'group_order': 128, 'label': '8A-1', 'order': 8, 'powers': [17], 'representative': 7, 'size': 4}
  • id: 43427243
    {'aut_label': '8A1', 'centralizer': '4.d1.b1', 'counter': 25, 'group_counter': 217, 'group_order': 128, 'label': '8B1', 'order': 8, 'powers': [17], 'representative': 67, 'size': 4}
  • id: 43427244
    {'aut_label': '8A1', 'centralizer': '4.d1.b1', 'counter': 26, 'group_counter': 217, 'group_order': 128, 'label': '8B-1', 'order': 8, 'powers': [16], 'representative': 103, 'size': 4}
  • id: 43427245
    {'aut_label': '8A1', 'centralizer': '4.d1.a1', 'counter': 27, 'group_counter': 217, 'group_order': 128, 'label': '8C1', 'order': 8, 'powers': [16], 'representative': 35, 'size': 4}
  • id: 43427246
    {'aut_label': '8A1', 'centralizer': '4.d1.a1', 'counter': 28, 'group_counter': 217, 'group_order': 128, 'label': '8C-1', 'order': 8, 'powers': [17], 'representative': 39, 'size': 4}
  • id: 43427247
    {'aut_label': '8A1', 'centralizer': '4.d1.b1', 'counter': 29, 'group_counter': 217, 'group_order': 128, 'label': '8D1', 'order': 8, 'powers': [17], 'representative': 99, 'size': 4}
  • id: 43427249
    {'aut_label': '8A1', 'centralizer': '4.d1.b1', 'counter': 30, 'group_counter': 217, 'group_order': 128, 'label': '8D-1', 'order': 8, 'powers': [16], 'representative': 71, 'size': 4}
  • id: 43427250
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 31, 'group_counter': 217, 'group_order': 128, 'label': '8E1', 'order': 8, 'powers': [6], 'representative': 2, 'size': 4}
  • id: 43427251
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 32, 'group_counter': 217, 'group_order': 128, 'label': '8E-1', 'order': 8, 'powers': [7], 'representative': 14, 'size': 4}
  • id: 43427252
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 33, 'group_counter': 217, 'group_order': 128, 'label': '8E3', 'order': 8, 'powers': [7], 'representative': 6, 'size': 4}
  • id: 43427253
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 34, 'group_counter': 217, 'group_order': 128, 'label': '8E-3', 'order': 8, 'powers': [6], 'representative': 10, 'size': 4}
  • id: 43427254
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 35, 'group_counter': 217, 'group_order': 128, 'label': '8F1', 'order': 8, 'powers': [8], 'representative': 66, 'size': 4}
  • id: 43427255
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 36, 'group_counter': 217, 'group_order': 128, 'label': '8F-1', 'order': 8, 'powers': [9], 'representative': 86, 'size': 4}
  • id: 43427256
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 37, 'group_counter': 217, 'group_order': 128, 'label': '8F3', 'order': 8, 'powers': [9], 'representative': 70, 'size': 4}
  • id: 43427257
    {'aut_label': '8E1', 'centralizer': '4.m1.a1', 'counter': 38, 'group_counter': 217, 'group_order': 128, 'label': '8F-3', 'order': 8, 'powers': [8], 'representative': 82, '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: 91866
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1a', '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], 'schur_index': 1}
  • id: 91877
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1b', '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], 'schur_index': 1}
  • id: 91883
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1c', '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], 'schur_index': 1}
  • id: 91884
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1d', '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], 'schur_index': 1}
  • id: 91885
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1e', '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], 'schur_index': 1}
  • id: 91886
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1f', '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], 'schur_index': 1}
  • id: 91887
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1g', '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], 'schur_index': 1}
  • id: 91888
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1h', '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], 'schur_index': 1}
  • id: 91889
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 91867
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 91868
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 91869
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 91870
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 91871
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 91872
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 91873
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 91874
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2e', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 91875
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2f', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 91876
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2g', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, -2, 2, 0, 0, 2, 2, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 91878
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2h', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 2, -2, 0, 0, -2, -2, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 91881
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.4a', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, -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], 'schur_index': 2}
  • id: 91882
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.4b', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 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], 'schur_index': 2}
  • id: 91879
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2i', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 91880
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '128.217', 'group_order': 128, 'image': None, 'label': '128.217.2j', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 83184
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.217.1a', '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]]]}
  • id: 83195
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 64, 'label': '128.217.1b', '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]]]}
  • id: 83206
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 64, 'label': '128.217.1c', '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]]]}
  • id: 83216
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 64, 'label': '128.217.1d', '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]]]}
  • id: 83217
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 64, 'label': '128.217.1e', '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]]]}
  • id: 83218
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 64, 'label': '128.217.1f', '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]]]}
  • id: 83219
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.217.1g', '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]]]}
  • id: 83220
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.217.1h', '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]]]}
  • id: 83221
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 32, 'label': '128.217.1i1', 'nt': [4, 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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 83185
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 32, 'label': '128.217.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 83186
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 32, 'label': '128.217.1j1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 83187
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 32, 'label': '128.217.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 83188
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 32, 'label': '128.217.1k1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 83189
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 32, 'label': '128.217.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 83190
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 32, 'label': '128.217.1l1', 'nt': [4, 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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 83191
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 32, 'label': '128.217.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 83192
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1.a1', 'kernel_order': 16, 'label': '128.217.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[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]]]}
  • id: 83193
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 16, 'label': '128.217.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[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]]]}
  • id: 83194
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.217.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[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]]]}
  • id: 83196
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 16, 'label': '128.217.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[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]]]}
  • id: 83197
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 4, 'label': '128.217.2e1', 'nt': [8, 17], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83198
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 4, 'label': '128.217.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83199
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 4, 'label': '128.217.2f1', 'nt': [8, 17], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83200
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 4, 'label': '128.217.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[-1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83201
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.b1', 'kernel_order': 4, 'label': '128.217.2g1', 'nt': [8, 17], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83202
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.b1', 'kernel_order': 4, 'label': '128.217.2g2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[1, 0], [1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83203
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.b1', 'kernel_order': 4, 'label': '128.217.2h1', 'nt': [8, 17], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83204
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.11', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.b1', 'kernel_order': 4, 'label': '128.217.2h2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83205
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 29, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.217.2i1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]]]}
  • id: 83207
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 30, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.217.2i2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]]]}
  • id: 83208
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 31, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.217.2i3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]]]}
  • id: 83209
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 32, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.217.2i4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]]]}
  • id: 83210
    {'center': '4.e1.b1', 'center_index': 4, 'center_order': 32, 'counter': 33, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.217.2j1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]]]}
  • id: 83211
    {'center': '4.e1.b1', 'center_index': 4, 'center_order': 32, 'counter': 34, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.217.2j2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]]]}
  • id: 83212
    {'center': '4.e1.b1', 'center_index': 4, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.217.2j3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]]]}
  • id: 83213
    {'center': '4.e1.b1', 'center_index': 4, 'center_order': 32, 'counter': 36, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.217.2j4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]]]}
  • id: 83214
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.d1.b1', 'kernel_order': 4, 'label': '128.217.4a', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 83215
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.217', 'group_counter': 217, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.d1.a1', 'kernel_order': 4, 'label': '128.217.4b', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 8130582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.217.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.217', 'subgroup_hash': 217, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 2}
  • id: 8130603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.214', 'subgroup_hash': 214, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.85', 'subgroup_hash': 85, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.112', 'subgroup_hash': 112, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.7', 'subgroup_hash': 7, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.7', 'subgroup_hash': 7, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.c1', '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': '64.7', 'subgroup_hash': 7, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.d1', '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': '64.7', 'subgroup_hash': 7, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.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': ['U1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', '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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', '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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.b1', '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8130605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1.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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 8130615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.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': ['Phi', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 8130622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 8130623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8130629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.t1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.c1', '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.8.t1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.d1', '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8130646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', '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: 8130648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.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': ['Z', 'U2'], '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: 8130649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.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': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], '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: 8130650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', '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: 8130651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', '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: 8130652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', '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: 8130654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.c1', '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.d1', '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130670
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.c1', '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130673
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.d1', '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130676
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130677
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8130678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.217.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C5'], '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: 8130679
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130681
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130682
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130683
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130685
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8130686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130687
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130688
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130689
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.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': 32, 'quotient_simple': 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: 8130690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130586
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.217.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130588
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 8130589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 105, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.89', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 89, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2^2\\times C_8):C_2', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], '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: 8130590
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 106, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.101', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 101, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', '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: 8130591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 107, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.217.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.100', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 100, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_4', '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: 8130592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.217.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, '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: 8130593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.217', 'ambient_counter': 217, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 109, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.217.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '128.217', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 217, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 8130586
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4457, -1, 5873, -1, 4480, -1, 5925, -1], 'generators': [5], 'label': '128.217.32.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.j1.b1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130582
    {'ambient': '128.217', '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': '16.b1.a1', 'complements': ['128.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6904, 3819, 3137, 3911, 6935, 3887, 3167, 3944], 'generators': [1, 2, 64], 'label': '128.217.1.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.d1.b1', '2.d1.c1', '2.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '16.11', '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': '16.11'}
  • id: 8130583
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.h1.a1', '8.j1.a1', '8.o1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1575, 8363, 8363, 7372, 1584, 8531, 8442, 7434], 'generators': [1, 64, 48], 'label': '128.217.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130584
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.l1.a1', '16.l1.b1', '16.n1.a1', '16.n1.b1', '16.n1.c1', '16.n1.d1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6152, -1, 2835, -1, 5983, -1, 2861, -1], 'generators': [52], 'label': '128.217.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130585
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4457, -1, 6087, -1, 4480, -1, 6141, -1], 'generators': [65], 'label': '128.217.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130587
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.c1.a1', '64.d1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6486, -1, 3273, -1, 6319, -1, 3304, -1], 'generators': [64, 8], 'label': '128.217.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130588
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6821, -1, 3047, -1, 6656, -1, 3075, -1], 'generators': [68], 'label': '128.217.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.l1.a1', 'projective_image': '64.100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130589
    {'ambient': '128.217', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.g1.b1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3957, 5521, 8274, 3454, 3978, 5623, 8352, 3736], 'generators': [32], 'label': '128.217.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.89', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.89', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130590
    {'ambient': '128.217', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '32.h1.a1', '32.i1.a1', '32.j1.a1', '32.j1.b1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5191, 4869, 5279, 1229, 5218, 4958, 5334, 1240], 'generators': [40], 'label': '128.217.64.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.101', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.101', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130591
    {'ambient': '128.217', 'aut_centralizer_order': 2048, 'aut_label': '64.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '32.k1.a1', '32.l1.a1'], 'contains': ['128.a1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6486, 4218, 3162, 2025, 6319, 4294, 3191, 2042], 'generators': [8], 'label': '128.217.64.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.d1.a1', '32.d1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '64.100', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.100', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130592
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.h1.a1', '32.k1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5513, -1, 4952, -1, 5542, -1, 5001, -1], 'generators': [64], 'label': '128.217.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.217', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130593
    {'ambient': '128.217', 'aut_centralizer_order': None, 'aut_label': '128.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': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1'], 'contains': [], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5356, 4869, 5167, 2025, 5376, 4958, 5114, 2042], 'generators': [], 'label': '128.217.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.c1.a1', '64.b1.a1', '64.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.217', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130594
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.g1.b1', '8.h1.b1', '8.j1.b1', '8.o1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1575, 8363, 7399, 9566, 1584, 8531, 7468, 9648], 'generators': [5, 64, 48], 'label': '128.217.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.b1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130595
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.h1.b1', '8.k1.a1', '8.p1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3618, 6390, 4614, 5442, 3637, 6519, 4657, 5488], 'generators': [1, 4, 48], 'label': '128.217.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '16.11', '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': '16.11'}
  • id: 8130596
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.g1.b1', '8.h1.a1', '8.k1.b1', '8.p1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3618, 6390, 6637, 6451, 3637, 6519, 6699, 6506], 'generators': [65, 4, 48], 'label': '128.217.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'normal_contains': ['8.d1.a1', '8.g1.b1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130597
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.d1.a1', '8.q1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 1783, 2676, 4433, 7280, 1819, 2701, 4471], 'generators': [3, 48], 'label': '128.217.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '16.11', '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: 8130598
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '4.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.q1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 1783, 3599, 2076, 7280, 1819, 3633, 2094], 'generators': [67, 48], 'label': '128.217.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '16.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130599
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.l1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8703, 3204, 1417, 3594, 8748, 3269, 1431, 3624], 'generators': [2, 48], 'label': '128.217.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130600
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.d1.a1', '8.l1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8703, 3204, 1688, 2917, 8748, 3269, 1704, 2941], 'generators': [66, 48], 'label': '128.217.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130601
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.a1', '8.g1.a1', '8.g1.b1', '8.m1.a1', '8.r1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2031, 7431, 7702, 8807, 2042, 7581, 7774, 8882], 'generators': [1, 68, 48], 'label': '128.217.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.f1.a1', '8.g1.a1', '8.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '32.22', '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': '16.11'}
  • id: 8130602
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.h1.b1', '8.n1.a1', '8.s1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4117, 9295, 6975, 8130, 4139, 9483, 7041, 8199], 'generators': [5, 68, 48], 'label': '128.217.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.b1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '32.22', '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': '16.11'}
  • id: 8130603
    {'ambient': '128.217', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493360', 'aut_weyl_index': 4, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3870, 7077, 6063, 6915, 3890, 7045, 6120, 6966], 'generators': [1, 64, 4, 48], 'label': '128.217.2.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.b1.b1', '4.c1.a1', '4.c1.b1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130604
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.k1.b1', '8.r1.a1', '8.s1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5104, -1, 5167, -1, 5131, -1, 5215, -1], 'generators': [1, 64, 4], 'label': '128.217.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '16.11', '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': '8.5'}
  • id: 8130605
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '8.l1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9741, -1, 608, -1, 9792, -1, 614, -1], 'generators': [2, 64], 'label': '128.217.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.i1.a1', 'projective_image': '16.11', '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': '4.2'}
  • id: 8130606
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.j1.a1', '8.j1.b1', '8.m1.a1', '8.n1.a1', '8.p1.a1', '8.p1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3074, -1, 5593, -1, 3091, -1, 5646, -1], 'generators': [1, 64, 52], 'label': '128.217.4.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': '32.22', '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': '8.5'}
  • id: 8130607
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.q1.a1', '8.q1.b1', '8.t1.a1', '8.t1.b1', '8.t1.c1', '8.t1.d1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8020, -1, 2150, -1, 8062, -1, 2170, -1], 'generators': [3, 64, 32], 'label': '128.217.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '32.22', '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': '4.2'}
  • id: 8130608
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.k1.a1', '8.k1.b1', '8.m1.a1', '8.n1.a1', '8.o1.a1', '8.o1.b1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2532, -1, 6234, -1, 2545, -1, 6293, -1], 'generators': [1, 112, 4], 'label': '128.217.4.l1.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.l1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130609
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.e1.a1', '8.l1.a1', '8.l1.b1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9198, -1, 1047, -1, 9246, -1, 1057, -1], 'generators': [2, 112], 'label': '128.217.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.m1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130610
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.i1.a1', '8.o1.a1', '8.o1.b1', '8.p1.a1', '8.p1.b1', '8.r1.a1', '8.s1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4517, -1, 5896, -1, 4541, -1, 5951, -1], 'generators': [1, 112, 52], 'label': '128.217.4.n1.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.n1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130611
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.i1.a1', '8.q1.a1', '8.q1.b1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6560, -1, 3137, -1, 6594, -1, 3167, -1], 'generators': [3, 112], 'label': '128.217.4.o1.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.o1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130612
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.g1.a1', '16.o1.a1', '16.o1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7542, 2751, 2981, 2555, 7582, 2807, 3010, 2577], 'generators': [64, 4, 32], 'label': '128.217.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '16.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130613
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.e1.a1', '16.j1.a1', '16.j1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2593, 6344, 8866, 5531, 2606, 6473, 8949, 5578], 'generators': [64, 48, 8], 'label': '128.217.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.22', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130614
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 8, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.k1.a1', '4.o1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6560, 1783, 3137, 2076, 6594, 1819, 3167, 2094], 'generators': [3, 64, 48], 'label': '128.217.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130615
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.f1.a1', '16.l1.a1', '16.l1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6499, 4923, 3687, 1399, 6533, 5023, 3722, 1411], 'generators': [64, 52, 32], 'label': '128.217.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '32.22', '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': '4.2'}
  • id: 8130616
    {'ambient': '128.217', 'aut_centralizer_order': 256, 'aut_label': '8.d1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.f1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7021, 923, 3335, 4043, 7058, 942, 3366, 4077], 'generators': [4, 48], 'label': '128.217.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130617
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5621, 3838, 4040, 515, 5651, 3915, 4078, 520], 'generators': [112, 4], 'label': '128.217.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '16.d1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130618
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4865, 7431, 6152, 4647, 4891, 7581, 6210, 4686], 'generators': [68, 48], 'label': '128.217.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '32.22', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130619
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.f1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.k1.a1', '16.k1.c1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [259, 8426, 9701, 7298, 260, 8597, 9792, 7360], 'generators': [1, 48, 8], 'label': '128.217.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.a1', '4.f1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '32.22', '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': '16.11'}
  • id: 8130620
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.c1.b1', '4.f1.a1'], 'contains': ['16.c1.a1', '16.h1.b1', '16.k1.b1', '16.k1.d1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [259, 8426, 9298, 8991, 260, 8597, 9386, 9068], 'generators': [69, 48, 8], 'label': '128.217.8.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': ['4.b1.b1', '4.c1.b1', '4.f1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130641
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.h1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.i1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5243, -1, 5049, -1, 5271, -1, 5096, -1], 'generators': [5, 68], 'label': '128.217.8.s1.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.s1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130621
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.b1', '4.g1.a1'], 'contains': ['16.c1.a1', '16.i1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1558, 9467, 8499, 6451, 1566, 9658, 8578, 6506], 'generators': [65, 48], 'label': '128.217.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.b1', '4.g1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '32.22', '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': '16.11'}
  • id: 8130622
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.c1.a1', '4.g1.a1'], 'contains': ['16.c1.a1', '16.i1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1558, 9467, 7957, 8145, 1566, 9658, 8032, 8214], 'generators': [5, 48], 'label': '128.217.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.b1.b1', '4.c1.a1', '4.g1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130623
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '8.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.o1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.g1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5978, 1666, 4281, 3440, 6009, 1699, 4322, 3468], 'generators': [112, 52], 'label': '128.217.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.f1.a1', '16.e1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '32.22', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130624
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.i1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2005, -1, 6440, -1, 2016, -1, 6500, -1], 'generators': [1, 64], 'label': '128.217.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '32.22', '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': '8.5'}
  • id: 8130625
    {'ambient': '128.217', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 8, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.e1.b1', '4.i1.a1', '4.m1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8703, 4426, 1553, 604, 8748, 4515, 1567, 609], 'generators': [2, 64, 48], 'label': '128.217.2.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.e1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130626
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.h1.b1', '16.i1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2005, -1, 5593, -1, 2016, -1, 5646, -1], 'generators': [5, 64], 'label': '128.217.8.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130627
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.i1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4509, -1, 4523, -1, 4533, -1, 4565, -1], 'generators': [1, 4], 'label': '128.217.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '16.11', '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': '4.2'}
  • id: 8130628
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.h1.b1', '16.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4509, -1, 5305, -1, 4533, -1, 5355, -1], 'generators': [65, 4], 'label': '128.217.8.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130629
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.p1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 173, -1, 9255, -1, 175, -1], 'generators': [2, 32], 'label': '128.217.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.l1.a1', 'projective_image': '16.11', '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': '2.1'}
  • id: 8130630
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.p1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 574, -1, 9255, -1, 579, -1], 'generators': [66, 32], 'label': '128.217.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.l1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130631
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.h1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1158, -1, 7686, -1, 1164, -1, 7759, -1], 'generators': [1, 116], 'label': '128.217.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.22', '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': '8.5'}
  • id: 8130632
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '16.i1.b1', '16.m1.a1', '16.m1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3231, -1, 6808, -1, 3248, -1, 6871, -1], 'generators': [5, 116, 32], 'label': '128.217.8.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': '32.22', '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': '8.5'}
  • id: 8130633
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.i1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [758, -1, 8227, -1, 762, -1, 8305, -1], 'generators': [1, 112], 'label': '128.217.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130634
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.e1.a1', '16.h1.b1', '16.i1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [758, -1, 7416, -1, 762, -1, 7486, -1], 'generators': [5, 112], 'label': '128.217.8.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130635
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.i1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3731, -1, 4779, -1, 3751, -1, 4823, -1], 'generators': [1, 52], 'label': '128.217.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130636
    {'ambient': '128.217', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 3204, 2406, 5265, 7280, 3269, 2428, 5310], 'generators': [1, 2], 'label': '128.217.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '16.11', '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': '16.11'}
  • id: 8130637
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.f1.a1', '16.h1.b1', '16.i1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3731, -1, 5896, -1, 3751, -1, 5951, -1], 'generators': [65, 52], 'label': '128.217.8.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.p1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130638
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.k1.a1', '4.o1.a1'], 'contains': ['16.f1.a1', '16.n1.a1', '16.n1.c1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8181, -1, 2150, -1, 8224, -1, 2170, -1], 'generators': [3, 32], 'label': '128.217.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.q1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130639
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.k1.a1', '4.o1.a1'], 'contains': ['16.f1.a1', '16.n1.b1', '16.n1.d1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8181, -1, 2549, -1, 8224, -1, 2574, -1], 'generators': [67, 32], 'label': '128.217.8.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.q1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130640
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.h1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4131, -1, 7146, -1, 4152, -1, 7213, -1], 'generators': [1, 68], 'label': '128.217.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8130642
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.l1.a1', '16.n1.a1', '16.n1.d1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8694, -1, 921, -1, 8740, -1, 929, -1], 'generators': [3, 96], 'label': '128.217.8.t1.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': '8.t1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130643
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.l1.a1', '16.n1.b1', '16.n1.c1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8694, -1, 1803, -1, 8740, -1, 1820, -1], 'generators': [35, 96], 'label': '128.217.8.t1.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': '8.t1.b1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130644
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.l1.b1', '16.n1.a1', '16.n1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8694, -1, 1509, -1, 8740, -1, 1523, -1], 'generators': [3, 64], 'label': '128.217.8.t1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.c1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130645
    {'ambient': '128.217', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.l1.b1', '16.n1.c1', '16.n1.d1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8694, -1, 1215, -1, 8740, -1, 1226, -1], 'generators': [35, 64], 'label': '128.217.8.t1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.d1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130646
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.h1.a1', '32.k1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5352, 5213, 4943, 3240, 5380, 5318, 4990, 3268], 'generators': [64, 8, 32], 'label': '128.217.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.22', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130647
    {'ambient': '128.217', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.b1', '4.e1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 3204, 3599, 3233, 7280, 3269, 3633, 3260], 'generators': [1, 66], 'label': '128.217.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.b1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130648
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.l1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7007, 533, 3823, 1436, 7045, 545, 3859, 1448], 'generators': [4, 32], 'label': '128.217.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1'], 'normal_contains': ['32.a1.a1', '32.d1.a1', '32.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '16.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130649
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.g1.a1', '8.g1.b1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2793, 7431, 8486, 6046, 2807, 7581, 8566, 6098], 'generators': [48, 8], 'label': '128.217.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.g1.a1', '8.g1.b1', '8.h1.b1', '8.h1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.22', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130650
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4879, 6199, 5263, 434, 4904, 6325, 5313, 438], 'generators': [116, 32], 'label': '128.217.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '32.22', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130651
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.i1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '32.f1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3974, 2995, 6887, 2437, 3995, 3056, 6952, 2458], 'generators': [112, 8], 'label': '128.217.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.i1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.22', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130652
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.i1.a1', '8.p1.a1', '8.p1.b1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.a1.a1', '32.i1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6417, 1765, 4223, 4043, 6450, 1800, 4262, 4077], 'generators': [52, 32], 'label': '128.217.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.c1.a1', '8.d1.a1', '8.i1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.22', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130653
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.i1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.l1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5825, 4226, 4622, 5045, 5856, 4312, 4666, 5087], 'generators': [68, 32], 'label': '128.217.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.a1.a1', '8.f1.a1', '8.i1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.22', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130654
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.j1.a1', '8.k1.a1', '8.m1.a1', '8.o1.a1', '8.p1.a1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1610, -1, 7686, -1, 1619, -1, 7759, -1], 'generators': [1, 8], 'label': '128.217.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130655
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.j1.b1', '8.k1.b1', '8.m1.a1', '8.o1.b1', '8.p1.b1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.g1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1610, -1, 7287, -1, 1619, -1, 7355, -1], 'generators': [69, 8], 'label': '128.217.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130656
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.j1.a1', '8.k1.b1', '8.n1.a1', '8.o1.a1', '8.p1.b1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3383, -1, 6063, -1, 3401, -1, 6120, -1], 'generators': [65, 32], 'label': '128.217.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130657
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '8.j1.b1', '8.k1.a1', '8.n1.a1', '8.o1.b1', '8.p1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.j1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3383, -1, 5664, -1, 3401, -1, 5717, -1], 'generators': [5, 32], 'label': '128.217.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.i1.b1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130658
    {'ambient': '128.217', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.a1', '4.e1.b1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 3204, 2676, 4588, 7280, 3269, 2701, 4627], 'generators': [65, 66], 'label': '128.217.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.d1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130659
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.f1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2201, -1, 8887, -1, 2213, -1, 8970, -1], 'generators': [64, 48], 'label': '128.217.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130660
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.b1.b1', '32.e1.a1', '32.f1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2201, -1, 8087, -1, 2213, -1, 8163, -1], 'generators': [64, 56], 'label': '128.217.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.j1.b1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130661
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.b1.a1', '32.g1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1158, -1, 9827, -1, 1164, -1, 9920, -1], 'generators': [1, 48], 'label': '128.217.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130662
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1'], 'contains': ['32.b1.a1', '32.g1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1158, -1, 9404, -1, 1164, -1, 9492, -1], 'generators': [69, 48], 'label': '128.217.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.d1', 'old_label': '16.k1.b1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130663
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.b1.b1', '32.g1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1158, -1, 9616, -1, 1164, -1, 9706, -1], 'generators': [1, 56], 'label': '128.217.16.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '16.k1.c1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130664
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1'], 'contains': ['32.b1.b1', '32.g1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1158, -1, 9192, -1, 1164, -1, 9279, -1], 'generators': [69, 56], 'label': '128.217.16.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.c1', 'old_label': '16.k1.d1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8130665
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.t1.a1', '8.t1.b1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.i1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7599, -1, 3023, -1, 7639, -1, 3051, -1], 'generators': [96, 52], 'label': '128.217.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130666
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.t1.c1', '8.t1.d1'], 'contains': ['32.c1.b1', '32.h1.a1', '32.i1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7599, -1, 3423, -1, 7639, -1, 3455, -1], 'generators': [64, 52], 'label': '128.217.16.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.b1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130667
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1'], 'contains': ['32.c1.a1', '32.j1.a1', '32.j1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4426, -1, 6369, -1, 4450, -1, 6429, -1], 'generators': [5, 84], 'label': '128.217.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130668
    {'ambient': '128.217', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1'], 'contains': ['32.c1.b1', '32.j1.a1', '32.j1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4426, -1, 6581, -1, 4450, -1, 6643, -1], 'generators': [5, 116], 'label': '128.217.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.m1.b1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8130669
    {'ambient': '128.217', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.b1', '4.e1.a1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 3204, 3869, 3911, 7280, 3269, 3906, 3944], 'generators': [65, 2], 'label': '128.217.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.d1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 8130670
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.t1.a1', '8.t1.c1'], 'contains': ['32.i1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8050, -1, 1494, -1, 8093, -1, 1508, -1], 'generators': [3], 'label': '128.217.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130671
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '8.t1.b1', '8.t1.c1'], 'contains': ['32.i1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8050, -1, 1917, -1, 8093, -1, 1935, -1], 'generators': [67], 'label': '128.217.16.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.b1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130672
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.t1.b1', '8.t1.d1'], 'contains': ['32.i1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8050, -1, 1705, -1, 8093, -1, 1722, -1], 'generators': [35], 'label': '128.217.16.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.c1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130673
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '8.t1.a1', '8.t1.d1'], 'contains': ['32.i1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8050, -1, 1246, -1, 8093, -1, 1259, -1], 'generators': [99], 'label': '128.217.16.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.d1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130674
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.d1.a1', '32.k1.a1', '32.l1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8503, -1, 2223, -1, 8547, -1, 2244, -1], 'generators': [64, 4], 'label': '128.217.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.o1.a1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130675
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.d1.b1', '32.k1.a1', '32.l1.a1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8503, -1, 2623, -1, 8547, -1, 2648, -1], 'generators': [64, 36], 'label': '128.217.16.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.o1.b1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130676
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1'], 'contains': ['32.d1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9089, -1, 267, -1, 9133, -1, 487, -1], 'generators': [2], 'label': '128.217.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '16.p1.a1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130677
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1'], 'contains': ['32.d1.b1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9089, -1, 803, -1, 9133, -1, 890, -1], 'generators': [66], 'label': '128.217.16.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '16.p1.b1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130678
    {'ambient': '128.217', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.h1.b1', '16.i1.a1', '16.i1.b1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4848, 4543, 5637, 2917, 4873, 4626, 5684, 2941], 'generators': [8, 32], 'label': '128.217.32.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.f1.a1', '16.e1.a1', '16.g1.a1'], 'normal_contains': ['64.c1.a1', '64.b1.a1', '64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.22', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130679
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.j1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.a1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2496, 6824, 8887, 5030, 2510, 7267, 8970, 5585], 'generators': [48], 'label': '128.217.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.89', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130680
    {'ambient': '128.217', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, '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.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.i1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5830, 4380, 4037, 994, 5861, 4469, 4075, 1003], 'generators': [64, 4, 48], 'label': '128.217.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '16.11', '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: 8130681
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.j1.b1', '16.k1.c1', '16.k1.d1'], 'contains': ['64.a1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2496, 6824, 8592, 3992, 2510, 7267, 8673, 4538], 'generators': [56], 'label': '128.217.32.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.b1', 'projective_image': '64.89', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130682
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.b1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5182, 5566, 5172, 434, 5209, 5983, 5227, 438], 'generators': [84], 'label': '128.217.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.d1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.101', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130683
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.l1.b1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5182, 5566, 5384, 965, 5209, 5983, 5441, 973], 'generators': [116], 'label': '128.217.32.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.b1', 'normal_contained_in': ['16.d1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.b1', 'projective_image': '64.101', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130684
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.o1.a1', '16.p1.a1'], 'contains': ['64.c1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7951, 2353, 2317, 1495, 7796, 2391, 2339, 1508], 'generators': [4], 'label': '128.217.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '32.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.44', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130685
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.o1.b1', '16.p1.b1'], 'contains': ['64.c1.a1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7951, 2353, 2623, 2025, 7796, 2391, 2648, 2042], 'generators': [36], 'label': '128.217.32.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.b1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.b1', 'projective_image': '32.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.44', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130686
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '64.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4123, -1, 7942, -1, 4144, -1, 8017, -1], 'generators': [64, 32], 'label': '128.217.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130687
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3787, -1, 8169, -1, 3807, -1, 8246, -1], 'generators': [112], 'label': '128.217.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8130688
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.k1.a1', '16.k1.c1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1610, -1, 9357, -1, 1619, -1, 9445, -1], 'generators': [1], 'label': '128.217.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130689
    {'ambient': '128.217', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.k1.b1', '16.k1.d1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1610, -1, 8381, -1, 1619, -1, 8459, -1], 'generators': [69], 'label': '128.217.32.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.b1', 'old_label': '32.g1.b1', 'projective_image': '64.89', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8130690
    {'ambient': '128.217', 'aut_centralizer_order': 512, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.l1.a1', '16.l1.b1'], 'contains': ['64.b1.a1', '64.d1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5517, -1, 4943, -1, 5546, -1, 4990, -1], 'generators': [64, 40], 'label': '128.217.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.101', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}